Advanced Digital 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 Quantization:
  

  • Introduction
  • Quantization Error
  • Uniform Quantizers: Mir-Rise and Mid-Tread
  • Python Example: Uniform Quantizers
  • Python Example: Real-time Quantization Example

• 02 Quantization - Signal to Noise Ratio (SNR):
  

  • Signal to Noise Ratio (SNR)
  • SNR for Uniformly Distribution Signals
  • SNR for a Sine Wave
    • PDF of Time Series

• 03 Quantization - Non-Uniform Quantization:
  

  • Companding
    • µ-LAw and A-Law
    • Python Example: µ-LAw
    • Python Example: Real-Time Mid-Tread, Mid-Rise, µ-Law

• 04r Quantization - Revision: Histogram, PDFs, Numerical Integration
  

  • Histograms
  • Probability Density Functions
  • Numerical Integration
    • Riemann Sum
    • Trapezoidal Rule

• 04 Quantization - Lloyd-Max Quantizer
  

  • Lloyd-Max Quantizer
  • Lloyy-Max Quantizer Examples

• 05 Quantization - Vector Quantizer (VQ) and Linde-Buzo-Gray (LBG) Algorithm
  

  • Vector Quantization
  • Linde-Buzo-Gray Algorithm
  • Python Examples: Vector Quantization in an Encoder and Decoder
    • Iron Maiden - The Number of the Beast Introduction
    • Iron Maiden - Aces High Introduction

• 06 Sampling - Sampling a Discrete Time Signal
  

  • Sampling Introduction
  • Sampling a Discrete Time Signal
    • Downsampling
    • Upsampling
  • Python Example: Live Spectrogram: Sampling, LP Filtering

• 07a The z-Transform - Theory and Properties
  

  • The z-Transform Definition
  • Properties of the z-Transform
    • Shift Property
    • Linearity
    • Convolution
  • z-Transform Example: Exponential Decaying Sequence

• 07b Filters - FIR and IIR Filters
  

  • Filters: Linear Time-Invariant Systems
  • Finite Impulse Response (FIR) Filters
  • Infinite Impulse Response (IIR) Filters
  • Filter Example: Exponential Decaying Signal
    • Computing the Resulting Frequency Response
    • The z-Plane
    • Impulse Response

• 08 Filters and Noble Identities
  

  • Filter Design
    • Linear Phase and Signal Delay
    • General Phase and Groud Delay
    • Magnitude
  • Multirate Noble Identities
  • Polyphase Vectors
  • Python Example: Noble Identities and Polyphase Vectors

• 09 Allpass Filters and Frequency Warping
  

  • Allpass Filters
    • Allpass Filter as Fractional Delay
    • IIR Fractional Delay Filter Design
    • Simple IIR Allpass Filters
  • Frequency Warping Introduction
  • Frequency Warping and Bark Scale

• 10 Frequency Warping and Minimum Phase Filters
  

  • Frequency Warping
  • Minimum Phase Filters
    • Python Example
    • Impulse Response
    • Frequency Response

• 11 Complex Signals and Filters, Hilbert Transform
  

  • Complex Signals and Filters
  • Hilbert Transformer
    • Python Example
    • Impulse Response
    • Frequency Response
  • Example for the Measurement of the (Instantaneous) Amplitude

• 12 Wiener Filters
  

  • Wiener Filters
    • Python Example for Denoising Speech
    • Scipy Wiener Filter Example: Iron Maiden - The Number of the Beast Speech Intro

• 13 Matched Filters
  

  • Matched Filters
    • Python Example: Closed Form Solution
    • Convolutional Neural Network Implementation: PyTorch

• 14 Prediction
  

  • Prediction
    • Wiener-Hopf Closed Form Solution
    • Encoder-Decoder System
    • Neural Network Implementation - PyTorch
  • Linear Predictive Coding (LPC)
  • Least Mean Squares (LMS) Algorithm
    • LMS with Quantizer

YouTube Playlist

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.