[docs]defmoving_transform(x,y=None,sf=100,window=.3,step=.1,method='corr',
- interp=False):
- """Moving transformation of one or two time-series.
-
- Parameters
- ----------
- x : array_like
- Single-channel data
- y : array_like, optional
- Second single-channel data (only used if method in ['corr', 'covar']).
- sf : float
- Sampling frequency.
- window : int
- Window size in seconds.
- step : int
- Step in seconds.
- A step of 0.1 second (100 ms) is usually a good default.
- If step == 0, overlap at every sample (slowest)
- If step == nperseg, no overlap (fastest)
- Higher values = higher precision = slower computation.
- method : str
- Transformation to use.
- Available methods are::
-
- 'mean' : arithmetic mean of x
- 'min' : minimum value of x
- 'max' : maximum value of x
- 'ptp' : peak-to-peak amplitude of x
- 'prop_above_zero' : proportion of values of x that are above zero
- 'rms' : root mean square of x
- 'slope' : slope of the least-square regression of x (in a.u / sec)
- 'corr' : Correlation between x and y
- 'covar' : Covariance between x and y
- interp : boolean
- If True, a cubic interpolation is performed to ensure that the output
- has the same size as the input.
-
- Returns
- -------
- t : np.array
- Time vector
- out : np.array
- Transformed signal
-
- Notes
- -----
- This function was inspired by the `transform_signal` function of the
- Wonambi package (https://github.com/wonambi-python/wonambi).
- """
- # Safety checks
- assertmethodin['mean','min','max','ptp','rms',
- 'prop_above_zero','slope','covar','corr']
- x=np.asarray(x,dtype=np.float64)
- ifyisnotNone:
- y=np.asarray(y,dtype=np.float64)
- assertx.size==y.size
-
- ifstep==0:
- step=1/sf
-
- halfdur=window/2
- n=x.size
- total_dur=n/sf
- last=n-1
- idx=np.arange(0,total_dur,step)
- out=np.zeros(idx.size)
-
- # Define beginning, end and time (centered) vector
- beg=((idx-halfdur)*sf).astype(int)
- end=((idx+halfdur)*sf).astype(int)
- beg[beg<0]=0
- end[end>last]=last
- # Alternatively, to cut off incomplete windows (comment the 2 lines above)
- # mask = ~((beg < 0) | (end > last))
- # beg, end = beg[mask], end[mask]
- t=np.column_stack((beg,end)).mean(1)/sf
-
- ifmethod=='mean':
- deffunc(x):
- returnnp.mean(x)
-
- elifmethod=='min':
- deffunc(x):
- returnnp.min(x)
-
- elifmethod=='max':
- deffunc(x):
- returnnp.max(x)
-
- elifmethod=='ptp':
- deffunc(x):
- returnnp.ptp(x)
-
- elifmethod=='prop_above_zero':
- deffunc(x):
- returnnp.count_nonzero(x>=0)/x.size
-
- elifmethod=='slope':
- deffunc(x):
- times=np.arange(x.size,dtype=np.float64)/sf
- return_slope_lstsq(times,x)
-
- elifmethod=='covar':
- deffunc(x,y):
- return_covar(x,y)
-
- elifmethod=='corr':
- deffunc(x,y):
- return_corr(x,y)
-
- else:
- deffunc(x):
- return_rms(x)
-
- # Now loop over successive epochs
- ifmethodin['covar','corr']:
- foriinrange(idx.size):
- out[i]=func(x[beg[i]:end[i]],y[beg[i]:end[i]])
- else:
- foriinrange(idx.size):
- out[i]=func(x[beg[i]:end[i]])
-
- # Finally interpolate
- ifinterpandstep!=1/sf:
- f=interp1d(t,out,kind='cubic',bounds_error=False,
- fill_value=0,assume_sorted=True)
- t=np.arange(n)/sf
- out=f(t)
-
- returnt,out
-
-
-def_zerocrossings(x):
- """Find indices of zero-crossings in a 1D array.
-
- Parameters
- ----------
- x : np.array
- One dimensional data vector.
-
- Returns
- -------
- idx_zc : np.array
- Indices of zero-crossings
-
- Examples
- --------
-
- >>> import numpy as np
- >>> from yasa.main import _zerocrossings
- >>> a = np.array([4, 2, -1, -3, 1, 2, 3, -2, -5])
- >>> _zerocrossings(a)
- array([1, 3, 6], dtype=int64)
- """
- pos=x>0
- npos=~pos
- return((pos[:-1]&npos[1:])|(npos[:-1]&pos[1:])).nonzero()[0]
-
-
-
[docs]deftrimbothstd(x,cut=0.10):
- """
- Slices off a proportion of items from both ends of an array and then
- compute the sample standard deviation.
-
- Slices off the passed proportion of items from both ends of the passed
- array (i.e., with ``cut`` = 0.1, slices leftmost 10% **and**
- rightmost 10% of scores). The trimmed values are the lowest and
- highest ones.
- Slices off less if proportion results in a non-integer slice index.
-
- Parameters
- ----------
- x : 1D np.array
- Input array.
- cut : float
- Proportion (in range 0-1) of total data to trim of each end.
- Default is 0.10, i.e. 10% lowest and 10% highest values are removed.
-
- Returns
- -------
- trimmed_std : float
- Sample standard deviation of the trimmed array.
- """
- x=np.asarray(x)
- n=x.size
- lowercut=int(cut*n)
- uppercut=n-lowercut
- atmp=np.partition(x,(lowercut,uppercut-1))
- sl=slice(lowercut,uppercut)
- returnatmp[sl].std(ddof=1)
-
-
def_merge_close(index,min_distance_ms,sf):"""Merge events that are too close in time.
diff --git a/docs/build/html/_modules/yasa/others.html b/docs/build/html/_modules/yasa/others.html
new file mode 100644
index 0000000..2a821ca
--- /dev/null
+++ b/docs/build/html/_modules/yasa/others.html
@@ -0,0 +1,387 @@
+
+
+
+
+
+ yasa.others — yasa 0.1.7 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+"""
+This file contains several helper functions to manipulate 1D and 2D EEG data.
+"""
+importnumpyasnp
+fromscipy.interpolateimportinterp1d
+from.numbaimport_slope_lstsq,_covar,_corr,_rms
+
+__all__=['moving_transform','trimbothstd','sliding_window']
+
+
+
[docs]defmoving_transform(x,y=None,sf=100,window=.3,step=.1,method='corr',
+ interp=False):
+ """Moving transformation of one or two time-series.
+
+ Parameters
+ ----------
+ x : array_like
+ Single-channel data
+ y : array_like, optional
+ Second single-channel data (only used if method in ['corr', 'covar']).
+ sf : float
+ Sampling frequency.
+ window : int
+ Window size in seconds.
+ step : int
+ Step in seconds.
+ A step of 0.1 second (100 ms) is usually a good default.
+ If step == 0, overlap at every sample (slowest)
+ If step == nperseg, no overlap (fastest)
+ Higher values = higher precision = slower computation.
+ method : str
+ Transformation to use.
+ Available methods are::
+
+ 'mean' : arithmetic mean of x
+ 'min' : minimum value of x
+ 'max' : maximum value of x
+ 'ptp' : peak-to-peak amplitude of x
+ 'prop_above_zero' : proportion of values of x that are above zero
+ 'rms' : root mean square of x
+ 'slope' : slope of the least-square regression of x (in a.u / sec)
+ 'corr' : Correlation between x and y
+ 'covar' : Covariance between x and y
+ interp : boolean
+ If True, a cubic interpolation is performed to ensure that the output
+ has the same size as the input.
+
+ Returns
+ -------
+ t : np.array
+ Time vector, in seconds, corresponding to the MIDDLE of each epoch.
+ out : np.array
+ Transformed signal
+
+ Notes
+ -----
+ This function was inspired by the `transform_signal` function of the
+ Wonambi package (https://github.com/wonambi-python/wonambi).
+ """
+ # Safety checks
+ assertmethodin['mean','min','max','ptp','rms',
+ 'prop_above_zero','slope','covar','corr']
+ x=np.asarray(x,dtype=np.float64)
+ ifyisnotNone:
+ y=np.asarray(y,dtype=np.float64)
+ assertx.size==y.size
+
+ ifstep==0:
+ step=1/sf
+
+ halfdur=window/2
+ n=x.size
+ total_dur=n/sf
+ last=n-1
+ idx=np.arange(0,total_dur,step)
+ out=np.zeros(idx.size)
+
+ # Define beginning, end and time (centered) vector
+ beg=((idx-halfdur)*sf).astype(int)
+ end=((idx+halfdur)*sf).astype(int)
+ beg[beg<0]=0
+ end[end>last]=last
+ # Alternatively, to cut off incomplete windows (comment the 2 lines above)
+ # mask = ~((beg < 0) | (end > last))
+ # beg, end = beg[mask], end[mask]
+ t=np.column_stack((beg,end)).mean(1)/sf
+
+ ifmethod=='mean':
+ deffunc(x):
+ returnnp.mean(x)
+
+ elifmethod=='min':
+ deffunc(x):
+ returnnp.min(x)
+
+ elifmethod=='max':
+ deffunc(x):
+ returnnp.max(x)
+
+ elifmethod=='ptp':
+ deffunc(x):
+ returnnp.ptp(x)
+
+ elifmethod=='prop_above_zero':
+ deffunc(x):
+ returnnp.count_nonzero(x>=0)/x.size
+
+ elifmethod=='slope':
+ deffunc(x):
+ times=np.arange(x.size,dtype=np.float64)/sf
+ return_slope_lstsq(times,x)
+
+ elifmethod=='covar':
+ deffunc(x,y):
+ return_covar(x,y)
+
+ elifmethod=='corr':
+ deffunc(x,y):
+ return_corr(x,y)
+
+ else:
+ deffunc(x):
+ return_rms(x)
+
+ # Now loop over successive epochs
+ ifmethodin['covar','corr']:
+ foriinrange(idx.size):
+ out[i]=func(x[beg[i]:end[i]],y[beg[i]:end[i]])
+ else:
+ foriinrange(idx.size):
+ out[i]=func(x[beg[i]:end[i]])
+
+ # Finally interpolate
+ ifinterpandstep!=1/sf:
+ f=interp1d(t,out,kind='cubic',bounds_error=False,
+ fill_value=0,assume_sorted=True)
+ t=np.arange(n)/sf
+ out=f(t)
+
+ returnt,out
+
+
+def_zerocrossings(x):
+ """Find indices of zero-crossings in a 1D array.
+
+ Parameters
+ ----------
+ x : np.array
+ One dimensional data vector.
+
+ Returns
+ -------
+ idx_zc : np.array
+ Indices of zero-crossings
+
+ Examples
+ --------
+
+ >>> import numpy as np
+ >>> from yasa.main import _zerocrossings
+ >>> a = np.array([4, 2, -1, -3, 1, 2, 3, -2, -5])
+ >>> _zerocrossings(a)
+ array([1, 3, 6], dtype=int64)
+ """
+ pos=x>0
+ npos=~pos
+ return((pos[:-1]&npos[1:])|(npos[:-1]&pos[1:])).nonzero()[0]
+
+
+
[docs]deftrimbothstd(x,cut=0.10):
+ """
+ Slices off a proportion of items from both ends of an array and then
+ compute the sample standard deviation.
+
+ Slices off the passed proportion of items from both ends of the passed
+ array (i.e., with ``cut`` = 0.1, slices leftmost 10% **and**
+ rightmost 10% of scores). The trimmed values are the lowest and
+ highest ones.
+ Slices off less if proportion results in a non-integer slice index.
+
+ Parameters
+ ----------
+ x : 1D np.array
+ Input array.
+ cut : float
+ Proportion (in range 0-1) of total data to trim of each end.
+ Default is 0.10, i.e. 10% lowest and 10% highest values are removed.
+
+ Returns
+ -------
+ trimmed_std : float
+ Sample standard deviation of the trimmed array.
+ """
+ x=np.asarray(x)
+ n=x.size
+ lowercut=int(cut*n)
+ uppercut=n-lowercut
+ atmp=np.partition(x,(lowercut,uppercut-1))
+ sl=slice(lowercut,uppercut)
+ returnatmp[sl].std(ddof=1)
+
+
+
[docs]defsliding_window(data,sf,window,step=None,axis=-1):
+ """
+ Calculate a sliding window of a 1D or 2D EEG signal.
+
+ .. versionadded:: 0.1.7
+
+ Parameters
+ ----------
+ data : numpy array
+ The 1D or 2D EEG data.
+ sf : float
+ The sampling frequency of ``data``.
+ window : int
+ The sliding window length, in seconds.
+ step : int
+ The sliding window step length, in seconds.
+ If None (default), ``step`` is set to ``window``,
+ which results in no overlap between the sliding windows.
+ axis : int
+ The axis to slide over. Defaults to the last axis.
+
+ Returns
+ -------
+ times : numpy array
+ Time vector, in seconds, corresponding to the START of each sliding
+ epoch in ``strided``.
+ strided : numpy array
+ A matrix where row in last dimension consists of one instance
+ of the sliding window.
+
+ Notes
+ -----
+ This is a wrapper around the
+ :py:func:`numpy.lib.stride_tricks.as_strided` function.
+ """
+ fromnumpy.lib.stride_tricksimportas_strided
+ assertaxis<=data.ndim,"Axis value out of range."
+ assertisinstance(sf,(int,float)),'sf must be int or float'
+ assertisinstance(window,(int,float)),'window must be int or float'
+ assertisinstance(step,(int,float,type(None))),('step must be int, '
+ 'float or None.')
+ ifisinstance(sf,float):
+ assertsf.is_integer(),'sf must be a whole number.'
+ sf=int(sf)
+ assertisinstance(axis,int),'axis must be int.'
+
+ # window and step in samples instead of points
+ window*=sf
+ step=windowifstepisNoneelsestep*sf
+
+ ifisinstance(window,float):
+ assertwindow.is_integer(),'window * sf must be a whole number.'
+ window=int(window)
+
+ ifisinstance(step,float):
+ assertstep.is_integer(),'step * sf must be a whole number.'
+ step=int(step)
+
+ assertstep>=1,"Stepsize may not be zero or negative."
+ assertwindow<data.shape[axis],("Sliding window size may not exceed "
+ "size of selected axis")
+
+ shape=list(data.shape)
+ shape[axis]=np.floor(data.shape[axis]/step-window/step+1
+ ).astype(int)
+ shape.append(window)
+
+ strides=list(data.strides)
+ strides[axis]*=step
+ strides.append(data.strides[axis])
+
+ strided=as_strided(data,shape=shape,strides=strides)
+ t=np.arange(strided.shape[-2])*(step/sf)
+ returnt,strided
Values in ``hypno`` that will be included in the mask. The default is (2, 3), meaning that the bandpower are sequentially calculated for N2 and N3 sleep. This has no effect when ``hypno`` is None.
