Hours:
16 hours (4 credits)

Room:

From remote by using Microsoft Teams. The link will be sent in due time to all students who registered to the seminar.

To register to the course, click here

Short Abstract:

In signal processing, spectrum analysis plays a key role to characterize and understand many phenomena. For instance, in biomedical applications, some features such as the ratio between the powers in low and high frequencies can be the basis of a physiological interpretation. Having a visual representation of how the spectrum of an audio signal varies over time can help the practitioner. Different families of methods have been developed for spectrum analysis. When dealing with stationary signals, several approaches exist. They differ on two main features: they can be parametric or not, with low or high resolution. Among the low-resolution non-parametric methods, the periodogram and the correlogram are based on the short-time Fourier transform (STFT). As an alternative, high-resolution non parametric methods such as the ones proposed by Capon and Borgiotti-Lagunas consist in designing very-selective frequency filters, whose finite impulse response depends on the input signal covariance matrix, and then in looking at the filter output power. Among the other solutions, parametric methods based on an a priori model such as the autoregressive with moving average (ARMA) can be used. The last class includes subspace methods such as MUSIC and ESPRIT and their variants. It should be noted that some links can be drawn between all these methods. When dealing with non-stationary signal, the above methods can be used by designing “sliding” methods, which consist in using a sliding window and then in applying a stationary-signal spectrum analysis on each signal frame. Nevertheless, the whole non-stationary signal can be studied directly by using alternative approaches such as the Cohen class which includes the Wigner-Ville distribution and its variants, the wavelet-based method or the empirical mode decomposition, to cite a few.

The purpose of this PhD course is to present an overview of these different families of approaches, their advantages and drawbacks.

Course Contents in brief:

1. Stationary case
   1. Fourier based methods (periodogram, correlogram, etc.)
   2. Filtering based methods (Capon, Borgiotti-Lagunas algorithm)
   3. ARMA-model based methods
   4. Subspace methods (Music, Esprit, etc.)
2. Non-stationary case
   1. Sliding-window methods
   2. Whole-signal analysis
      1. Cohen classes
   3. Wavelet methods
   4. EMD
3. Some illustrations
   1. Speech analysis
   2. Biomedical applications

Schedule:

1. Day1 - 7 June 2021 - 9:00-13:00 - 2 slots of 2 hours dedicated to some prerequisites (if it is necessary), Fourier-based methods and filtering-based methods.
2. Day2 - 8 June 2021 - 9:00-13:00 - 2 slots of 2 hours dedicated to ARMA-model based methods and subspace methods.
3. Day3 - 9 June 2021 - 9:00-13:00 - 2 slots of 2 hours dedicated to examples and illustrations (if possible Matlab laboratory).
4. Day4 - 10 June 2021 - 9:00-13:00 - 2 slots of 2 hours dedicated to examples and a brief overview of the non-stationary case.