Ense3 rubrique Formation 2022

Signal and Image Processing - 4EUS4TSI

  • Number of hours

    • Lectures 30.0
    • Projects -
    • Tutorials -
    • Internship -
    • Laboratory works 30.0


    ECTS 5.0


The purpose of this module is to go beyond the basic one-dimensional and deterministic approach of signals, providing theoretical and practical foundations for analysing and processing:

  • random signals (spectral analysis and optimal filtering),
  • images (foundations of image processing by covering both basic and more advanced topics illustrated on some real examples)




Image processing

  • Definition of a digital image
  • Color theory and color spaces
  • Point-wise image transformations with applications in image enhancement
  • Linear and non-linear image filtering
  • Representation and processing of images in the Fourier domain
  • Edge detection
  • Mathematical morphology
  • Image segmentation
  • Image processing based on machine/deep learning

Spectral analysis

  • Non parametric (or Fourier) spectral analysis
    • Definition of the power spectral density
    • Estimation of the auto-correlation function, bias and variance
    • Correlogram (Balckman-Tuckey) : bias and variance trade-off, normalization, application
    • Welch's periodogram, bias and variance trade-off, normalization
  • Parametric spectral analysis
    • Presentation of the approach, usefulness and interest
    • Interpretation of the spectral estimator by ARMA(p,q) model, link with peaks and valleys of the PSD
    • AR estimation
    • ARMA estimation
  • High resolution methods (optional)
    • Prony
    • CAPON
    • MUSIC
  • Application (lab): analysis of the vibration pollution of an industrial system

Optimal filtering

  • Wiener filtering
    • Principles, assumptions, Wiener-Hopf equation
    • Non-causal optimal filtering
    • Optimal causal filtering: Bode-Shannon decomposition
    • Continuous and discrete time filters (IIR)
  • Discrete Wiener filter
    • Wiener-Hopf equation of the FIR filter
    • Linear prediction, coding (analysis and synthesis) and AR parametric modeling
    • Applications: periodic noise denoising (lab), LPC vocoder
  • Adaptive algorithms
    • Assumptions, notion of recursion (prediction/correction structure) and adaptivity (example of the estimator of a mean)
    • RLS filter with exponential forgetting: algorithm, adaptivity/convergence trade-off
    • LMS filter: algorithm, adaptivity/convergence trade-off
    • Applications: echo cancellation in audio systems, estimation of foetal ECG (lab: Widrow's experiment)


  • Mathematics for engineers
    • complex variable functions,
    • Fourier transform,
    • Laplace transform,
    • Z transform.
  • Basics in continuous-time signal processing
    • deterministic and random signals,
    • time domain and frequency domain representations,
    • linear and time-invariant filters, modulation,
    • sampling.
  • Basics in discrete-time signal processing
    • discrete Fourier transform,
    • analysis and design of digital filters.


First session

  • ER assessment : 2 hours supervised written + Image processing project
  • EN assessment : work assignments + Lab reports
    If distant learning mandatory:
  • ER assessment : 2 hours homework + Image processing project and lab reports
  • EN assessment : work assignments + other Lab reports


Second session

  • EN assessment: retaking this assessment is not possible

ER 67% + EN 33%


The course exists in the following branches:

see the course schedule for 2023-2024

Additional Information

Course ID : 4EUS4TSI
Course language(s): FR

You can find this course among all other courses.


  • Modern spectral estimation - theory and application, S.M. KAY, Prentice Hall, 1988
  • Optimal Filtering, Brian D. O. Anderson and John B. Moore. Dover Publications, 2005
  • Introduction au traitement d'images, D. Lingrand, Vuibert, 2d ed., 2008
  • Digital Image Processing, W. K. Pratt, Wiley, 4th ed., 2007.