Rémi Flamary

Signal Processing from Fourier to machine learning

Courses

Course overview:

• Fourier analysis and analog filtering [PDF]
  • Fourier Transform
  • Convolution and filtering
  • Applications of analog signal processing
• Digital signal processing [PDF]
  • Sampling and properties of discrete signals
  • z Transform and transfer function
  • Fast Fourier Transform
  • Applications to signal and image processing
• Random signals [PDF]
  • Correlation and spectral representation of random signals
  • Filtering and prediction of stationary random signals
  • Autoregressive model and Wiener filtering
• Signal representation and dictionary learning [PDF]
  • Non stationary signals and short time FT
  • Common signal representations (Fourier, wavelets)
  • Source separation and dictionary learning
  • Signal processing with machine learning

Exercises

• Exercises Part 1 : Analog signal processing [PDF]
• Exercises Part 2 : Digital signal processing [PDF]
• Exercises Part 3 : Random signal processing [PDF]

Practical sessions

• Practical Session 1 : Digital signal processing [PDF] [Data_PS1.zip]
• Practical Session 2 : Random signal processing [PDF] [Data_PS2.zip]
• Practical Session 3 : Signal representation and dictionary learning [PDF] [data_PS3.zip]

Practical sessions will require a working Python environnement with the libraries Numpy/Scipy and Matplotlib installed. You can get such an environnement for Windows/Linux/MacOSX on Anaconda.

Here is a list of nice references and Python tutorials :

• Tutorial Numpy
• Doc Numpy
• Doc Scipy
• Doc ScMatplotlib/pylab

Acknowledgments

The course is partly based on the original MAP555 taught by S. Mallat, E. Moulines and F. Roueff at Ecole Polytechnique. I want to thank Lucas Versini for his help in correcting many small errors and typos in the course.

Bibliography

• Polycopié MAP555, S .Mallat, E. Mouline, F. Roueff, 2015
• Théorie du Signal, C. Jutten, 2018 [PDF]
• Signals and Systems, Oppenheim & Willsky, 1996 [PDF]
• Signals and systems, Haykin & Van Veen, 2002 [URL]
• Discrete-Time Signal Processing, Oppenhein, 1999 [PDF]
• Probability, Random Variables and Stochastic Processes, A. Papoulis, 2002 [PDF]
• Wavelet tour of signal processing, S. Mallat, 2008 [PDF]