+ win_sec : int or float
+ The length of the sliding window, in seconds, used for the Welch PSD
+ calculation. Ideally, this should be at least two times the inverse of
+ the lower frequency of interest (e.g. for a lower frequency of interest
+ of 0.5 Hz, the window length should be at least 2 * 1 / 0.5 =
+ 4 seconds). relative : boolean If True, bandpower is divided by the total power between the min and max frequencies defined in ``band``.
@@ -285,10 +292,7 @@
[docs]defirasa(data,sf=None,ch_names=None,band=(1,30),
+ hset=np.arange(1.1,1.95,0.05),return_fit=True,win_sec=4,
+ kwargs_welch=dict(average='median',window='hamming')):
+ """
+ Separate the aperiodic (= fractal, or 1/f) and oscillatory component of the
+ power spectra of EEG data using the IRASA method.
+
+ .. versionadded:: 0.1.7
+
+ Parameters
+ ----------
+ data : :py:class:`numpy.ndarray` or :py:class:`mne.io.BaseRaw`
+ 1D or 2D EEG data. Can also be a :py:class:`mne.io.BaseRaw`, in which
+ case ``data``, ``sf``, and ``ch_names`` will be automatically
+ extracted, and ``data`` will also be converted from Volts (MNE default)
+ to micro-Volts (YASA).
+ sf : float
+ The sampling frequency of data AND the hypnogram.
+ Can be omitted if ``data`` is a :py:class:`mne.io.BaseRaw`.
+ ch_names : list
+ List of channel names, e.g. ['Cz', 'F3', 'F4', ...]. If None,
+ channels will be labelled ['CHAN001', 'CHAN002', ...].
+ Can be omitted if ``data`` is a :py:class:`mne.io.BaseRaw`.
+ band : tuple or None
+ Broad band frequency range.
+ Default is 1 to 30 Hz.
+ hset : :py:class:`numpy.ndarray`
+ Resampling factors used in IRASA calculation. Default is to use a range
+ of values from 1.1 to 1.9 with an increment of 0.05.
+ return_fit : boolean
+ If True (default), fit an exponential function to the aperiodic PSD
+ and return the fit parameters (intercept, slope) and :math:`R^2` of
+ the fit.
+
+ The aperiodic signal, :math:`L`, is modeled using an exponential
+ function in semilog-power space (linear frequencies and log PSD) as:
+
+ .. math:: L = a + \\text{log}(F^b)
+
+ where :math:`a` is the intercept, :math:`b` is the slope, and
+ :math:`F` the vector of input frequencies.
+ win_sec : int or float
+ The length of the sliding window, in seconds, used for the Welch PSD
+ calculation. Ideally, this should be at least two times the inverse of
+ the lower frequency of interest (e.g. for a lower frequency of interest
+ of 0.5 Hz, the window length should be at least 2 * 1 / 0.5 =
+ 4 seconds).
+ kwargs_welch : dict
+ Optional keywords arguments that are passed to the
+ :py:func:`scipy.signal.welch` function.
+
+ Returns
+ -------
+ freqs : :py:class:`numpy.ndarray`
+ Frequency vector.
+ psd_aperiodic : :py:class:`numpy.ndarray`
+ The fractal (= aperiodic) component of the PSD.
+ psd_oscillatory : :py:class:`numpy.ndarray`
+ The oscillatory (= periodic) component of the PSD.
+ fit_params : :py:class:`pandas.DataFrame` (optional)
+ Dataframe of fit parameters. Only if ``return_fit=True``.
+
+ Notes
+ -----
+ The Irregular-Resampling Auto-Spectral Analysis (IRASA) method is
+ described in Wen & Liu (2016). In a nutshell, the goal is to separate the
+ fractal and oscillatory components in the power spectrum of EEG signals.
+
+ The steps are:
+
+ 1. Compute the original power spectral density (PSD) using Welch's method.
+ 2. Resample the EEG data by multiple non-integer factors and their
+ reciprocals (:math:`h` and :math:`1/h`).
+ 3. For every pair of resampled signals, calculate the PSD and take the
+ geometric mean of both. In the resulting PSD, the power associated with
+ the oscillatory component is redistributed away from its original
+ (fundamental and harmonic) frequencies by a frequency offset that varies
+ with the resampling factor, whereas the power solely attributed to the
+ fractal component remains the same power-law statistical distribution
+ independent of the resampling factor.
+ 4. It follows that taking the median of the PSD of the variously
+ resampled signals can extract the power spectrum of the fractal
+ component, and the difference between the original power spectrum and
+ the extracted fractal spectrum offers an approximate estimate of the
+ power spectrum of the oscillatory component.
+
+ Note that an estimate of the original PSD can be calculated by simply
+ adding ``psd = psd_aperiodic + psd_oscillatory``.
+
+ References
+ ----------
+ .. [1] Wen, H., & Liu, Z. (2016). Separating Fractal and Oscillatory
+ Components in the Power Spectrum of Neurophysiological Signal.
+ Brain Topography, 29(1), 13–26.
+ https://doi.org/10.1007/s10548-015-0448-0
+
+ .. [2] https://github.com/fieldtrip/fieldtrip/blob/master/specest/
+
+ .. [3] https://github.com/fooof-tools/fooof
+
+ .. [4] https://www.biorxiv.org/content/10.1101/299859v1
+ """
+ importfractions
+ # Check if input data is a MNE Raw object
+ ifisinstance(data,mne.io.BaseRaw):
+ sf=data.info['sfreq']# Extract sampling frequency
+ ch_names=data.ch_names# Extract channel names
+ data=data.get_data()*1e6# Convert from V to uV
+ else:
+ # Safety checks
+ assertisinstance(data,np.ndarray),'Data must be a numpy array.'
+ data=np.atleast_2d(data)
+ assertdata.ndim==2,'Data must be of shape (nchan, n_samples).'
+ nchan,npts=data.shape
+ assertnchan<npts,'Data must be of shape (nchan, n_samples).'
+ assertsfisnotNone,'sf must be specified if passing a numpy array.'
+ assertisinstance(sf,(int,float))
+ ifch_namesisNone:
+ ch_names=['CHAN'+str(i+1).zfill(3)foriinrange(nchan)]
+ else:
+ ch_names=np.atleast_1d(np.asarray(ch_names,dtype=str))
+ assertch_names.ndim==1,'ch_names must be 1D.'
+ assertlen(ch_names)==nchan,'ch_names must match data.shape[0].'
+
+ # Check the other arguments
+ hset=np.asarray(hset)
+ asserthset.ndim==1,'hset must be 1D.'
+ asserthset.size>1,'2 or more resampling fators are required.'
+ hset=np.round(hset,4)# avoid float precision error with np.arange.
+ band=sorted(band)
+ assertband[0]>0,'first element of band must be > 0.'
+ assertband[1]<(sf/2),'second element of band must be < (sf / 2).'
+ win=int(win_sec*sf)# nperseg
+
+ # Calculate the original PSD over the whole data
+ freqs,psd=signal.welch(data,sf,nperseg=win,**kwargs_welch)
+
+ # Start the IRASA procedure
+ psds=np.zeros((len(hset),*psd.shape))
+
+ fori,hinenumerate(hset):
+ # Get the upsampling/downsampling (h, 1/h) factors as integer
+ rat=fractions.Fraction(str(h))
+ up,down=rat.numerator,rat.denominator
+ # Much faster than FFT-based resampling
+ data_up=signal.resample_poly(data,up,down,axis=-1)
+ data_down=signal.resample_poly(data,down,up,axis=-1)
+ # Calculate the PSD using same params as original
+ freqs_up,psd_up=signal.welch(data_up,h*sf,nperseg=win,
+ **kwargs_welch)
+ freqs_dw,psd_dw=signal.welch(data_down,sf/h,nperseg=win,
+ **kwargs_welch)
+ # Geometric mean of h and 1/h
+ psds[i,:]=np.sqrt(psd_up*psd_dw)
+
+ # Now we take the median PSD of all the resampling factors, which gives
+ # a good estimate of the aperiodic component of the PSD.
+ psd_aperiodic=np.median(psds,axis=0)
+
+ # We can now calculate the oscillations (= periodic) component.
+ psd_osc=psd-psd_aperiodic
+
+ # Let's crop to the frequencies defined in band
+ mask_freqs=np.ma.masked_outside(freqs,*band).mask
+ freqs=freqs[~mask_freqs]
+ psd_aperiodic=np.compress(~mask_freqs,psd_aperiodic,axis=-1)
+ psd_osc=np.compress(~mask_freqs,psd_osc,axis=-1)
+
+ ifreturn_fit:
+ # Aperiodic fit in semilog space for each channel
+ fromscipy.optimizeimportcurve_fit
+ intercepts,slopes,r_squared=[],[],[]
+
+ deffunc(t,a,b):
+ # See https://github.com/fooof-tools/fooof
+ returna+np.log(t**b)
+
+ foryinnp.atleast_2d(psd_aperiodic):
+ y_log=np.log(y)
+ # Note that here we define bounds for the slope but not for the
+ # intercept.
+ popt,pcov=curve_fit(func,freqs,y_log,p0=(2,-1),
+ bounds=((-np.inf,-10),(np.inf,2)))
+ intercepts.append(popt[0])
+ slopes.append(popt[1])
+ # Calculate R^2: https://stackoverflow.com/q/19189362/10581531
+ residuals=y_log-func(freqs,*popt)
+ ss_res=np.sum(residuals**2)
+ ss_tot=np.sum((y_log-np.mean(y_log))**2)
+ r_squared.append(1-(ss_res/ss_tot))
+
+ # Create fit parameters dataframe
+ fit_params={'Chan':ch_names,'Intercept':intercepts,
+ 'Slope':slopes,'R^2':r_squared,
+ 'std(osc)':np.std(psd_osc,axis=-1,ddof=1)}
+ returnfreqs,psd_aperiodic,psd_osc,pd.DataFrame(fit_params)
+ else:
+ returnfreqs,psd_aperiodic,psd_osc
+
+
[docs]defstft_power(data,sf,window=2,step=.2,band=(1,30),interp=True,norm=False):"""Compute the pointwise power via STFT and interpolation.
@@ -339,11 +543,11 @@
Source code for yasa.spectral
Returns -------
- f : ndarray
+ f : :py:class:`numpy.ndarray` Frequency vector
- t : ndarray
+ t : :py:class:`numpy.ndarray` Time vector
- Sxx : ndarray
+ Sxx : :py:class:`numpy.ndarray` Power in the specified frequency bins of shape (f, t) Notes
diff --git a/docs/build/html/_static/documentation_options.js b/docs/build/html/_static/documentation_options.js
index fee47dc..cfcf13a 100644
--- a/docs/build/html/_static/documentation_options.js
+++ b/docs/build/html/_static/documentation_options.js
@@ -1,6 +1,6 @@
var DOCUMENTATION_OPTIONS = {
URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'),
- VERSION: '0.1.6',
+ VERSION: '0.1.7',
LANGUAGE: 'None',
COLLAPSE_INDEX: false,
FILE_SUFFIX: '.html',
diff --git a/docs/build/html/api.html b/docs/build/html/api.html
index cfb85f4..b98336c 100644
--- a/docs/build/html/api.html
+++ b/docs/build/html/api.html
@@ -3,7 +3,7 @@
- API reference — yasa 0.1.6 documentation
+ API reference — yasa 0.1.7 documentation
@@ -12,6 +12,7 @@
+
@@ -37,7 +38,7 @@
yasa
- 0.1.6
+ 0.1.7
(2, 3), meaning that the bandpower are sequentially calculated
for N2 and N3 sleep. This has no effect when hypno is None.
+
win_secint or float
The length of the sliding window, in seconds, used for the Welch PSD
+calculation. Ideally, this should be at least two times the inverse of
+the lower frequency of interest (e.g. for a lower frequency of interest
+of 0.5 Hz, the window length should be at least 2 * 1 / 0.5 =
+4 seconds).
+
relativeboolean
If True, bandpower is divided by the total power between the min and
max frequencies defined in band.
1D or 2D EEG data. Can also be a mne.io.BaseRaw, in which
+case data, sf, and ch_names will be automatically
+extracted, and data will also be converted from Volts (MNE default)
+to micro-Volts (YASA).
+
+
sffloat
The sampling frequency of data AND the hypnogram.
+Can be omitted if data is a mne.io.BaseRaw.
+
+
ch_nameslist
List of channel names, e.g. [‘Cz’, ‘F3’, ‘F4’, …]. If None,
+channels will be labelled [‘CHAN001’, ‘CHAN002’, …].
+Can be omitted if data is a mne.io.BaseRaw.
+
+
bandtuple or None
Broad band frequency range.
+Default is 1 to 30 Hz.
Resampling factors used in IRASA calculation. Default is to use a range
+of values from 1.1 to 1.9 with an increment of 0.05.
+
+
return_fitboolean
If True (default), fit an exponential function to the aperiodic PSD
+and return the fit parameters (intercept, slope) and \(R^2\) of
+the fit.
+
The aperiodic signal, \(L\), is modeled using an exponential
+function in semilog-power space (linear frequencies and log PSD) as:
+
+\[L = a + \text{log}(F^b)\]
+
where \(a\) is the intercept, \(b\) is the slope, and
+\(F\) the vector of input frequencies.
+
+
win_secint or float
The length of the sliding window, in seconds, used for the Welch PSD
+calculation. Ideally, this should be at least two times the inverse of
+the lower frequency of interest (e.g. for a lower frequency of interest
+of 0.5 Hz, the window length should be at least 2 * 1 / 0.5 =
+4 seconds).
+
+
kwargs_welchdict
Optional keywords arguments that are passed to the
+scipy.signal.welch() function.
Dataframe of fit parameters. Only if return_fit=True.
+
+
+
+
+
Notes
+
The Irregular-Resampling Auto-Spectral Analysis (IRASA) method is
+described in Wen & Liu (2016). In a nutshell, the goal is to separate the
+fractal and oscillatory components in the power spectrum of EEG signals.
+
The steps are:
+
+
Compute the original power spectral density (PSD) using Welch’s method.
+
Resample the EEG data by multiple non-integer factors and their
+reciprocals (\(h\) and \(1/h\)).
+
For every pair of resampled signals, calculate the PSD and take the
+geometric mean of both. In the resulting PSD, the power associated with
+the oscillatory component is redistributed away from its original
+(fundamental and harmonic) frequencies by a frequency offset that varies
+with the resampling factor, whereas the power solely attributed to the
+fractal component remains the same power-law statistical distribution
+independent of the resampling factor.
