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makesig.py
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makesig.py
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from __future__ import division
import numpy as np
import bisect
#######################################################################################################################
# https://pythonhosted.org/pyrwt/_modules/rwt/utilities.html
MAKESIG_SIGNALS = [ 'AllSig',
'Blocks',
'Bumps',
'HeaviSine',
'Doppler',
'QuadChirp',
'MishMash',
'Ramp',
'Cusp',
'Sing',
'HiSine',
'LoSine',
'LinChirp',
'TwoChirp',
'WernerSorrows',
'Leopold'
]
def makesig(signal_name='AllSig', N=512, t=None, y=None):
"""
Creates artificial test signal identical to the
standard test signals proposed and used by D. Donoho and I. Johnstone
in WaveLab (- a matlab toolbox developed by Donoho et al. the statistics
department at Stanford University).
Input: signal_name - Name of the desired signal (Default 'all')
'AllSig' (Returns a matrix with all the signals)
'HeaviSine'
'Bumps'
'Blocks'
'Doppler'
'Ramp'
'Cusp'
'Sing'
'HiSine'
'LoSine'
'LinChirp'
'TwoChirp'
'QuadChirp'
'MishMash'
'WernerSorrows' (Heisenberg)
'Leopold' (Kronecker)
N - Length in samples of the desired signal (Default 512)
Output: x - vector/matrix of test signals
N - length of signal returned
References:
WaveLab can be accessed at
www_url: http://playfair.stanford.edu/~wavelab/
Also see various articles by D.L. Donoho et al. at
web_url: http://playfair.stanford.edu/
Author: Jan Erik Odegard <[email protected]>
This m-file is a copy of the code provided with WaveLab
customized to be consistent with RWT.
"""
if t is None:
t = np.linspace(1, N, N)/N
else:
N = len(t)
if y is None:
y = np.zeros_like(t)
else:
y = np.copy(y)
signals = []
if signal_name in ('HeaviSine', 'AllSig'):
y += 4 * np.sin(4*np.pi*t) - np.sign(t - 0.3) - np.sign(0.72 - t)
signals.append(y)
if signal_name in ('Bumps', 'AllSig'):
pos = np.array([ .1, .13, .15, .23, .25, .40, .44, .65, .76, .78, .81])
hgt = np.array([ 4, 5, 3, 4, 5, 4.2, 2.1, 4.3, 3.1, 5.1, 4.2])
wth = np.array([.005, .005, .006, .01, .01, .03, .01, .01, .005, .008, .005])
for p, h, w in zip(pos, hgt, wth):
y += h / (1 + np.abs((t - p) / w)) **4
signals.append(y)
if signal_name in ('Blocks', 'AllSig'):
pos = np.array([ .1, .13, .15, .23, .25, .40, .44, .65, .76, .78, .81])
hgt = np.array([ 4, -5, 3, -4, 5, -4.2, 2.1, 4.3, -3.1, 2.1, -4.2])
for p, h in zip(pos, hgt):
y += (1 + np.sign(t - p))*h/2
signals.append(y)
if signal_name in ('Doppler', 'AllSig'):
y += np.sqrt(t * (1-t)) * np.sin((2*np.pi*1.05) / (t+.05))
signals.append(y)
if signal_name in ('Ramp', 'AllSig'):
y += t.copy()
y[t >= .37] -= 1
signals.append(y)
if signal_name in ('Cusp', 'AllSig'):
y += np.sqrt(np.abs(t - 0.37))
signals.append(y)
if signal_name in ('Sing', 'AllSig'):
k = np.floor(N * .37)
y += 1 / np.abs(t - (k+.5)/N)
signals.append(y)
if signal_name in ('HiSine', 'AllSig'):
y += np.sin(N*0.6902*np.pi*t)
signals.append(y)
if signal_name in ('LoSine', 'AllSig'):
y += np.sin(N*0.3333*np.pi*t)
signals.append(y)
if signal_name in ('LinChirp', 'AllSig'):
y += np.sin(N*0.125*np.pi*t*t)
signals.append(y)
if signal_name in ('TwoChirp', 'AllSig'):
y += np.sin(N*np.pi*t*t) + np.sin(N*np.pi/3*t*t)
signals.append(y)
if signal_name in ('QuadChirp', 'AllSig'):
y += np.sin(N*np.pi/3*t*t*t)
signals.append(y)
if signal_name in ('MishMash', 'AllSig'):
#
# QuadChirp + LinChirp + HiSine
#
y += np.sin(N*np.pi/3*t*t*t) + np.sin(N*0.125*np.pi*t*t) + np.sin(N*0.6902*np.pi*t)
signals.append(y)
if signal_name in ('WernerSorrows', 'AllSig'):
y += np.sin(N/2*np.pi*t*t*t)
y += np.sin(N*0.6902*np.pi*t)
y += np.sin(N*np.pi*t*t)
pos = np.array([.1, .13, .15, .23, .25, .40, .44, .65, .76, .78, .81])
hgt = np.array([4, 5, 3, 4, 5, 4.2, 2.1, 4.3, 3.1, 5.1, 4.2])
wth = np.array([.005, .005, .006, .01, .01, .03, .01, .01, .005, .008, .005])
for p, h, w in zip(pos, hgt, wth):
y += h/(1 + np.abs((t - p)/w))**4
signals.append(y)
if signal_name in ('Leopold', 'AllSig'):
#y += (t == np.floor(.37 * N)/N).astype(np.float)
y[bisect.bisect(t, 0.37)] += 1
signals.append(y)
if len(signals) == 1:
return signals[0]
return signals
#######################################################################################################################
def add_noise(signal, SNR_dB=70):
"""
add noise to a signal
Signal: a numpy array
SNR_DB: SNR level signal + noise
Output: signal with superimposed noise
"""
if not SNR_dB:
return signal
signal_power = np.float32(np.sum(np.abs(signal) ** 2, axis=0)) / signal.shape[0]
noise = np.float32(np.random.normal(0.0, 1.0, signal.shape))
noise_power = np.abs(noise) ** 2
K = (signal_power / noise_power) * 10**(-SNR_dB/10)
new_noise = np.sqrt(K) * noise
noisy_signal = np.float32(signal + new_noise)
return noisy_signal
#######################################################################################################################