Signal, Metrology - 3EMTABT0

Goal(s)

The purpose of this lecture is to introduce various aspects of signal processing.
The random nature of measurements and recorded time series is emphasized and illustrated by examples. 4 lectures are presented, each of which is focused on a different aspect, ranging from detection problems in telecommunication to non stationary spectral analysis of biological series.
All proposed algorithms, methods or strategies are examined and discussed in terms of their precision, robustness and reliability.
6 sessions (2h) are organized for classroom exercices.

Content(s)

4 2h long course:
1.introduction to binary hypothesis testing. MAP, MV, and Bayes strategies. Application to the detection of a communication binary signal embedded in noise.
2. Definition of information, entropy and channel capacity (additive Gaussian symmetric case).
3. Basics of numerical signal processing. Filtering and FFT, Transfer functions. The FFT algorithm.
4. Sliding window approaches for non stationary signal analysis. Example on biological time series.

First semester SP lecture. Correlation and convolution. Transfer functions, sampled signals. PSD and Fourier transform, matched filters.