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Signal 1


Hilbert spaces:

  • Linear forms, prehilbertian spaces
  • Hilbert spaces, Projection on a convex spaces
  • Hilbertian bases, Examples (Fourier, orthogonal polynomials)


Fourier Transform:

  • Fourier decompositions of a periodic function, Fourier Transform of a function defined on R. Convolution
  • Discrete Fourier Transform, FFT algorithm.


Numerical signal and Image processing, compression, denoising. Examples of sound processing. 


At the end of this module, the student will have understood and be able to explain (main concepts):

  •  Signal and Image processing basic notions : sampling, windowing and sampling 
  • FFT algorithm
  • Basis notions of Hilbert spaces and Hilbert bases.


The student will be able to:

  • Use the FFT and understand the output on a Signal or an image.
  • Apply several transformations to a signal and an image using the FFT

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...