digital filters, estimation and applications

This module has several objectives:
Firstly, we briefly review the concepts covered in 1st year in continuous signals, digital signal processing and random processes and signals, providing additional information on the influence of poles and zeros in characterizing the frequency response of filters, and on the use of the FFT.
Then, we propose to start from the concepts of digital filters to tackle the problems of a priori modeling of a signal by autoregressive modeling and estimating the parameters of this model from available data. An example based on the modeling of a speech signal will illustrate the point. This modeling and parameter extraction approach can also be used to extract signatures, the first step in a machine learning approach.
In addition, we propose to discuss several methods for synthesizing digital filters. These will illustrate how to combine the notions seen in 1st year to set up signal processing approaches. We'll look at filter synthesis using the bilinear transform and the impulse response invariance method for RII filter synthesis. In the case of RIF filter synthesis, we present the window method.
The notion of adaptive filtering is introduced.
Finally, this module provides an initial overview of signal processing tools (FFT, windowing, filtering) through a project. It also introduces the basic concepts of signal processing, which will be used in applications: 1/ requiring a priori signal modeling 2/ involving estimation problems

Introduction to digital signal processing

1/ Reminders from TdSI, Fast Fourier Transform, influence of poles and zeros.2/ A priori signal modeling and estimation
3/ Filter synthesis methods4/ Adapted filtering5/ Various applications through practical exercises. 6/ Project

Signal and image processing

1 course support/TD/TD on machine/Project