Summary of Advanced Signal Processing Module 01

This module covers advanced topics in signal processing, bridging analog filter design with modern discrete-time and multirate systems, and introduces wavelet theory. The course is structured into five main chapters.

Chapter 1: Analog Filter Review (3 weeks)

·       Introduces general filter characteristics and various types of analog filters.

·       Focuses on the design and dimensioning of standard filter families: Butterworth, Bessel, Chebyshev (Type I & II), and Elliptic filters.

·       Covers crucial practical steps: frequency normalization and denormalization.

Chapter 2: Discrete-Time Linear Time-Invariant (LTI) Systems (3 weeks)

·       Begins with a review of sampling theory.

·       Covers the Z-Transform and its inverse as fundamental tools for discrete-time analysis.

·       Details the characteristics of discrete LTI systems: linearity, recurrence equations, recursivity, time-invariance, impulse response, transfer function, causality, and stability criteria.

Chapter 3: Analysis and Design of Digital Filters (4 weeks)

·       Defines digital filters and their frequency specifications (gabarit fréquentiel).

·       Explores structures, stability, and implementation of Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) filters.

·       Discusses minimum-phase filters.

·       Presents design methods:

o   FIR synthesis: using windowing and frequency sampling techniques.

o   IIR synthesis: using impulse invariance and bilinear transformation methods.

Chapter 4: Multirate Digital Filters (2 weeks)

·       Covers fundamental operations: downsampling (decimation) and upsampling (interpolation).

·       Introduces multirate systems and their spectral analysis.

·       Explains filter banks and polyphase decomposition techniques.

·       Discusses key applications of multirate signal processing.

Chapter 6: Wavelet Transform (3 weeks)

·       Discusses the time-frequency duality and introduces the Short-Time Fourier Transform (STFT), along with its limitations.

·       Presents Continuous Wavelet Transforms (CWT) and Discrete Wavelet Transforms (DWT), including dyadic wavelets.

·       Provides examples of DWT families (e.g., Haar, Daubechies).

·       Explains the framework of Multiresolution Analysis (MRA).

·       Introduces the efficient lifting scheme implementation of the DWT.

The module progresses from foundational analog and discrete-time system concepts to advanced digital filter design, multirate systems, and culminates with an introduction to time-frequency analysis via wavelets.