# Rémi Flamary

Professional website

## MAP555 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 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 :

### 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]