This course covers the following concepts: Analog-to-Digital Conversion The TF has discrete time and the TFD LA transforms it into Z (TZ) The digital filters Numerical methods of synthesizing the filters digital RIF and RII, Random signals Modeling of random signals The course is based on on concrete examples of audio processing (speech and music) to illustrate the dierents theoretical aspects addressed, in order to facilitate assimilation and to generate more interest and awareness. curiosity of the students. The Matlab Mini-project module is linked to this course and in particular aims to the assimilation of different notions by the implementation under the Matlab environment.
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Digital signal processing
Information is the resolution of uncertainty, Claude Shannon.
Content of the module
1. Introduction: evidence of the importance of the interest shown by common everyday applications
of Signal Processing. The mathematical modelling component at the heart of TS is
highlighted.
2. Digital Analog Conversion: Sampling, Sampling Frequency, Theoreme
de Shanon, Anti-folding filter, quantification, coding.
3. TF with Discrete Time and TFD: Denition of TF with discrete time, time window,
Spectral resolution, Gibbs phenomenon, TFD denition and interest, resolution of the
TFD
4. Linear and time invariant filter: denition, impulse response, algorithm
of contempt, stability and causality.
5. TZ: denomination, convergence domain, link with TFD, TZ and characterization of a
ltre LIT (z-transfer function, causalite and stability).
6. Analysis and synthesis of digital filters: RIF filter, RII filter, one filter template,
Synthesis of a RIF filter by Fourier series synthesis, Synthesis of a RIF filter by
Frequency sampling, Bilinear transformation, Synthesis of an RII lter by
biliary transformation (case study).
7. Random signals: introduction by current examples of random signals, character
Statistical erization of the temporal content (mean, correlation, etc.), stationarity,
ergodicite, power spectral density, Wiener Khintchine theorem, ltrage (LIT)
random signals (temporal and frequential).
8. Random signal modeling: Interests of modeling (coding, prediction, etc.),
Presentation of the AR, MA and ARMA models, Calculation of the parameters of the AR model by the
auto correlation method: Yule Walker equation, Calculation of model parameters
MA by spectral factorization, Estimation of AR parameters of an ARMA model:
Modified Yule Walker equations, Estimate of MA, and ARMA parameters.