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
- Lloyd-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