Multirate Signal Processing Notebooks and Tutorials

Prof. Dr. -Ing. Gerald Schuller
Jupyter Notebooks and Videos: Renato Profeta

Applied Media Systems Group
Technische Universität Ilmenau

Content

• 01 Introduction:

  • What is Multirate Signal Processing? Where is it used?
  • Python Example of a Discrete Time Signal
  • Python Example for a Live Plot of a Microphone Signal
  • Javascript Example for a Live Plot of a Microphone Signal
  • Nyquist Theorem
  • Simple Sample Rate Conversion Example
  • Basic Building Blocks of Multirate Signal Processing
  • Critical Sampling
  • Analysis Filter Bank
  • Synthesis Filter Bank

• 02 Multiresolution:

  • Uniform Filter Banks
  • Python Example: Live Spectrogram and Aliasing
  • Non-Uniform Frequency Decomposition
  • Frequency Domain and Notation
  • Common Types of Frequency Transforms:
    • Discrete Time Fourier Transform (DTFT)
    • Discrete Fourier Transform (DFT)
    • Discrete Cosine Transform (DCT)
    • z-Transform
    • Short-Time Fourier Transform (STFT)

• 03 Frequency Response:

  • Frequency Response
  • Example: Obtaining the Frequency Response of a "Black Box" system using Noise
  • Example: Obtaining the Frequency Response of a "Black Box" system using Sweeping Sinusoid
  • Frequency Response: z-Transform and the DTFT
    • Example: Low Pass Filter as Moving Average
      • Discrete Convolution as Matrix Multiplication (Sylvester Matrix)
      • Plotting Poles and Zeros in the Complex Plane
      • Complex Conjugate Symmetry
  • dB Revision
    • dB for Voltage and Power
    • Cascading Filters

• 04 Filters:

  • Ideal Low Pass Filter
    • Frequency Response
    • Impulse Response
  • Delay (Shift Operator)

• 05 Filters and Windows:

  • Ideal Low Pass Filter
    • Quadratic Error
    • Parseval Theorem
  • Rectangular Window
  • Approximation of an Ideal Low Pass Filter using a Rectangular Window and Delay

• 06a Windows:

  • Rectangular Window
  • Raised Cosine Window
  • Kaiser Window
  • Vorbis Specification

• 06b Filter Design with the Window Method:

  • Design Method
  • Design using Modulation

• 07 Sampling:

  • Sampling a Discrete Time Signal
  • Real-Time Python Example
  • Downsampling
  • Upsampling

• 08 Effects in the z-Domain:

  • Modulation
  • Time-Reversal

• 09 Non-Ideal Filters:

  • Filter Banks
  • Analysis Filter Bank
  • Block Transforms
  • Python Example
  • Fast Implementation

• 10 Transforms as Filter Banks:

  • Equivalent Analysis Filters of a DFT
  • Equivalent Synthesis Filter Bank
  • Python Example
  • Example Transform as Filter Bank

• 11 DCT and Polyphase Representation:

  • Notation
  • Discrete Cosine Transfomr (DCT)
  • Introduction to Polyphase Representation
  • Analysis Filter Bank
  • Python Polyphase Example
    • Faster Implementation
  • Application Example
  • Auxiliary Functions

• 12 Polyphase Representation:

  • Polyphase Representation
  • Synthesis filter Bank
  • Perfect Reconstruction

• 13 MDCT:

  • Modified Discrete Cosine Transform (MDCT)
  • MDCT Filters: Python Example
  • Symmetries of a Cosine Modulation Function
  • Sparse Matrices and the MDCT
    • Python Computation
  • The Delay Matrix
    • Python Sympy Example
    • Faster Numerical Python Implementation
  • The Python Folding Matrix Function
  • The Factorization
  • Perfect Reconstruction
    • Example in Python
  • MDCT Python Implementation, Analysis
  • MDCT Synthesis Filter Bank

• 14 LDFB:

  • Low Delay Filter Banks (LDFB)
  • Zero-Delay Matrix
  • Maximum-Delay Matrix
  • Python Fast Implementation Example

• 15 Optimization of Filter Banks:

  • Goal
  • Approach
  • Newton's Method
  • Gradient Descent
  • Python Example for the Optimization of an MDCT Filter Bank

• 16 Artificial Neural Networks:

  • Artificial Neural Networks
  • Gradient Descent and Back-Propagation
  • Python Example for the MNIST Digit Recognition
  • Convolution Neural Networks
  • Python Keras Convolutional Neural Network Example
  • Implementation using Python Pytorch
  • Implementation using a Dense Net
  • Real-Time Online-Implementation of Convolutional Neural Networks

• 16b Pytorch MNIST Digit Recognition with Webcam:

  • Train the Pytorch Version of the MNIST handwitten digit recognizer
  • Capture a handwritten digit using the webcam
  • Try to recognize it with the recognizer, using suitable pre-processing to obtain the same format as the MNIST digit images.

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Requirements

Please check the following files at the 'binder' folder:

• environment.yml
• postBuild

Note

Examples requiring a microphone will not work on remote environments such as Binder and Google Colab.