+
It follows that taking the median of the PSD of the variously
+resampled signals can extract the power spectrum of the fractal
+component, and the difference between the original power spectrum and
+the extracted fractal spectrum offers an approximate estimate of the
+power spectrum of the oscillatory component.
+
+
Note that an estimate of the original PSD can be calculated by simply
+adding psd=psd_aperiodic+psd_oscillatory.
Wen, H., & Liu, Z. (2016). Separating Fractal and Oscillatory
+Components in the Power Spectrum of Neurophysiological Signal.
+Brain Topography, 29(1), 13–26.
+https://doi.org/10.1007/s10548-015-0448-0
Slices off a proportion of items from both ends of an array and then
compute the sample standard deviation.
Slices off the passed proportion of items from both ends of the passed
diff --git a/docs/build/html/genindex.html b/docs/build/html/genindex.html
index 7daf96a..e52c781 100644
--- a/docs/build/html/genindex.html
+++ b/docs/build/html/genindex.html
@@ -4,7 +4,7 @@
diff --git a/docs/build/html/searchindex.js b/docs/build/html/searchindex.js
index 4e7f971..64a4af6 100644
--- a/docs/build/html/searchindex.js
+++ b/docs/build/html/searchindex.js
@@ -1 +1 @@
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\ No newline at end of file
diff --git a/docs/changelog.rst b/docs/changelog.rst
index 72056fe..df8e0de 100644
--- a/docs/changelog.rst
+++ b/docs/changelog.rst
@@ -3,12 +3,12 @@
What's new
##########
-v0.1.7
-------
+v0.1.7 (August 2019)
+--------------------
a. Added :py:func:`yasa.sliding_window` function.
b. Added :py:func:`yasa.irasa` function.
-b. Reorganized code into several sub-files for readability (internal changes with no effect on user experience).
+c. Reorganized code into several sub-files for readability (internal changes with no effect on user experience).
v0.1.6 (August 2019)
--------------------
diff --git a/notebooks/11_IRASA.ipynb b/notebooks/11_IRASA.ipynb
index ac6f7b3..ab29d14 100644
--- a/notebooks/11_IRASA.ipynb
+++ b/notebooks/11_IRASA.ipynb
@@ -6,7 +6,7 @@
"source": [
"# Aperiodic and oscillatory components of the power spectrum\n",
"\n",
- "This notebook demonstrates how to use YASA to separate the aperiodic (= fractal = $1/f$) components of the EEG power spectra.\n",
+ "This notebook demonstrates how to use YASA to separate the aperiodic (= fractal = $1/f$) components of the EEG power spectra using the IRASA method.\n",
"\n",
"Please make sure to install YASA first by typing the following line in your terminal or command prompt:\n",
"\n",
@@ -95,7 +95,7 @@
},
{
"data": {
- "image/png": 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44WGHlnSPPvoo9913H2lp6XTqdwiFfX9CemYLiqNVbFizmPSsPDJbtAw7zK1q3WlXOvbZnwXfvMcVV1zByy+/rEt0Ig1MI6JGkpaRRZehF1LcazBr167lnHPOYcSIEc3q2ZV33313U4WE7kPPocOA40nPbAFAJJJGi1bFTToJbVQ0ICgBNHnyZF599dWwwxFp9hKerGBmaQTP7BQBlcBCYIa7p/Tsh2RMVtiWaDTKsun/Yc5nLxGNRjniiCO45557aNmy6f+B3pbvvvuOo446ipUrV9JlwDCK+h8Tdkj1smzmu8z++Gl22WUXxo8fT1oIU8tFUlBCkxXqnIjM7EDgMuBQIP6vZxRYAfwLeMDdP0gkoLA1dCLaaPWCL5n78d9YX7KW3r17c+edd5Kbm8uGDRvYaaedaN++fYP1nSwTJ07k//7v/5gyZQozZswgGo1S1G0Qnff5ZZOYgFAfVZXlzBj/J9auWsZf//rXZnkZVaQBNGwiMrOdgYeAnQgeGP0XQQWDZQSX+NoDg4ADgdOAmcCv3D2l7vg2ViKCYJr3/ImPsXLJnM3aMzMzOfnkk7n44ovp0aNHg8aQiMrKSkaOHMldd9216dJiWno67bv2p3iPs0jPql51KTUtmf4mcz55nkGDBjFu3DgikYR+x0R2JA2eiP4L/Mndt/vouZlFgOOB37n73okEFpbGTEQAleXrWfLFS5Qum0laeiaRSBrLFn5LNBolLS2NSy+9lKuvvrrB46itRYsWcfnll/POO+8QiUTo2O8wWnbajZyCzqSlZ4YdXlJVVZTxzb9uoGTtSp588kl+9KMfhR2SSFPX4IkoUtf7P4m8JmyNnYhqsn71IlbMnMCi6R9QVVXJc889x3777bdpe0VFBRs2bKCiooLMzExycxum2Pi6devIzMwkKyuL0tJSRo0axQMPPEBJSQm5+a3ptNcvaFW8S4P03VQs8deZ89kYunTpwtFHH82gQYM48MADKSgoCDs0kaaoce4RAZjZY8Dd7v55tfZCYKK790wkmKagKSSijRZ/+Rpzp/6Tnj178vrrr9OiRQvGjBnDNddcw9q1QYHxrKwsbrjhBs4666yk9RuNRjddequsrKRDhw6Ul5dvWnOpQ/fdaT/oZLJymv8f48ry9Xw74XZWr1i0qa2oqIjRo0ez++67hxiZSJOUUCJK9I7yOcCHZnZ6tfZ0oFuCx5RqCu1QCgo7M2vWLO677z6eeeYZLr30UtauXUtmVjbZOXmUlZVx3XXX8fHHHwNBErnrrrs48sgjGTt2LHV9o1FZWckf/vAHbr/9dioqKoAICxcuZNmyZbTp0J2df3Q5nff55Q6RhADSM1vQ48dX0+uAi+g04CjaFvdk8eLFnHjiiYwdO3aL/SsqKpg1a1bsZycitZHoiKgKuAK4BXgYuMrdq8ysAzDf3VP2CcCmNCICWLN4OtMn/IWMjIxNf9y67nY87fsGs7gWfT6GeV+8TseOHRk3bhy33nor//jHPza9fq+99uLGG29kt912225fJSUlXHbZZbz66qtkZGax096/oHXnQZSVrKSyvJScgk4pPxuuvqJVlSyc8jwL/B0Ahg0bxn777Uf//v2ZMGECzz33HIsWLaJbt25ccMEFnHrqqeTkNI/JGyK10KiX5qqAYqATwQy6b4FTCEZYC5SIkmvBp0+x4Jv3ANhpz5Mp3PmHm+bRqkq+f/deli2YTn5+fmy01IJ2vQ9i9ff/pWTtSgBOOukkrrnmGgoLC/nnP//Jk08+SV5eHsOHD2fw4MF8+eWXXHTRRcyYMYMWOXl0HXoBLYt2DuV8m7poNMqyGW8x59MXiEa3fCA5Myub8rINALRp04Zhw4Zx2GGHccABBygpSXPXqImoEujo7otj94WeA3oDZwOvKxElV0VZCcu+epnsNr0o2GnwFtvL1i1n5oQ7KF23mpy8Vuy074XktetOZXkpy755nYVfvUFFRTk5OTkUFBRssXDf0KFD+eTTTynbsIGCwi50HHwOOa07NtbppawNa5eyZtHXlK+cxYZV88gu6Ep+lyHkF/Zk5byprJ41gWULZm7av1Xr1ox+7DGGDh0aYtQiDarxR0Tuvjj2fTowArgAyFIianzrln7Lmrn/paDnj2jRqsNm2zasXcqyr15m4cxJABQUdqZVj4OoXL+SJd9MoGxDUA27ox1IhwE/bdTlupuzaDRK6cp5rFnwOaWLP2f5wu/Iy8vj2Wef1UQHaa4aNRFdD9zp7iXV2s8Cznb3lH3gIlUTUW2UrJhDZXkp+e17b7rXU75+DctmvkeL1p0o6DIo5Aibr2hVFQs+fZKFMz6idevWjB49mkWLFvHBBx/Qtm1bLr300gabhi/SiBr8OaJ+tT2ou3+ZSDBNQXNORBKuaFUl8yaOZvF3n22xzcx4+OGH6d07WKk2Go2qkoOkogZfGG8aQT25SLXP1TuPEkzjFpE4kbR0Og0+G6JVLJ//Fe069SG9dQ/WzfsUd+fII49k2LBhTJ8+HXdn6NChPPzwwxopSbNXlxFR9eeDIgTJ6UhgdvwGd59NitKISBraxt+5jSOeyvL1LJz8DItmTtxi36FDh/L444+Tl9d0FhAU2YbGu0e0kZmtAQa5+6yED9LEKBFJGKLRKKvmTaGsZEVQty8jm7kfPcK61cvZe++9+fvf/05+fn7YYYpsT4NfmksZZpYBPE5QKXwB8At3Xx9uVCJbF4lEKOiy+UPH3Q4YzvfvjWTixIkce+yxjBw5kv79+4cUoUjDaa6PyZ8IzHX3A4CJwJkhxyNSZy1aFtHtgMto1a4j7sES86NGjWpWq/qKQPNNRPsA42Nfvw4cFGIsIgnLzi+kx4+uplPfgygrK+Omm25i//3358EHH2T58uVhhyeSFLW+NGdmF2/l9Wea2dL4Rnd/oL6B1VMrYHXs6zVsvpKsSEpJz8imeLdTySnqx+Kp/2D27NncfPPN3H777fTv35+BAwcyZMgQjjnmGNLTNWFVUk9d7hH9Tw1tCwkqcceLAmEnotX8kHxaEiQjkZTWutMAWhX3Z/WCL1g75wMWz57K5MmTmTx5Mk888QSfffYZN954Y9hhitRZrRORuze9Nau3biJwODABOAz4KNxwRJIjkpZG684DaN15AB32KKF0xRzWLfuWRV+M49FHH2XIkCEceeSRYYcpUid1uTQ3neC+y+vAG+7elEcZzwNHmdn7wFLgtJDjEUm6jKxcWnYwWnYwMjKz+f6T57nyyivp168f3bt332zf77//ni+++IK8vDxatmxJ3759VQlcmoy6PNDah2B0cThwAPAVPySmj9y9WUzl0XNEkoqi0WhQPujbT+jfvz9PPvkkRUVFALz44ov85jdXURZbmgKgqKgDTzzxOAMGDAgr5K164oknePbZZznzzDM5+eSTycholk+ZNFeNWvQ0HRjKD4lpZ+BdYonJ3WckEsx2+twbeMXdi+LaBgGjgIHALOBcd/+4nv10R4lIUlBlWSmz3ryDNSsWkZ+fz/Dhw1mzZg0jR44EoH2XvqSnp1OyZimrly8iNzeXUaNGccghh2z1mGPHjmX06NGcdtppnHrqqaSlNexE26effpqrrrpq0/e9evXimmuuYdiwYaq9lxoav7LCRmbWGjiEIDEd6u5JW1HNzCLAecCfAdy9INaeBXwD3A3cT/Ds0INAN3dfXfPRatVfd5SIJEVtWLeMJZ+/wOLvJm9qS0tLp+seJ9Gud/AUQ1VlOQs/e5qFMz4iLS2NSy65hNNPP51u3X6o4lVRUcEtt9zCww8/vKltyJAh3H777ey88+a/3mPHjuXVV1+lVatWtG7dmj59+nD00UeTm5tLVVUVzz//PKNGjSIzM5OhQ4ey7777sv/++29RtmjcuHFceOGFVFVVUbTzgaxf9g2rly8E4LjjjuO2226jdevWSf+ZSVKFl4gakpn9CTgKeBr4Y1wiOhz4q7t3jtv3PeBxd3+kHv11R4lIUtzqBV+y7KuxlK5dSZfBZ9Gq4+bF86PRKEu+HMfcz1/d1DZ48GB23nlnsrKy+OKLL/j4449JT0+nsPeBrJn3GSVrV5KZmcm9997LscceC8A///lPLrzwwi36b9myJccffzyfffYZ06ZN22J7Tk4Ow4YN4+ijj2bp0qVMmTKF559/nrKyMroMOoaiXYZRVVnB8lnvs3DaWMo2rKdLly6MHDmSvffeO8k/LUmihktEZmZAF2Bi/CQFMzva3V9JpOPaMrNO7j7fzA4GXopLRJcDR7v7oXH7PgqUuPvwevTXHSUiaQai0ShEq4ikbf3ZojWLvmHt3I9YOnsy5WWbV8HKbVlAl73PJb99byrKSlgy7SUWfPMeaWlpjBw5kt69e3Pcccexfv16inc5lKy8Iio2rKVs+VcsnTd903HyW7ejcJejycwpYN3SGZQvn86Sed/UGE+nfofSYcAJm12GW79mMQs/eYLlC2eRkZHB7bffzmmnaf5RE9UwtebM7BLgUsCB3c3sMncfE9v8J6BBE5G7z9/KpnygpFpbCaCa+SLEqntHtv2Aa8sOfWjZoQ9FA09h9cKvqNywjqqqciKRNAq67EZmTnApLCMrl+LdTye9RWvmTh3HpZdeSps2bYIk1Gc/Og6MTx4/oXDlXNbO/ZRIVj7teu6/adXflh0MgKK1S1n5/ceUr/iG9BZtSMvrTH5hT3Lbdd/iXlCLlkV0O/AKWkx7mflfvs5vfvMbZs+ezdVXX637Rs1Ebaaj/ArY093XmVkP4B9m1sPdR5Bg9kuSdUD1+ae5wNoQYhFJaemZLWjTddvLl0ciEYr6HQWRCHOnvMKyZcto13FnigedskVCyC3oQm5Bl60eKzu/kA79hgHDahVfJC2d4oEnkJnfnjmTnuXee+9l+vTp/P73v6dnz561OoY0XbVJRBnuvg7A3b+NXSL7h5l1IdxE9CVwRbW2vsATIcQissMo2uVIMrLy2LB8JoW7nkhaemaj9d2u5/5ktGjDnP+O5rXXXuPf//43J5xwAt27d2fSpElMnTqVHj168LOf/Yxjjz1W6ziliO3eIzKzCcCV7j45ri0DGA2c4e6NUtyqhntEWcBMYARwH8GsuYeBXu6+pB79dEf3iESatA1rl7L8m9dZNPMDqiora9wnLy+P4cOHc/HFF2932vknn3zCm2++SUFBAe3bt2f33Xdnp512aojQm7sGW4/oF0BFfIO7VwC/MLOHEuk0Gdy9zMyGETxH9CfgO+D4+iQhEUkN2fmFdNzjdNr2OZyV371LVWUlLdr2ILfNTqxdPJ2S+RNZMte57bbb+OCDD7j33nspLCys8VhPPvkkv//976mMS2hZWVk899xzDB48uLFOaYdWp+nbZnaWuz/egPGETiMikeZh1fwvmP/J3yldt5qiog7cc8/dHHjggZu2V1VVccsttzBq1CgAinoNJSOrBWWrF7B03te0b9+eV199lU6dOhGNRpk0aRIdO3akS5et3/vammg0SklJCStWrCA3N5e2bZvt35aERkR1fUz6ETN7x8x2TaQzEZHG0rpTf3odcg3tOhuLFy/i9NNP59prr2XdunWMGzdu00KD6enpdB/yc7oM/jnFg06m636XUNilH0uWLOH888/n008/5bTTTuP444/n4IMP5tlnn6W2b+BLS0v57W9/S+/evenTpw9Dhgxh991355ZbbqGkpPqk3x1XXUdEuwIjgf1in69392Y1S00jIpHmJVpVyVJ/nfnTxlFZWUl2djYbNgR193LyWtN58Fm0Ku672WsqNqzl2zf/zJqVize1ZWRmUVFeBsAJJ5zA9ddfT/v27TdtX7VqFTNmzKC4uJiOHTsyffp0LrzwQr755ptNr8/Ja8XaVcuIRqN06tSJm2++mSOOOKKhfwSNqVFrzZ0G3EEworrS3Z9LpPOmSIlIpHkqWTGHhZ8+ycolc2jVpoiCnj+ibY+hm55x2mL/lXOZ9eYIKirKKbaDKbQjWD1/GvM+e27Tw79du3Zll1124bvvvtuUcABatGhBVVUVZWVltG7XmY6Dz9o0nX3dsu9Y8vnzLF/4LRAktZtuuok2bdo08E+gUTRuiR8zywWuJZhC/S5wibvX/Lh0ClEiEmm+qirLKV05l9w2O22z4rVnlcIAABbgSURBVMRGZSUrAcjKLdjUtn71IpZ9OYYVC76hbMMP1SjSMzIpaNeJ0nWrKFkbvK64z350GHgS6RnZmx03WlXFsplvs/Dzf1JWtp6ioiLOO+88WrZsSU5ODvvuu29C96KagHBqzZnZzsA9wI+Bu4Cb3b20XgcNkRKRiNRGtKqK9asXUrpqHll57cht03XTM1UVZSVUVZRtlsBqsn7NYhZNfppl83yz9pycHG699VZOOeWUpMVbWlrK6NGjmT9/PoWFhbRr147ly5czc+ZMvv/+e7p168Z+++3H/vvvT+fOnbd7vEmTJjFy5EhWrFjBWWedxXHHHUdGRka4RU/N7BiChBRJsdVcN6NEJCKNKVpVxfLZ/6V8zXyoqqC8ZBlLvg8KxZ500knceuut230wt6KigqlTp7JkyRL23XdfWrZsudn2Dz74gKuuuorZs2fXKqaBAwfy05/+lOOOO27TulYAS5YsYeLEiTz11FO89dZbm72mR48evPfee41+aa4HwTpAA+I+70yQiBrlIdeGoEQkImGKRqOs+O6j2L2oDfTq1YtRo0bRr9/mFdSXL1/Oa6+9xvjx4/noo49YuzaYN5adnc0hhxzC7rvvzoIFC5g5cyZvv/02AG2KdiK302CqytcSqSghmt6CzLwisvLasX71fCpWzmLF/K/ZsP6HGX15eXmbnsGKT2RZ2Tm073MwGTltWTHjDVYvX8i8efMaPhGZ2cZF6HYFNqbob4HJwJSNH+5eu7TbBCkRiUhTULpqPgsmPc7KJXPIys7m+uuuo3v37kydOpWJEyfy7rvvUlHxQ62BgsJOZGbn11jZPD09g467DqOwz2GkpW+7jkFVRRmr5k+jdMEnLJ0zjYqK8k3bsrJb0Ka4N5kFPWnbc38ysvOBYGbi8m8/4IOX/twoiegjNk86UzV9W0SkYVRVlLH48xeZ7+9ssS0tLZ32XfuRXTSQVsW7kJUX/L0qK1nByjmfUrV+JZHs1mTltSOvbbdN2+siGo1SWV5KxYa1RCsraNGqwzYnefzzruMarMTPJu6+TyKdiIhI3aVlZFG8+2lkt+vNqpn/ISMrl4z8zmS26kKrjv3IbNFyi9dk5bahyLa+/HtdRCKRoM+shl1dp06JaCMz+znwKfC1u9dccVBERJKizU570WanvcIOo8EklIiAO4H2QJmZTSO4XPdZ7POUjctGiIiIbE9Cicjdi82sM7BH7GMI8HMgE4gmelwREdnxJJww3H0eMA/4J4CZdQKeAZ5MTmgiIrIjqGv17a1y9/nAecBRyTqmiIg0fwklIjOrcYUpd59OcKlORESkVhK9NLfYzOYRTFDY+PEVsDdQcylbERGRGiSaiPYBdicY/RwJXA1kA5XAb5ITmoiI7AgSnTU3EZi48XszSwe6A8vdfUVyQhMRkR1Bre8RmdlW65m7e6W7z6yehMysSaz0ZGaXm9lVYcchIiJbqstkhbfN7Ldm1np7O5pZoZn9EdiyQFIjM7MHgV+HHYeIiNSsLpfm9gNuBuaa2fvAv4AvgKUEq/K1BwYBBwEHAI/HXhO2fwP/BWqc6SciIuGqdSKKVdm+3Mz+F/gV8DOCCQsbS7GWE8yeGwf8MvZcUaMws3OBi+Oa5rv7sbG4XzKzsxsrFhERqZs6T1Zw94XAjcCNZpYGtAOq3H1ZsoOrQ0yjgdFh9S8iIomrV004d68CliQpFhER2QElugxEFUFx05qUEdSgexq4QctEiIjItiQ6IvoVcBNwPfBhrG1vgkt2jwDTgBsIZuX9oX4h1p+7/y3sGEREpGaJJqKrgPPcfVxc21QzmwPc4+59zWwBQTXuhBKRme0NvOLuRXFtg4BRwEBgFnCuu3+c4DmIiEgTkGj17c4EiaC6ucBOcV/XeZF0M4uY2fnAeOLq1plZFjAWeBYoAG4BxptZq7r2ISIiTUeiieg94A4z25RozKwd8L/A+7GmE4FvEjj2jcBFBM8sxTsYyHT3u9293N2fIXiO6dQE+hARkSYi0UT0S6AHMM/MvjIzJxgBdQYuMLOjCEYsiVyWG+XuewKTqrX3I6jwHe9rYEACfYiISBORaNHTObH7NT8muF9TDkxz9wkAZrYW6OruSxM49tYehM0HSqq1lQC5de1DRESajoRXaI1Ny64iSEJpQJaZZcS2LUkkCW3HOiCnWlsusDbJ/YiISCNK9DmiYuAlgvWIviOoNdcN+NrMDnX3xUmL8AdfAldUa+sLPNEAfYmISCNJdPr2PUAF0MPd5wGYWSfgKWAEcGZywtvMm0DEzK4A7iOYDDEQGNMAfYmISCNJ9NLcT4DhG5MQbLq38xuCFVuTzt3LgGEECWg5wUSI491dJYZERFJYoiOi9dRc4ifKD9W468Xd3yJ4Xii+bRqwfzKOLyIiTUOiI6LxwAgz67CxIfb1XQTr/4iIiNRKoiOi/wEmALPNbHasrRswlWCdIhERkVpJ9DmihWY2kOBeUT+gFPjK3f+TzOBERKT5q3UiMrN+NTTPIq7m3MZ93P3L+ocmIiI7grqMiKYRTEaIxLVVn7AQIYkTFkREpPmrSyLq0WBRiIjIDqvWicjdZ29/LxERkbpJuNaciIhIMigRiYhIqJSIREQkVHV+jsjMCoGjgf5AK2AVMBl41d1XJjc8ERFp7uo0IjKzK4HZBNWvNz7MegQwGphjZsOTHqGIiDRrdXmg9RzgJuAq4G/uXhq3rQVwNnCnmc1z9xeSHaiIiDRPdbk0Nxz4rbs/WH2Du68HRplZPnAZoEQkIiK1UpdLc33YfmXtl4FdEg9HRER2NHVJRDnA6u3sswpom3g4IiKyo6nr9O2aFsMTERFJWF2nb59tZmu3sb1lfYIREZEdT10S0ffARbXcT0REpFbqUvS0ewPGISIiO6hElwpv8sysDfAUwSSLUuAMd18eblQiIlJdnRKRmbUCjgfGuPsaM4sA/0NQZWEJcJe7T0x+mAm5BHjB3R81s/OBi4GbQ45JRESqqfWsOTPrBXxFUN6nfax5BHAbsAhYCbxhZvsmO8gEjQSejH2dAZSHGIuIiGxFXUZENwGfAqe4e6mZtSMYdTzv7qcDmNl04Abg8GQHujVmdi7BaGej+e5+rLuvim3flWCSxcGNFZOIiNReXRLRIcBRcTXmjgDSgSfi9nkduDZJsdWKu48mKLq6BTPbB3gYONndVzRmXCIiUjt1SUStgcVx3/+Y4HLXW3FtawiSU+jMrB/wEHCMljkXEWm66lJZ4TuCZR8ws3TgSOAddy+J2+dHwKykRVc/1wF5wONm9lZsCQsREWli6jIi+hsw0sxuIBgNFRPcIwLAzA4AbgHuTWJ8CXP308KOQUREtq8uiehOgoKm9wBVwO/cfQyAmY0kNl06tl+9mNnewCvuXhTXNggYBQwkGHWd6+4f17cvEREJV10qK1QCV8c+qnsYeMzdJ9cnmNhzSecBf67WngWMBe4GDgROBMabWTd3315FcBERacLqskJrLkEiOAnYAIwBrnH31e7+eZLiuRE4iuDB0z/GtR8MZLr73bHvnzGzXwOnAo8kqW8REQlBXSYr3AgcA9xB8CDrUSQ/CYxy9z2BSdXa+xE8TBvva2BAkvsXEZFGVpd7RCcBP3P3NwHM7G3gHTPLdPekVC1w9/lb2ZQPlFRrKwFyk9GviIiEpy4joi4Eo5CNPo69vkNSI6rZOoLipfFygW2tjSQiIimgLokoHajc+I27RwnuFWUlO6gafAlYtba+sXYREUlhqbIMxJtAxMyuICi6eiLBNO4xoUYlIiL1Vt+lwjOAM81safxO7v5AvSPb/HhlZjaM4DmiPxFUeTje3Zcksx8REWl89V0qfCFwTrW2KFCvROTubwEF1dqmAfvX57giItL0aKlwEREJVV0mK4iIiCSdEpGIiIRKiUhEREKlRCQiIqFSIhIRkVApEYmISKiUiEREJFRKRCIiEiolIhERCZUSkYiIhEqJSEREQqVEJCIioVIiEhGRUCkRiYhIqJSIREQkVEpEIiISKiUiEREJlRKRiIiESolIRERClRF2AA3FzFoBzwItgc+A4e4eDTcqERGprjmPiM4HXnH3/YE8YEjI8YiISA2abSJy9xHAKDPLAIqA1SGHJCIiNUj5S3Nmdi5wcVzTfHc/NvZ1GjANWAHMaezYRERk+1I+Ebn7aGD0VraVA2ZmlwDXAH9ozNhERGT7mu2lOTP7nZkdE/t2HVAZZjwiIlKzlB8RbcMTwONmdiXB/aGzQo5HRERq0GwTkbvPAw4NOw4REdm2JpmIzGxvgqnXRXFtg4BRwEBgFnCuu38cUogiIpIkTeoekZlFzOx8YDyQFdeeBYwleEC1ALgFGB97aFVERFJYk0pEwI3ARcDN1doPBjLd/W53L3f3Z4AvgFMbOT4REUmyppaIRrn7nsCkau39gK+qtX0NDGiUqEREpME0qUTk7vO3sikfKKnWVgLkNmxEIiLS0JpUItqGdUBOtbZcYG0IsYiISBKlSiL6ErBqbX1j7SIiksKa5PTtGrwJRMzsCuA+4ESCadxjQo1KRETqLSVGRO5eBgwjSEDLCWrGHe/uS0INTERE6q1Jjojc/S2C54Xi26YB+4cSkIiINJiUGBGJiEjzpUQkIiKhUiISEZFQKRGJiEiolIhERCRUSkQiIhIqJSIREQmVEpGIiIRKiUhEREKlRCQiIqFSIhIRkVApEYmISKiUiEREJFRKRCIiEqomuQxEyNIByktXhh2HiEhKMbPuwFx3r6jL65SIttQRYO6Ho8KOQ0Qk1XwL9AC+q8uLlIi29DFwALAAqAw5FhGRVDO3ri+IRKPRhghERESkVjRZQUREQqVEJCIioVIiEhGRUCkRiYhIqJSIREQkVEpEIiISKiUiEREJlR5obQbM7FzgIWBDXPMl7v54SCEllZntDbzi7kWx77OA+4CTCB46HuHut4UYYlLUcJ7ZwBqgLG63D9z98DDiqy8zOwz4X2BnYDFwp7s/ZGYFwKPAYcBa4I/u/tfwIk3cNs6xJzADKInb/Rl3Pz+EMOvNzI4GbiWoorAYuCN2ngn9bioRNQ97AHe5+zVhB5JMZhYBzgP+XG3TjYABvYDWwL/MbJ67P9HIISbFNs5zALDc3YsbP6rkMrOuwAvAWcBYYE/g32b2HXA2wR+tjkCfWPssd387lGATtJ1zbAlMdPd9QgswScysI/AP4AR3f83M9gDeN7OPgZNJ4HdTl+aahz2ByWEH0QBuBC4Cbq7WfhZwi7uvcPfvCP6A/6qRY0umrZ1nc/p37Q485e5j3L3K3T8G3gIOIXj3fK27l7j7ZOAR4ILQIk1cd2o+x/1oRv+W7r4AaB9LQmlAO6CCYPSe0O+mRkQpzszSgYHAz81sBMHQ/1HgdndP9fpNo9z9OjM7eGND7DJOR+DLuP2+Jhg9pKotzjNmD6DIzKYCHYB3gMvdfV5jB1hf7v4u8O7G782sLUFNx3eBKDA9bvevgWMbNcAk2MY5/h24EMgzs2+AfOBV4Cp3T8ky/+6+xsxygVUEeeR2YAkJ/m5qRJT62gOTgMcJrteeRPDu+qIwg0oGd59fQ3N+7HP8tfYSILfhI2oYWzlPgHXA+wSjBgNKgTGNFVdDMbPWwMvAf4FPgPXV3jSl9L8nbHGOY4EVwOvAYII3GDsBD4cWYHKsB/IIzulc4LJYe51/NzUiSnHuvhA4KK5pspmNBE4EHggnqga1LvY5J64tl+Amd7Pi7lfGf29mVwJLzKyru88JKax6MbM+BH+YvwTOAHYBWphZJC4ZpfS/Z/VzdPcq4LS4XVaZ2e+B98wso65r9zQVsfMqAyaZ2cPAXrFNdf7d1IgoxZlZfzO7sVpzFsG7lWbH3VcACwlGCBv1ZfPLAc2Cmf3JzHaJa8qKfU7Jf1szO5BghPAScJK7rye4JBchGM1vlLL/njWdo5nlmtkdZtYhbtcsgvsqKbfUjJkdZGafVGvOJhj1JfS7qRFR6lsJ/MbM5gKPAbsDw4FfhxpVw/o7cH3s3kk+cBVwT7ghNYiBwF5m9rPY9/cA49x9SYgxJcTMegGvAH9w95Eb2919rZmNAW4zs/MIZlv9kmAmXUrZxjmWxKZ1tzOzXwMFBFO8/5ai93EnA51jI/R7gCEEsz5PIEhEdf7d1IgoxcVuXB9LMDNlNcH00Zvc/R+hBtawrgOmAV8QLGT4AtAcl9Q9j+Bd5gyCFS/LgJ+HGVA9XEIwhfk2M1sb93E7wf/dKmA2wU38W9z9tRBjTdS2zvEEoAiYD3wOTCX4I51y3H0VcCTwU2A5wb2u82PT7RP63dTCeCIiEiqNiEREJFRKRCIiEiolIhERCZUSkYiIhEqJSEREQqVEJCIiodIDrbLDiZXl77aVzZmpWnIlGWKFV9+MfXs/QfXkb4EB7j6t2r5nA39298LtHPN/gd/Gvj3G3V9JZsyS+jQikh3V7wkqBW/2sSMnoWp6Ab9L0rFuJvj5itRIIyLZUa2JFYyVmi2Old9pV98DuftaYK2ZbXdf2TEpEYlUY2Y3ENTPSgP2AYa7++NmdhVwKcFCYJMJ1pP5KPaaDOA2ghppEeBOgtUq73P3v5nZW8Akd78qrp8ocZeqtnP8vxGU1M8hWOpjGfCou98c255OMMr7JdCWoLzKrwlKsMwBjnD3N+L6nkFQSicpS3LHLtPVdKy33P1HyehDmi9dmhOp2U8IFqLbB3jVzH5FsN7KxQSFZV8FJpjZxqrRNwC/iH0cSlD/b9fadlaL4wOcD8wlKLf/KHCTme0Z23YdQbHby2OvnwOMAxYDE4DT4/raB+gMvFjb+GrhWTa/zHkKQXXpO5LYhzRTGhHJjuqu2E30eEe7+1uxr0uB22JrrhBbP+Yadx8X235r7Mb+JWb2PwRLW9+0sVinmZ1BUKy0trZ6fH4ojjnT3a+NfX2zmV0B7GlmnxJbatzdX4z1fwlBcmwDPAncbWYXuXs58DPglVjxytqaaGZV1doyiK014+6lBD8zzKwrcB9wY4oWL5VGpkQkO6rbCP5Ax4tfgvvbuCSUT7Ci5iNm9lDcPtnABoJVctsTrDYKgLt/Z2a1WryuFsffaDqbWwNkAoWx/j+O638N8JvY8V8EHgSOMLPXCEYrF9Ymtjgn1tD/T4Grq51LC4KR1ofALXXsQ3ZQSkSyo1rq7tsasZTGfZ0e+3wW8FkN+5VQs/gkslmZ+9g9pdoef6OyGvqIxLXXWEo/NungJeDUWEzZBJf+6mJO9Z+XmS2uYb+HCZZC+EWKrrUjIdA9IpHtiF3CWgh0dvcZGz8IJgMcEZsVNhsYuvE1sdlm3eMOUwa0jvu+Z22PX8v4FgN7xPWfY2aLzGxIrOlJgjVkjgeed/eaklq9xC4VHg+c4O6rk318ab40IhKpnTuA68xsAcElsJ8RJIqDYttvI1gQbRbgwO0EI4+NPgYuM7MngFXACDYfMW3v+NvzF+Da2MO63wB/iPWzcYQ1HigHziWYiJFUZvZjgnM+B1hmZsUbt2mavGyPEpFI7dxDMHX6DqADwR/7k9z9fQB3fyg2CnoQaEEwfXto3OvvAnYB/g0sJZjl1r22x6+FOwkuiT0a+/w+cNTGkY+7V5rZcwQrhb5TlxOvpV8Q3K+qft8NgsuHIlulFVpFGoiZLSV4FuhvYccCYGbPAzPcfasVE+JK/LSMXXJMZv+bPTclspFGRCLNnJkdRPBs0VHU/tmmIjOLxGbf1bf/fCC/vseR5kuTFUSav9OAPwFXu/usWr5mJsF9r2T4I7AgSceSZkiX5kREJFQaEYmISKiUiEREJFRKRCIiEiolIhERCZUSkYiIhEqJSEREQvX/VPg+sJqH2MEAAAAASUVORK5CYII=\n",
+ "image/png": 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\n",
"text/plain": [
""
]
@@ -127,15 +127,16 @@
"cell_type": "markdown",
"metadata": {},
"source": [
+ "As can be seen on the plot above, there is a strong alpha oscillatory peak around 10-11 Hz.\n",
+ "\n",
"## Extract the aperiodic and periodic component of the spectrum\n",
"\n",
- "The Irregular-Resampling Auto-Spectral Analysis (IRASA) method is\n",
- "described in [Wen & Liu (2016)](https://doi.org/10.1007/s10548-015-0448-0). In a nutshell, the goal is to separate the\n",
+ "The Irregular-Resampling Auto-Spectral Analysis (IRASA) method ([Wen & Liu (2016)](https://doi.org/10.1007/s10548-015-0448-0)) allows to separate the\n",
"fractal and oscillatory components in the power spectrum of EEG signals.\n",
"\n",
"The steps are:\n",
"\n",
- "1. Compute the original power spectral density (PSD) using Welch's method.\n",
+ "1. Compute the original power spectral density (PSD).\n",
"2. Resample the EEG data by multiple non-integer factors and their\n",
"reciprocals ($h$ and $1/h$).\n",
"3. For every pair of resampled signals, calculate the PSD and take the\n",
@@ -178,7 +179,7 @@
"outputs": [
{
"data": {
- "image/png": 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\n",
+ "image/png": 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\n",
"text/plain": [
""
]
@@ -205,7 +206,7 @@
"outputs": [
{
"data": {
- "image/png": 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\n",
+ "image/png": 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xc+dOXL9+XaaL4ury/PlzfPnll0hNTUVYWBiOHj3KfaOdOXMm/vrrL+zcuRPp6en4/fffsWfPHkydOlWmD/2AgABcvXoVu3btwqNHjxAeHo6vv/661m/stWnRogUAIC4uDqWlpRCJRMjNza3zDKX3338fly5dwqFDh/D48WMcOHAAkZGRGDhw4Gv3ZWpqitTUVERFRSEjIwP79+/HsWPHpEK3sU2aNAm2traYPHkyLl68iIyMDERERCAgIAC6urqYPXs2BAIBVqxYgQEDBsDHxwe5ublSr/+GksTFixdRVlaGDz74AHZ2dlKvyZMn4/79+0hMTMTPP/+MO3fuYO3atWjVqhW3Xck1NG8i6gpTE9ra2vjxxx+xf/9+fPfdd8jMzISRkRE8PDxw4sQJrh9bV1cXu3fvxvr16zFmzBhoaWnB29sbK1euBPDi22hpaSk39uLq6ordu3dzXUqvY25ujjVr1mDnzp3YuXMnrK2tMWnSJBw7dgxxcXEYNGgQxo4di0uXLmHEiBG4dOkSFi9eDB6PhxUrVqC0tBROTk44cOCAVN97bUaMGIF169bBz8/vlcstX74c69evx8cffwyRSAQPDw+sX78eADBlyhSUlZVh06ZNyMvLg52dHXbt2gU3NzeZjrc2Xbt2hba2NsaNG4fWrVvjiy++wPDhwwG8GH/Ztm0btm7dip07d8LCwgJz587F9OnTZdp29+7dERwcjODgYGzfvh1mZmb46KOP8OGHH8q0vp2dHTw9PREQEIAlS5Zg6NCh8Pb2RlBQUK2nkru4uGDDhg3YsWMHNmzYgI4dO2LHjh3o1KkTnj9//sp9TZ06FQkJCZg9ezZ4PB66deuG//3vfwgMDMSzZ89kqrehtLS0EBISgj179uCbb77Bs2fPYGpqioEDB2L+/PkwNTXF7du3kZeXh+vXr2PAgAE1tmFtbY0//vijxvTffvsN7u7utbZu33nnHQQHB+PEiROIiYkBYwzz5s2TWsbExAS3b99W3MGqER6Tt91KSCNLSkrCO++8g+vXr8PIyEjZ5QB4cR3LlStXZL5GRBX88MMPsLKywogRI5RdCnlDUIuFqJy8vDxERkbi0KFD8PX1VZlQUUclJSX4/fffFXKrHkJkRWMsROWUlZVh5cqVKC8vx+LFi5VdjlozMDDAkSNHFHKrHkJkRV1hhBBCFIpaLIQQQhSq2QdLdXU1MjMz35jbiBNCiLI1+2B59uwZvL29m+z0R0IIedM1+2AhhBDStChYCCGEKBQFCyGEEIWiYCGEEKJQFCyEEEIUioKFEEKIQlGwEEIIUSgKFqKS0tLS6nyGCCFEtVGwEJXz8OFDDBgwgHuGDCFEvVCwEJWTlJQEAEhJSVFyJYQQeVCwEJVTUFAA4MVzywkh6oeChagcChZC1BsFC1E5kmApLi5WciWEEHlQsBCVIwmW0tJSetwBIWqIgoWoHEmwANRqIUQdUbAQlUPBQoh6o2AhKuflYKEBfELUDwULUTkULISoNwoWonKoK4wQ9UbBQlSKUCiUukcYtVgIUT8ULESlvNxaAShYCFFHFCxEpRQWFkq9p2AhRP1QsBCV8t8WC42xEKJ+KFiISqFgIUT9qUywREREYNy4cXB1dcXQoUNx5MgRAEBGRgbs7e3h4uLCvVatWqXkakljkQSLrq4ugJpdY4QQ1aep7AIAICsrC/Pnz8eGDRvg7e2N2NhYzJw5E9bW1igtLYWzszOOHj2q7DJJE5AES7t27ZCYmEgtFkLUkEoEy5MnT+Dr64uhQ4cCAJydneHu7o579+6huroa9vb2Sq6QNJX8/HwAgI2NDQULIWpKJYLFzc0Nbm5u3PuCggJERUVh9OjROHLkCMrKyjB8+HCUlpZi8ODB+Oyzz2BkZKTEikljkbRY2rdvD4C6wghRRyozxiJRXFyMOXPmoEePHvD29oaRkRE8PDxw/PhxhIWFISsrC4GBgcoukzQSSbDY2NgAoMF7QtSRSrRYJNLS0jB37lx07twZ33zzDTQ0NPDtt99y8w0NDbFo0SJMmjQJ1dXV0NRUqfKJArw8xgJQsBCijlSmxRIZGQl/f3/4+PggODgYOjo6EAqF2LhxI54/f84tV1VVBU1NTfD5fCVWSxqLJFgsLCygpaWF8vJyVFRUKLkqQkh9qESwPH78GLNmzcKCBQuwZMkS8Hg8AICenh5u3LiBLVu2oLy8HDk5Odi8eTPGjh3LLUOaF0mwmJiYwNDQEAC1WghRNyoRLD///DNKS0uxZcsWqetVNm3ahO3bt0MgEGDgwIEYNWoUunbtis8++0zZJZNG8nKwSE7QoNu6EKJeVGKQYsWKFVixYkWd83ft2tWE1RBlqaqqQklJCXg8HoyMjKjFQoiaUokWCyHAvy0TY2NjaGhocC0WOuWYEPVCwUJUhuTiSBMTEwDggoVaLISoFwoWojIk4yumpqYAQF1hhKgpChaiMl4euAf+DRYavCdEvVCwEJXx32AxNjYGQMFCiLqhYCEqg1oshDQPFCxEZfw3WGjwnhD1RMFCVEZdwUItFkLUCwULURnUFUZI80DBQlSGJFgkg/bUFUaIeqJgISqjrhYLBQsh6oWChagMyZX3kgskJS0XuqULIeqFgoWoDEmA1NZiYYwprS5CSP1QsBCVIBaLuWCRtFS0tbWhq6uL6upqlJeXK7M8Qkg9ULAQlVBcXAyxWAwDAwNoaWlx0yWtFuoOI0R9ULAQlfDfgXsJOjOMEPVDwUJUgiQ4JC0UCbpIkhD1Q8FCVEJpaSkAQF9fX2o6nXJMiPqhYCEqQRIsBgYGUtPpKZKEqB8KFqISJMHSokULqek0xkKI+tGUd0WxWIzU1FTk5eWBz+ejdevWaN++PXg8niLrI28I6gojpPmod7BERkbiwIEDuHHjBvdhAAA8Hg9GRkYYOHAgJk2aBFdXV4UWSpq31wULdYURoj5kDpb09HR8/vnnyMrKgo+PD7Zv345OnTrBxMQEjDEIBAI8fPgQkZGRWLx4MWxsbLBmzRrY2to2Zv2kmagrWCQXS1KLhRD1IXOwfPrpp5g3bx6GDBlS63xLS0tYWlrC09MTn376KS5duoRPP/0Ux48fl2n7ERER2Lx5M9LT09GqVSvMmDEDEyZMQFFREVavXo2IiAi0aNECn3zyCd555x1ZyyZqoq5gMTMzAwA8ffq0yWsihMhH5mA5evSozOMnPB4PQ4cOhY+Pj0zLZ2VlYf78+diwYQO8vb0RGxuLmTNnwtraGmFhYdDQ0MD169eRnp6OGTNmwMbGBu7u7rKWTtRAWVkZgJrB0rlzZwBAUlJSk9dECJGPzGeFvRwqK1euREJCQo1lBAIBvL29a13nVZ48eQJfX18MHToUGhoacHZ2hru7O27evInw8HAsXLgQenp6cHBwwLvvvotff/1V1rKJmqirxdKxY0doaGjg0aNHqKioUEZphJB6kut049DQUEyYMAFnzpyRmi4Wi+XqsnBzc8OaNWu49wUFBYiKikKbNm3A4/HQoUMHbl7Hjh2RmJgoT9lEhZWUlACoebqxjo4O2rVrB7FYjLS0NGWURgipJ7mvY/nkk08QGBiIoKAgiMVihRVUXFyMOXPmoEePHnB0dIS2trZUy0dPT4/udNsM1dUVBgBdunQBACQnJzdpTYQQ+cgdLL6+vjh8+DAuXryI6dOnQyAQNPgalrS0NPj7+6N169YIDg6Gvr4+KisrpZ7FIRQKa3yrJeqvrq4wgMZZCFE3cgWLJEAcHBy4s77GjRvXoC6qyMhI+Pv7w8fHB8HBwdDR0UH79u3BGENmZia3XGpqKvdBQ5qPum7pAlCLhRB1I1ewvNyCaNmyJfbt2wcfHx/MmjVLriIeP36MWbNmYcGCBViyZAkXXPr6+vDx8cHmzZtRWlqKhw8f4tixY/Dz85NrP0R11XVLF4BaLISoG7lu6fLxxx9LfQDw+XysXr0ajo6OCA0Nrff2fv75Z5SWlmLLli3YsmULN33SpElYs2YNvvzyS3h5eUFbWxuzZ8/G4MGD5SmbqLBXdYVJWiwpKSkQi8XQ0KBb3BGiynhMxoeJ16cbQpW6qjIzM+Ht7Y3Lly+jbdu2yi6H1KFLly4oKyvDw4cPazyTBQBcXV2RnZ2Nmzdvol27dkqokBAiK5lbLL6+vuDxeGCMSf0XkO4a4/F4ePDggeIrJc2WWCzmzgqr68SMTp06ITs7G8nJyRQshKg4mYPl8uXLUu8ZYxg1ahT27NkDKysrhRdG3hxCoRDAi1PJ+Xx+rct06dIFN27cQFJSEry8vJqyPEJIPckcLNbW1rVOt7CwqHMeIbJ41fiKBJ0ZRoj6oFFQonSyBAudGUaI+qBgIUr3qlONJV4OFhnPNyGEKAkFC1E6WVosFhYWMDAwQEFBAQQCQVOVRgiRg8xjLD///HONaSKRCKdOnYKpqanU9MmTJze8MvLGeNVV9xI8Hg9dunTB33//jaSkJLRq1aqpyiOE1JPMwRISElJjWuvWrWtcEMnj8ShYSL3I0hUGvOgOkwRL3759m6I0QogcZA6WP/74ozHrIG+wV93Z+GWS61eysrIavSZCiPxkDpZhw4bBw8MDHh4e6Nu37yu7LQipD8mzWF4XLJIWjSSICCGqSebB+927d6Nz5844ceIEvLy8MGHCBGzfvh337t1T6PNYyJtHlsF7gIKFEHUhc4vF1tYWtra2mDx5MkQiEf7++2/cuHEDGzZsQHp6Otzc3LgWTfv27RuzZtLMULAQ0rzIdXdjPp8PNzc3uLm5YcGCBSguLsbNmzcRERGB/fv348KFC4qukzRjso6xSOZTsBCi2uQKlv8yNDTEsGHDMGzYMEVsjrxhqMVCSPMi0xhLamoqbt68yQ2ySly5cqVRiiJvFllPN5bMlyxPCFFNrw2Wn3/+GXPnzsWBAwfg6+uLixcvcvOCg4MbtTjyZpC1xaKnpwfg37shE0JU02u7wo4cOYLQ0FC0aNECGRkZWLhwITIzM/HBBx/QPZuIQshy5T1AYyyEqIvXBotIJOK6IGxsbHDgwAEsXLgQz549o2AhCkFjLIQ0L6/tCmvdurXUEyENDAywe/du5OfnIzExsVGLI2+G+o6xULAQotpe22LZuHFjjaf6aWpqYuPGjXjvvfcarTDy5pD1dOOXg+XlR2MTQlTLa1ssFhYWMDMzAwCEhYVJzevVq1fjVEXeKLLe0oXP50NXVxeMMZSXlzdFaYQQOdTreSyBgYGYPHkydYERhRGLxVyL5XVdYcC/Z4ZRdxghqqtewRIaGgoNDQ2MGzcO69evp+sJSINJTh3W09Or0eVaGxpnIUT11StY7OzscPDgQWzYsAHnz5/H22+/jd9//12hBcXExKBfv37c+8rKSnTv3h0uLi7cKyAgQKH7JMoj6xlhEnSRJCGqT65buowcORJeXl7YuXMnPvvsMxw7dgyff/45bG1t5S6EMYbjx49jw4YNUtMTEhJgbGyMiIgIubdNVFd9g4WuZSFE9cn9zHs9PT0sWbIEv/32GzQ1NeHn54dvv/1W7kHV4OBg/PLLL5gzZ47U9Li4ONjb28tbJlFxsp5qLEFjLISoPrmDRaJDhw7Yu3cvtm7dijNnzmDEiBFybWfChAkIDQ1F9+7dpabHx8dDIBBg1KhR6N+/PxYsWIDs7OyGlk1UhLxdYRQshKguue9unJGRgYSEBCQmJnL/zcrKkvtqfHNz81qn6+npwdXVFfPmzYOmpibWrl2LefPm4fjx4/KWTlSIrLdzkaBgIUT11StYPv/8cyQmJiIxMZE7m6dt27ZwcHCAr68v7O3tFd5ttWLFCqn3y5cvR79+/ZCVlQVLS0uF7os0vfp2hdEYCyGqr17B8vDhQ9jb28PPzw/29vbo2rWrzF0Y8tq6dSt8fX3RqVMnAEBVVRUAQEdHp1H3S5qGrFfdS1CLhRDVV69gOXr0aGPVUaeEhATExsZi8+bNAIB169ZhyJAhaNmyZZPXQhSPxlgIaX7kGrw/efIkkpKSIBKJFF1PDevWrYORkRGGDh0KLy8vaGlpYePGjY2+X9I0ZL2di4TkrDC6joUQ1SXX4P2mTZsgEAigpaWFLl26wMHBgXvZ29vL3F9emz59+iAqKop7b2pqyrVWSCaabLAAACAASURBVPMj73Us9LAvQlSXXMESERGB7OxsxMXFIT4+HtHR0Th16hSqq6vB4/EQHx+v6DpJM0VjLIQ0P3Kfbmxubg5zc3N4eXkBALKzs7F48WL4+fkprDjS/NEYCyHNT4MvkJQwNzfHunXrcPXqVUVtkrwB6nu6Md0rjBDVJ1ewCASCWqd36NCBusFIvVCLhZDmR66usP79+8Pc3BwODg7o1q0bunXrho4dOyImJoa7zoQQWch75T0N3hOiuuQKlqNHjyI+Ph7x8fG4du0afvjhB1RWVoLP5+Ozzz5TdI2kGaMWCyHNj1zB4uzsDGdnZ+69SCTCkydPYGxsDGNjY4UVR5o/ecdYKFgIUV0yj7EUFRXVOY/P56Ndu3Y1QqWwsFD+ysgbob6nG0uWo8F7QlSXzMEyZcoU7NmzB8XFxa9dViAQYOfOnZgyZUqDiiPNH3WFEdL8yNwV9ssvv+C7777DoEGD4OrqioEDB6JLly4wNTUFYwwCgQAPHz5EZGQkoqKiMHbsWPzyyy+NWTtRc2KxuN5dYbq6ugCA8vJyiMViaGgo7Ix5QoiCyBws+vr6WLVqFT766CP8+uuvOHPmDB48eMDdL0xTUxPdunXD4MGD8dVXX9X5fBVCJCTdqy1atACfz5dpHQ0NDejp6UEoFEIoFDb63bUJIfVX78F7MzMzfPzxx/j4448hFotRUFAAHo8HU1PTxqiPNGOJiYkAgI4dO9ZrPX19fQiFQpSWllKwEKKC5L6lC/Di2yPdvp7IS3Ixbbdu3eq1Ho2zEKLa5AoWe3t78Hi8WudpaWnB3NwcI0eOxPz582Xu4iBvHgoWQponuYJlzZo12Lp1K+bPn4+ePXsCAO7fv4/g4GD4+/ujS5cu2L59OxhjWLRokUILJs2HvMEieSYLBQshqkmuYAkJCeGe5Chhb28PCwsLrFu3DufPn4eZmRkWL15MwUJqJRKJ8ODBAwD1DxZ67j0hqk2uczVzcnJgY2NTY7qFhQWysrK4/6cLJEld0tLSUF5eDktLy3qf+EFdYYSoNrmCxdXVFZs2bUJBQQE3LT8/H5s3b4arqysA4MKFC+jQoYNCiiTNj7zdYAAFCyGqTq6usLVr1+LDDz/EoEGDYG1tDbFYjKysLHTq1AnBwcG4evUqvv32W2zbtk3R9ZJmgoKFkOZLrmCxtLTEqVOncOvWLSQkJEBTUxNdunRBv379ALzoA7969SqdikzqpIhgofuFEaKa5L6Ohc/nQ0NDA5qamhCLxaiqqkJ1dTU0NTUpUMhrUYuFkOZLrmDJzc3FvHnzEB8fD2trazDG8PTpU9ja2mL//v1o1aqVouskzUh+fj6ysrKgq6sLW1vbeq9PD/siRLXJNXi/bt068Pl8XL58GeHh4bhw4QIuX74MExMTBAUFKbpG0sxIWisODg5yXUBLLRZCVJtcwfLXX39h9erVUjeaNDc3x2effYY///yzQQXFxMRwYzUAUFlZicDAQLi7u6Nv377YvXt3g7ZPlK8h3WAAPZOFEFUnV1eYjo5Orbd04fF43N2O64sxhuPHj2PDhg1S07dt24a0tDRcvHgRxcXFmDlzJszNzTFmzBi59kOUr6HBQlfeE6La5GqxeHh4ICgoCM+fP+emPX/+HOvXr8eAAQPkKiQ4OBi//PIL5syZIzU9LCwMs2fPhrGxMdq2bYsZM2bgyJEjcu2DqAZJsDg6Osq1PnWFEaLa5GqxLFu2DO+//z48PT1hZWUFAHj69Cm6du2KVatWyVXIhAkTsHDhQty+fZubVlRUhNzcXHTu3JmbZmtry91unagfgUCABw8egM/nw8HBQa5t0OA9IapNrmAxMzPD6dOn8ddffyE5ORm6urro1KkT+vfvL3chtT0YTPKNVPLUQOBFN0h5ebnc+yHKde7cOYhEIgwZMgQGBgZybYNaLISoNpmDJTk5ucY0GxsbqXuGSZZ5uYXREJK+9IqKCm6aUCiU+TG2RPWcPn0aAODn5yf3NmjwnhDVJnOw+Pr6gsfjgTHGTfvvAD5jDDwej7trbUMZGxvDzMwMqampXIsmLS1NYcFFmlZubi5u3LgBLS0tDB8+XO7tUIuFENUmc7Bcvny5Meuok5+fH3bs2IGuXbuirKwMISEhmDZtmlJqIQ1z9uxZiMVieHp6wsTERO7tULAQotpkDhZra+vGrKNOCxcuxPr16+Hr6wuxWIz33nsPEydOVEotpGF+++03AA3rBgP+7SKlwXtCVBOPvdy31QxlZmbC29sbly9fRtu2bZVdzhvr2bNncHNzg7a2NqKjo2FoaCj3thhjaNeuHcRiMR49egRNTblveUcIaQRyXcdCSH2dPXsWjDF4eno2KFSAF2N71B1GiOqiYCFN4ty5cwAa3g0mQcFCiOqqdx+CQCDA1atXkZSUhNLSUhgYGMDBwQGDBw+GkZFRY9RImoG0tDQAQK9evRSyPQoWQlRXvYJl37592Lp1K3g8Htq2bQtDQ0OUlJTg4MGD0NTUxKJFi+iMLVKDWCzmbv9jZmamkG1SsBCiumQOlhMnTmDr1q1YtmwZxo0bJ3U1fEVFBUJDQ7Fx40aYm5s36BoF0vzk5+ejuroaJiYm0NHRUcg2KVgIUV0yB8vBgwexdOlSTJo0qcY8HR0dTJw4EWVlZThw4AAFC5GSk5MDQHGtFYCChRBVJvPgfXp6+mvvXOzl5YWUlJQGF0Wal9zcXAAULIS8KWQOlvLy8tfeNNDQ0BCFhYUNLoo0L5IWS203GpWXJFhKSkoUtk1CiGLU63Tj2h7uRcjrNEaLpV27dgCgsPvSEUIUp15nhYWGhr7yzsJ0t1lSG0mLpU2bNgrbZp8+fQAAt27dUtg2CSGKIXOwWFlZ4ZdffnntcpaWlg0qiDQ/jdFicXNzg6amJmJjY1FUVETXUBGiQmQOlj/++KMx6yDNWHZ2NgDFtlhatGiBHj164O7du4iMjIS3t7fCtk0IaRi6pQtpdJIWiyKDBQD69esHgLrDCFE19QqWkpISnDx5kjsThzGGvXv3Ytq0afjkk08QExPTKEUS9dZYwSIZZ7l586ZCt0sIaRiZg+Xx48d4++23sWbNGuTn5wMAgoKCsGXLFrRu3RpGRkZ4//33ce/evUYrlqifiooKFBQUQFNTs0EP96pN7969oaGhgfv379OJI4SoEJmDZevWrXB0dMSNGzdgY2OD/Px8HD58GG+99Ra2bNmCNWvW4OOPP8b27dsbs16iZiT3CGvdujU0NBTb82poaAgnJydUV1fj7t27Ct02IUR+Mv9Lv3nzJubNm8fdI+z69esQiUQYM2YMt4yHhweio6MVXyVRW41xqvHL+vbtC4C6wwhRJTIHS3FxMVq1asW9v3XrFjQ1NeHu7s5N09fXh1gsVmyFRK01xn3CXiYJFhrAJ0R1yBws1tbWSE5OBgCIRCJcu3YNvXv35p4/Drz4x02P/yUva4zbubzM3d0dPB4P//zzD4RCYaPsgxBSPzIHy7hx47B27VqcPn0agYGBeP78OSZOnMjNj4qKwnfffYeRI0c2SqFEPTXGxZEvMzExgYODAyorK/HPP/80yj4IIfUjc7DMmDEDPj4+WLduHa5cuYLFixdj6NChAICvvvoKU6ZMQa9evTBjxoxGK5aon8YeYwEAFxcXAMD9+/cbbR+EENnJfOU9n8/HsmXLsGzZshrz/P39MX78eDg4OCi0OKL+GrvFAgCOjo4AgLi4uEbbByFEdjIHi1AoxNdff43w8HBoa2vDx8cHS5cuhYGBAbp27dqYNRI11