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Digital signal processing

174-2 Digital signal processing Physics Engineering and Embedded Systems - Apprenticeship S6
Lessons : 8 h TD : 9 h TP : 15 h Project : 0 h Total : 32 h
Co-ordinator : Miloud Frikel
Prerequisite
Mathematics for engineering sciences
Digital electronics
Signals and systems
Course Objectives
This lesson is an initiation into signal processing and into the particularities of signal digitizing. The notions of signal sampling and its consequence on the sampled signal spectrum are shown. The discrete Fourier Transform and optimised versions (Fast Fourier Transform – FFT) are also presented. Advanced notions of digital filtering are also addressed (transfert function, filter structure and stability, filter digitalization, …).
Syllabus
The lesson has the following schedule :

Introduction
• Digitalize ?
• What applications ?

Reminders on spectral analysis
• Fourier series
• Fourier transform
• Properties

Discrete time signals
• Sampling
• Sprectrum of a sampled signal
• Shannon theorem
• Applications and illustrations

Discrete transforms
• Discrete time Fourier transform
• Discrete Fourier transform
• Acquisition
• Windowing
• Fast transforms

Digital filters
• Reminders on Z transform
• Transfert function
• Finite and Infinite Impulse Response
• Filter stability
• Filter structure
• Frequency response
• Filter synthesis
Practical work (TD or TP)
Notions of sampling and discrete Fourier transforms are dealt in several exercices. These exercices are built either to manipulate the definitions or to analyse results (spectral analysis or recognization of signal processings). Exercices on digital filters are also proposed where the recognition and the coarse analysis of impulse and frequency responses are made. Some exercises on the synthesis of digital filters are finally proposed.

Practical works are made on the simulation software Matlab/Simulink. Their goals are to analyse known or unknown signals. The student will generate some spectrums thanks to Matlab and improve the analysis with differents tools (FFT size, windowing, …). The student will also study the complexity of differents algorithms for the calculation of frequency responses. The student will finally use Simulink to analyse different filters (FIR, Butterworth, Chebycheff, notch filters, …) in order to de-noise some signals.
Acquired skills
After this lesson, the student should be able to correctly analyze a signal in its frequency domain. The student should be also able to generate spectrums with different digital simulation tools, to improve the spectral analysis with a better spectral resolution or with an appropriate windowing. The student should finally able to correctly design a digital filter for basic signal operations (parasite removal, de-noising, …).
Bibliography
John G. Proakis – Digital communications – McGraw-Hill Editions.
P.P. Vaidyanathan – Multirate systems and filter banks – Prentice Hall

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