• FR
  • EN

Signal processing, an introduction

Code: S1314, ECTS: 1


Signal processing techniques have found their way into a wide variety of fields: instrumentation, processing and transmission of images, controls, telecommunications and even consumer electronics. The aim of this course is to present a number of concepts, results and tools which a modern engineer or an enlightened consumer cannot afford to ignore.


  • Introduction Time invariant signal processing Convolution, Fourier transform, regularity. Sampling, Shannon theorem, Discrete Fourier Transform Periodic signals, Fourier series, discretization, Fast Fourier Transform Caveat: compact support exclusion, time/frequency spread,  Gibbs oscillations Analog filter design (Butterworth Chebychev), filter discretization Discrete filter design.  Transforms on pass bands, stop bands, etc.. Signal resampling
  • TP1 Frequency analysis of signal of various natures. Implementation of the Butterworth and Chebychev filters. Experiments. 
  • Application to Image Processing Discrete Cosine Transform. JPEG algorithm. Time varying signal processing in the time frequency plane Windowed Fourier Transform . Continuous time analysis. Space/frequency resolution. Frames. Inverse transform. Continuous spectrogram. DFT windowing and time translation. Discrete spectrogram. 
  • TP2 Implementation of the DCT and approximation test on standard images. 
  • Wavelet Signal Processsing Perfect reconstruction filter banks. Filter cascade. The limit case. Multirésolution approximations, wavelets. Properties. The discrete/continuous link. Application to the approximation of 1-D signals and images and to denoising. 
  • TP3 Make your own wavelet toolbox.

Evaluation means

Computer project

Detailed schedule

This course alternates classical courses and computer sessions (labeled TPi in the program).
The course's slides will be in English, but the oral course will be in French.

Teaching team


Teaching staff

Code S1314
Year 2nd year
Level Graduate 1st year
ECTS Credits 1
Coefficient 1
Nb. of hours 12
Nb. of lessons 10
Course type Specialized courses
Semester 4
Period Spring
  • Mathématiques
  • Télécommunications
Last update:
20 Jun 2017 11:21 by julien