hQtlu7duwOgYCFEVcjcFRYcHIwrV65g5syZmD59Oq5du4bVq1c3Zm1Sjh8/DkdHR7i4uHCvsLCwJts/kU9jnxUGAA4ODuDxeEhKSkJ5eXmj7YcQIhuZWyzh4eH45ptvuNM73d3dMXnyZFRVVUFLS6vRCpSIj4/HBx98gKVLlzb6vohiMMYa7XYuL2vRogU6deqE5ORkJCYmwtnZudH2RQh5PZlbLNnZ2ejYsSP33snJCYwx5OXlNUph/xUXF0djOGqmqKgIFRUVMDAweOVzfBSBusMIUR0yB4tIJAKfz+fe83g8aGlpoaqqqlEK++++ExIScOrUKQwYMABDhw7Fnj17wBhr9H0T+TXFwL2EZAA/Nja20fdFCHm1ej1BUlkEAgG6d++OMWPGYPv27UhJScHcuXOhr6+PyZMnK7s8UoemGLiXoBYLIaqjQY8mFolEOHXqFExNTaWWU/SHvZmZGQ4dOsS9d3BwwJQpU3DhwgUKFhWmjBZLfHw8xGKxwm94SQiRXYMeTdy6dWuEhoZKTePxeAr/sE9KSsK5c+ewYMECblpVVRV0dHQUuh+iWI19O5eXtWrVChYWFnj27BnS09OlxgMJIU1LLR5NbGRkhH379sHCwgLjx49HfHw8Dh48iMDAQKXVRF6vKU41fpmjoyOePXuG2NhYChZClEgt+gvMzc2xc+dOHDlyBL169cKCBQswd+5cvPXWW8oujbxCU46xADTOQoiqUIvBe+DF883/2+1GVFdeXh6uXLkCALCxsWmSfdKtXQhRDWrRYiHqZ+XKlcjLy0P//v25i2obG7VYCFENFCxE4U6fPo0zZ85AX18fW7ZsabIztGxsbGBoaIicnBw8efKkSfZJCKmJgoUoVG5uLlauXAkAWL16dZN1gwGAhoYGBg4cCABSp6cTQpoWBQtRqG3btiE/Px8DBw7E1KlTm3z/H330EQDgwIEDKC0tbfL9E0IoWIiCSU5LX7JkCXg8XpPvv3fv3ujVqxcKCgpw5MiRJt8/IYSChShQRkYG0tLSYGRkxD3VURnmzJkDANi7dy+qq6uVVgchbyoKFqIwf/75JwDAw8MDmprKO5N92LBhsLW1RUZGBs6ePau0Ogh5U1GwEIW5du0aAGDQoEFKrYPP53NjLd9//z3dBZuQJkbBQhRCJBIhIiICgPKDBQDeffddmJqa4v79+3RdCyFNjIKFKERMTAwKCgrQvn17dOjQQdnlQE9PD35+fgBAj7AmpIlRsBCFUJVusJeNHTsWAHDy5EmIxWIlV0PIm4OChciMMYZjx47hzp07Neb99ddfAFQrWHr16oW2bdvi2bNnuH37trLLIeSNQcFCZBYeHo5PPvkEY8eOxQcffIDk5GQAQElJCaKioqChoQEPDw8lV/kvDQ0NjBkzBgB1hxHSlChYiMxOnDjB/f+FCxfg5eUFDw8PjBo1CtXV1ejZsyeMjY2VWGFNkmA5e/YsKisrlVwNIW8GChYik8LCQly+fBk8Hg/nz5/HlClTAADp6elITEwEAJV8Po6DgwPs7e1RUFCAq1evKrscQt4IFCxEJufOnUNFRQX69+8PJycnbNiwAXFxcfjzzz9x6tQpHD9+nLt2RNVIWi3Hjx9XciWEvBkoWIhMJA9ZGzduHDfN0NAQnTp1gpubG/r16wctLS1llfdKY8aMgYaGBs6ePYslS5ZAKBQquyRCmjUKFvJaWVlZuHHjBrS1tfH2228ru5x6s7GxwebNm6Grq4sjR47A19cXf/zxB3JycuiqfEIaAQULea3Tp0+DMQYfHx+VG5yXlb+/P3777Td07NgRDx8+xNSpU+Hi4oKePXtKnZRACGk4ChYAVVVV9M31FSSn6krGKtRVt27dcP78eXz88cdwd3eHkZERnj9/jmXLliEzM1PZ5RHSbLwxwSIUCjF69Gh4enoiKCgIUVFROHbsGCZNmoSOHTviiy++UHaJKik5ORn379+HoaEhvL29lV1Og+nr62PFihUICwtDfHw8Ro8ejfLycvzvf/9TdmmENBs81sy/qmdmZsLb2xvDhg3jBqBro6GhgStXrqBz585NWJ3q27x5M7Zs2YL33nsPW7ZsUXY5CpeVlYXBgwejtLQUhw4dgqenp7JLIkTtvTEtlrCwMGhpaeG7775DQEAAbG1t0adPHwQFBeGdd96BWCzG5s2ba12XMYbCwsImrlj5GGM4efIkAGD06NFKrqZxWFpaYtGiRQCA1atXo6KiQskVEdIMMDXx4MED5u/vz3r06MF8fX1ZdHS0TOtlZGQwOzs7Zm1tzbZu3VrrMpmZmaxDhw7MysqKxcXF1Zj/9ddfMysrKxYQEMCSkpIadBzqJCYmhllZWTFnZ2dWVVWl7HIaTUVFBRs8eDCzsrJib731FgsJCWG5ubk1lsvPz2dpaWlNXyAhakYtWiyVlZWYO3cu3n77bURGRmL27NmYMWMGSkpKZN6Go6Mj5s6dW+s8a2trTJ06FQCwadMmqXnZ2dnYu3cvAOD8+fPw9PTEihUr3ohvtqdOnQIA+Pr6KvWJkI1NW1sbmzZtgpGREWJiYhAYGAhXV1eMHz8eu3fvxsWLFzFv3jy4urpiwIABNZ5KKRAIkJubW+f2c3NzsWLFCly/fr2xD4UQlaAWYyzXr1/HihUruDvoAsDEiRMxduxY+Pv7v3JdyRhLSEgIBgwYUOdyubm56NevH4RCIX777Te4uroCAL788kvs2bMHXl5esLa2xuHDhyESibBo0SIsXbpUMQeogsRiMfr06YOnT5/i5MmT6N27t7JLanRCoRAXLlxAaGgorl69iurq6lqX09fXx5kzZ2BnZ4fIyEhMnz4dRUVFGDJkCCZNmgQfHx/uYlGhUIh33nkH0dHR0NXVRVhYGJydnZvysJSCMYYHDx7g9u3buHXrFp49e4aWLVuidevWaN26NSwtLWFhYYGOHTvC1tYWfD6/UeqorKzEP//8g+LiYhgZGcHIyAiGhoYwNDSEvr4+NDTq/m4tFotRVlaG4uJiFBcXo6CgANnZ2cjNzcXz589RUFCAgoIC8Pl8WFlZwcrKCjY2NmjXrh1sbGzA5/NRUlKC0tJSmJiYQF9fv9615+bm4unTp3j69CmAF123lpaWEIlEyM3NRU5ODgQCAVdLcXExSktLIRQKwefzoaWlBV1dXZibm8PS0hJt2rSBnp4edHV1UVFRgdTUVKSmpiIzMxO5ubnIzc0Fj8dDy5Yt0apVKxw4cECun7taBMv+/ftx9epV7N+/n5u2atUq6OnpYfXq1a9cVxIsly9fRtu2bV+5bFBQELZv344OHTrg9OnTAIA+ffpAKBQiPDwc3bt3R0REBPz9/aGlpYXw8HB07dq1xnYyMjKQkJCA4uJilJWVYdCgQbCxsan/gSvRnTt3MHbsWFhZWeH27duv/AfYHBUVFeHKlSu4ePEiUlNT4ePjA39/f3z99dc4deoUbG1tsXjxYnz66acoLy+XWrd9+/b48ssv4eXlhVmzZuHcuXPQ0tJCVVUVLCwscPbsWVhYWCjpyBpXbm4ujh49isOHDyM9PV2mdfT09ODo6Ag3NzcMHjwY7u7u0NXVBfAioNLS0nDt2jVER0fDzMwM7dq1Q7t27WBhYQFzc3Noa2sjJSUFSUlJyMnJQXl5OSoqKvDgwQPcuHEDpaWlde5bW1ube0n+xiWB8t/fa0MZGBigTZs20NbWBo/Hg4aGBnR1ddGiRQtoaWlBKBRCKBSiuLgYeXl5KCgoUOj+5fHkyRO51lOL/o2ysjLuD01CT09P4bfmWLBgAa5du4b79+/j/fffh6urK4RCIXx8fNC9e3cAgIeHByZPnoyff/4Zy5YtQ1hYmNQf5M6dO7Fp0yapb7tGRkY4dOgQevXqpdB6FW3z5s24d+8e+vbti/v37wN4MWj/poUK8OJ3Nnr06BonLXzzzTdITEzEgwcPMH/+fADA5MmTsXTpUoSFheHgwYNIS0vD9OnT0alTJ6SkpMDY2BjHjh1DYGAgbt++jYCAAKxZswZ6enpgjCEhIQFxcXEQCATw8fGBj49Pjb/3piQUCnH37l3cuXMHUVFRqKys5L7tm5iYcN++k5OTERsbi6SkJIhEIvB4PFRUVHAPVTM3N4eHhwf69u2Ljh07Ij8/H8+fP0dubi6ysrKQlZWFxMREPH36FFFRUYiKisKuXbugq6sLU1NTaGpqorKyEtnZ2Q06Hjs7O1hZWaGoqAhFRUUoKSnhXpWVla+867Wuri6MjY1haGgIY2NjtGnTBm3atEHr1q1hamoKY2NjVFVVca2KjIwMPH78GJmZmWCMwdDQEHp6eigoKOD2KSsNDQ2YmZnBysoKlpaWAMD93LS0tGBmZgYzMzO0atWK+70YGBjAwMAALVq0gFgsRlVVFUpLS5GdnY2srCzk5uaivLwc5eXl0NTUhK2tLTp27AgbGxvuuHg8HvLy8pCfny/3z1xtWizXrl3Dvn37uGmrVq1CixYtsGrVqleuW58WC/BiTMXPz0/qgrmXu8aAF3f69fT0RHZ2Nr744guMHDkSBQUF+PLLL7nnvnt4eKBVq1bIzs7G7du3oa+vj4MHD6JPnz71Pfwm8eeff2LixIk1pktaauRf6enpGDFiBAoLC/HJJ59g6dKl4PF4AF5cbLtv3z5s3rwZJSUl0NTUxOHDh+Hh4YG8vDyMHDkSGRkZr9y+kZERxowZg08//RQtW7ZslGMoLCxEdHQ0CgsL4erqCmtrawgEAvz444/48ccf5T4Lks/nw8fHB5MmTYKnp6dMXVwCgQAxMTGIiIjA1atXER8fLzXfxMQEgwYNQp8+fVBYWIhHjx4hIyMD2dnZyM7ORnl5OWxtbdGlSxe0bdsWurq60NbWhpWVFQYOHAgrK6ta9ysWi7lgqays5C6S5vF40NPTg56entxfqkQiETQ0NLi/C8YYCgoKkJubi+rqajDGIBaLIRQKUVZWhsrKSujp6aFFixYwNDRE69atYWJiorZf6tQiWP766y8EBgZK3fZ84sSJGDNmDN57771XrlvfYAGAxMREjBkzBoWFhRg0aBB++eWXGsucPXu21rv5tm7dGt999x13PUR1dTU++eQThIWFQU9PDwcPHkS/fv1kqqOxlJSU4MmTJ1w3XkVFBXx8fJCamooJEyaAz+fjxo0bcHR0xK5du7h/HORfGRkZePbsWZ1jTzk5OQgJCUGfPn3g5eXFTU9OTkZQUBD3gSgWi9GpUyc4OjpCR0cHp06d4lqLrVu3xoYNG+p8HIFIJEJERAQuXbqE9u3b47333oOBgUGN5fLz8xEdHY24uDjExcXh/v37SE1NlVrG2toa+fn5KCsrA/DicQP9+/dHnz59YGJigqKiIhQWFqKgoAD5+fkoLi5Gu3bt4OzsDHt7e671xefzoaOjI9fPVELy7V4kEgEA2rZt+8qAEovFavsB3FypRbBUVlZi6NCh+OCDDzB58mRcuHABgYGBuHTp0mu/0ckTLAAQGRmJ7du3Y+XKlbWOozDGsHz5cvz+++/Q0dGBrq4unJyc8OWXX6JNmzZSy4pEIixduhRHjx6Fubk5/vjjD5iYmMhci6KkpKRg//79OHr0KEpKSjBp0iR89dVX2Lt3L9avX49OnTrh0qVL0NbWbvLayL8ePnyI1atX4+bNmwBenJU3d+5c9OjRA8CLcDp27BiOHz+OZ8+ecesZGhpiwoQJsLS0REFBAXJycnDv3j3ueTkv09HRgaOjI4yNjXH37l0UFRUBAIYMGYIFCxaobMuaqAe1CBbgRSviiy++wMOHD9G2bVusXLlSpm/+8gaLoolEIowbNw5RUVF499138d133zXp/kNCQvD5559z7/l8PkQiERwdHZGSkoLy8nIcOXIEAwcObNK6SO3EYjH279+PdevWcYPIPXr0gLa2NiIjI7nl2rdvj1GjRiEqKgq3bt2qdVs6OjpwdnaGk5MTHB0d0a1bN9jb23NfIMRiMRISEqClpUV3niAKoTbBIi9VCRbgxTfN4cOHo7y8HD/99BN8fHy4eWKxGKmpqRAIBOjdu7dCu58iIyPxzjvvQCQSYcKECQgICABjDB999BEePXoEAPDz88P333+vsH0SxcjIyMC+ffvw66+/cmcJ6evrY9SoUfD394e7uzv3txIdHY3Q0FAwxmBiYgJTU1M4OTnBycmpwd1ThNQHBUsT27VrF7766itYWFhg7ty5SElJQUJCAmJjY7kzRiRnDSkiXPLz8zFs2DA8ffoUs2fPRmBgIDevsLAQK1euRFJSEn766SfuzBOieiSnvDPGMGzYsHpfE0FIU6JgaWIikQhjxozBvXv3asyztLREXl4eKisrMW3aNKxbtw4AcO/ePQgEAjg7O9fr+gfGGAICAnDhwgW4uLggNDSUxk8IIY1OLa5jaU74fD62b9+OtWvXwtTUFJ06dUKXLl3QvXt3tGnTBpcvX8aHH36IAwcOICEhAampqVK3C7GwsMDIkSOxatWq13ZvHDx4EBcuXICRkRG+//57ChVCSJOgFosKunr1KmbMmMEN2trY2MDGxgb3799HcXExAMDd3R0hISF1nhWXlZUFT09PFBcX4/vvv4efn1+T1U8IebNRi0UFDRkyBMeOHcOtW7cwePBgdOvWDTweD2KxGPfu3cOsWbNw584d+Pn54ZtvvkGnTp24K2YlAgMDUVxcjOHDh2PUqFFKPBpCyJuGWixqKCsrC++//z7i4uK4abq6uhg8eDDmzJmD58+fY+bMmdDX18fVq1frvPKYEEIaA7VY1JClpSVCQ0Oxbt063L17F0+ePEFBQQHCw8MRHh7O3Vl3xYoVFCqEkCZHwaKmDAwMEBQUxL3PycnBvn378NNPP6GwsBAuLi6YNm2aEiskhLypqCusmSkpKcGVK1fg4eHRaDcwJISQV6EWSzNjYGBAg/WEEKWiW4ISQghRKAoWQgghCkXBQgghRKEoWAghhCgUBQshhBCFomAhhBCiUM3+dGPJc7NffoQrIYQQ2VhYWEBTs35R0eyDRXLL+cmTJyu5EkIIUT/yXFze7K+8Ly8vR2xsLMzMzMDn85VdDiGEqBV5WizNPlgIIYQ0LRq8J4QQolAULIQQQhSKgoUQQohCUbAQQghRKAoWQgghCkXBQgghRKEoWAghhCgUBYsKOn78OBwdHeHiXB2XfAAAC/VJREFU4sK9wsLClF2WwsTExKBfv37c+8rKSgQGBsLd3R19+/bF7t27lVid4tR2nN27d5f6vQYEBCixQvlFRERg3LhxcHV1xdChQ3HkyBEAQFFRERYsWIBevXph4MCBOHHihJIrbZi6jjMjIwP29vZSv8tVq1YpuVr5XblyBaNGjYKLiwt8fHy445T73yYjKufLL79kmzZtUnYZCicWi9nRo0dZr169WK9evbjp33zzDZs8eTIrKChgGRkZbPjw4SwsLEyJlTZMXccZExPD+vfvr8TKFOPp06fMxcWFXbhwgYlEIhYdHc169+7N/vzzT7Zo0SK2cOFCVlZWxuLj41m/fv3Y7du3lV2yXF51nOfOnWPvvvuusktUiOzsbNa9e3d29epVxhhjsbGxzMnJicXGxsr9b5NaLCooLi4ODg4Oyi5D4YKDg/HLL79gzpw5UtPDwsIwe/ZsGBsbo23btpgxYwb3jUkd1XWccXFxsLe3V1JVivPkyRP4+vpi6NCh0NDQgLOzM9zd3XHz5k2Eh4dj4cKF0NPTg4ODA9599138+uuvyi5ZLnUd571795rN7xIA2rRpg5s3b2Lw4MEQi8UoKCgAn8+Hvr6+3P82KVhUjEgkQkJCAk6dOoUBAwZg6NCh2LNnD1gzuPPOhAkTEBoaiu7du3PTioqKkJubi86dO3PTbG1tkZiYqIwSFaK24wSA+Ph4CAQCjBo1Cv3798eCBQuQnZ2tpCrl5+bmhjVr1nDvCwoKEBUVhTZt2oDH46FDhw7cvI4dO6rt77Ku4+zWrRvi4+ORlJSE4cOHY8CAAVi1ahWKioqUWG3DGBgYQCgUwsnJCQEBAZg8eTJatmwp979NChYVIxAI0L17d4wZMwZ//PEH9+338OHDyi6twczNzWtMKysrAwDo6upy0/T09FBeXt5kdSlabccJvDguV1dX/PTTTzh//jx0dXUxb968Jq5OsYqLizFnzhz06NEDjo6O0NbWBo/H4+ar++9S4uXj9Pb2hpGRETw8PHD8+HGEhYUhKysLgYGByi6zQXR0dPD333/j+PHjOHHiBA4cOABAvn+bzf62+erGzMwMhw4d4t47ODhgypQpuHDhQrO89b+enh4AoKKigpsmFArRokULZZXUaFasWCH1fvny5ejXrx+ysrJgaWmppKrkl5aWhrlz56Jz58745ptvkJKSgsrKSjDGuHBpDr/L/x6nhoYGvv32W26+oaEhFi1ahEmTJqG6urredwJWFRoaGtDW1oaTkxP8/f0RGxsLQL5/m9RiUTFJSUkIDg6WmlZVVQUdHR0lVdS4jI2NYWZmhtTUVG5aWlqaVPO7udi6dStSUlK491VVVQCglr/byMhI+Pv7w8fHB8HBwdDR0UH79u3BGENmZia3XGpqqlr/Lms7TqFQiI0bN+L58+fcclVVVdDU1FTLR3PcuXMH48aNk5pWWVkJIyMjuf9tUrCoGCMjI+zbtw9Hjx6FWCxGbGwsDh48WOMX35z4+flhx44dEAgEyMzMREhICPz8/JRdlsIlJCRg/fr1KCoqQlFREdatW4chQ4agZcuWyi6tXh4/foxZs2ZhwYIFWLJkCdc60dfXh4+PDzZv3ozS0lI8fPgQx479X3v3G9LU28YB/IvZMM4k51glJlv1YswSWhZKiFOr0R+IiqIMptGWtgyRRLTIfzVqyyW12NIoEq0In5xIVpRSlNZYlNmLhBLqRX9Ai82IxbTNPS+kg0tz+9V5Hn+b1wfOi+3sXPe1I2eX9322+/5PyP4tf/c+58yZgydPnqC2thZutxuDg4M4ffo0tm7d6jcMGCpkMhkGBgZw+fJleL1e9PT0oKWlBdu3b//ja5PWY/kXstlsqKmpwbt37yAQCKBWq8NqGMxut6OgoADPnj0DMNbV1uv1uHv3LkZHR7Fz504UFRWF5EU63q/v0+l0QqfTobu7G16vFwqFAhUVFZg7d+40Z/rPnDx5Eg0NDROGRHbv3o28vDxUV1fj8ePH4PF42LdvH3JycqYp078z1fvMzs6GTqfD8+fPERERgU2bNqG0tDQke5/A2DcWdTod3rx5g7i4OBQWFkKpVP7xtUmFhRBCCKdoKIwQQginqLAQQgjhFBUWQgghnKLCQgghhFNUWAghhHCKCgshhBBOUWEhIS8rKwtSqXTSzePxTHd608put7Pn4tixY/jw4QOkUumkEwlarVakpKQEjGk0GtmYDx48+F+kTUJcaE5qQ8gvDh06NOnsBKE6bxPXOjs7IRAIMDQ09NextFotcnNzkZaWxkFmJBzRVUfCAsMwEIlE053Gv1ZsbCwYhuGksDAMA4ZhOMiKhCsaCiNh79y5c9BoNFCr1UhOTmaXeb506RIyMzMhl8uRnZ2N3t5e9hiPxwODwYDU1FSkpKTgwoUL2LZtG6xWKwBApVLBYDD4tfPr0NBU8cvKylBVVYXDhw9DLpcjKysLFouF3e/1emE2m5GRkQG5XA6VSoX+/n4MDg4iMTERNpvNr+1169Zxugyw1WqddGhRpVJx1gYJX1RYyIzQ1dWFlStXorm5GQqFAtevX0djYyMqKyvR2toKhUKB3NxcvH//HsBYMWpra4PBYEBDQwPu37+P/v7+oNsLFB8Abty4gfnz57MT/p09e5adqtxsNqOpqQlHjhxBa2sr4uLikJ+fD6FQiNTUVLS3t7Nxent7MTAwAKVSydHZAjZu3Iju7m52O3PmDCIjI6HRaDhrg4QvKiwkLOj1esjlcr/Nbrez+6OiopCfn48lS5YgNjYW9fX1KC4uRkZGBiQSCfbv34/k5GRcu3YNPp8Pzc3N0Gq1UCgUkMlkMBqN8Hq9QeczVfyfEhISUFRUhMWLF+PAgQOIiYnBq1ev4PP52KWNlUolJBIJKioqoFQq8fXrV2zevBkdHR3stPvt7e3IyMhAdHR00Pnt2LFjwvmqrKz0O18ikQgikQgejwfHjx9HQUEBFApF0G2QmYvusZCwkJ+fP2E67/ErOS5cuBAREWP/R7lcLnz69Anl5eV+H6YjIyPg8XhwOBxwOBxYunSp3/ELFiwIKpdA8X8Si8V+xzEMA4/HA6fTCYfDgaSkJHYfn89HWVkZgLFhr6qqKnR3dyM9PR137txBdXV1ULn9ZDKZ/JYQBoB79+7h4sWLfs8NDw/j4MGDWL58ObRa7T9qg8xcVFhIWBAIBBM+qMcbP5356OgogLFeTmJiot/roqKi/JZiHW98UfjV+K81B4o/VTyfz4fZs2cDwG+nJmcYBmvWrMHt27fB4/EwMjKC9PT03+Y2mbi4uAnnSygUTnhdeXk5XC4XTp06FfLLGJD/HxoKIzNOdHQ0RCIRBgYGIBaL2e3KlSvo6uoCwzCIj4/3u9nudDrx8eNH9jGPx8O3b9/Yx+PvnQSKH0x+QqEQfX197HNutxurV6/Gy5cvAYwtjvbo0SN0dnZi/fr1Uxa9P9XQ0IDOzk6YzWbw+XzO45PwRT0WMiNpNBpYLBbMmzcPSUlJuHnzJq5evYqmpiYAQF5eHmpra5GQkIBFixbBaDRiZGSEPX7ZsmVobGzEli1bwOfzodfr/T7cA8UPZM+ePbBYLIiPj4dEIkFdXR2io6Mhk8kAAGlpaYiMjERLS8uE4Ssu2Gw2GI1GnDhxAjExMfj8+TO7j77WTQKhwkJmpJycHLjdbtTU1ODLly+QSCQwmUxITk4GAOzatQtDQ0OoqqrC8PAw1Go1Xrx4wR6/d+9evH37Fmq1GgKBAIWFhX49mkDxA1Gr1XC5XDh69ChcLhdWrFiB+vp6tnjNmjULGzZsQEdHB1atWsXhmRnT1taGHz9+oKSkZMK+169fc94eCS+0giQhQUpJSUFpaemkv/CfDoWFhRCLxSguLv7ta+x2O3JyctDT08P5jxqlUinq6uqQmZnJaVwS+qjHQkiIefr0Kfr6+vDw4UO/37NMxeFwwOfzcXKvxOVy4fv3738dh4QvunlPSIi5desWTCYTSkpKkJCQENQxa9euRW1tLSftnz9/nuYJI1OioTBCCCGcoh4LIYQQTlFhIYQQwikqLIQQQjhFhYUQQginqLAQQgjhFBUWQgghnPovncm1dN+P2CkAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
diff --git a/setup.py b/setup.py
index add7a8b..7a9aab6 100644
--- a/setup.py
+++ b/setup.py
@@ -12,7 +12,7 @@
URL = 'https://github.com/raphaelvallat/yasa/'
LICENSE = 'BSD (3-clause)'
DOWNLOAD_URL = 'https://github.com/raphaelvallat/yasa/'
-VERSION = '0.1.6'
+VERSION = '0.1.7'
PACKAGE_DATA = {'yasa.data.icons': ['*.svg']}
INSTALL_REQUIRES = [
diff --git a/yasa/__init__.py b/yasa/__init__.py
index fa96d65..4af0f20 100644
--- a/yasa/__init__.py
+++ b/yasa/__init__.py
@@ -5,4 +5,4 @@
from .others import *
from .spectral import *
-__version__ = "0.1.6"
+__version__ = "0.1.7"
diff --git a/yasa/spectral.py b/yasa/spectral.py
index 3119b37..a0a2274 100644
--- a/yasa/spectral.py
+++ b/yasa/spectral.py
@@ -293,22 +293,22 @@ def irasa(data, sf=None, ch_names=None, band=(1, 30),
1. Compute the original power spectral density (PSD) using Welch's method.
2. Resample the EEG data by multiple non-integer factors and their
- reciprocals (:math:`h` and :math:`1/h`).
+ reciprocals (:math:`h` and :math:`1/h`).
3. For every pair of resampled signals, calculate the PSD and take the
- geometric mean of both. In the resulting PSD, the power associated with the
- oscillatory component is redistributed away from its original
- (fundamental and harmonic) frequencies by a frequency offset that varies
- with the resampling factor, whereas the power solely attributed to the
- fractal component remains the same power-law statistical distribution
- independent of the resampling factor.
+ geometric mean of both. In the resulting PSD, the power associated with
+ the oscillatory component is redistributed away from its original
+ (fundamental and harmonic) frequencies by a frequency offset that varies
+ with the resampling factor, whereas the power solely attributed to the
+ fractal component remains the same power-law statistical distribution
+ independent of the resampling factor.
4. It follows that taking the median of the PSD of the variously
- resampled signals can extract the power spectrum of the fractal component,
- and the difference between the original power spectrum and the extracted
- fractal spectrum offers an approximate estimate of the power spectrum of
- the oscillatory component.
+ resampled signals can extract the power spectrum of the fractal
+ component, and the difference between the original power spectrum and
+ the extracted fractal spectrum offers an approximate estimate of the
+ power spectrum of the oscillatory component.
- Note that the original PSD can be calculated by simply adding
- ``psd_aperiodic`` and ``psd_oscillatory``.
+ Note that an estimate of the original PSD can be calculated by simply
+ adding ``psd = psd_aperiodic + psd_oscillatory``.
References
----------
