Graduate School and Research Center in Digital Sciences

Statistical signal processing

T Technical Teaching


  • The proper treatment of modern communication systems requires the modelling of signals as random processes.
  • Often the signal description will involve a number of parameters such as carrier frequency, timing, channel impulse response, noise variance, interference spectrum.
  • The values of these parameters are unknown and need to be estimated for the receiver to be able to proceed.
  • Parameters may also occur in the description of other random analysis of communication networks, or in the descriptions of sounds and images, or other source signals.
  • This course provides an introduction to the basic techniques for estimation of a finite set of parameters, of a signal spectrum or of one complete signal on the basis of a correlated signal optimal filtering).
  • Finally, we consider a prototype parameter estimation problem: sinusoids in noise.




  • Parameter estimation : Random parameters, Bayesian estimation : minimum mean squared error estimation, orthogonality principle, maximum a posteriori estimation, performance bounds, linear estimation, the linear model. Deterministic unknown parameters : minimum variance estimation, bias, efficiency, consistency, Cramer-Rao lower bound, maximum likelihood estimation, EM algorithm, least-squares and BLUE methods, method of moments, the linear model.
  • Spectrum estimation : Non-parametric techniques : periodogram, windowing, spectral leakage and resolution. Parametric techniques : autoregressive processes, linear prediction, maximum entropy, Levinson and Schur algortihms, lattice filters. Time and frequency domain localization, short-time Fourier transform, wavelet transform, QMF, subbands, perfect reconstruction filter banks.
  • Optimal filtering : Wiener filtering, non-causal, causal and FIR, application to channel equalization. Kalman filtering : time-varying and time-invariant state-space models. Application to channel tracking.
  • Adaptive Filtering : Some elements from optimisation theory, steepest-descent algorithm. The LMS (least mean Square) and RLS (Recursive Least-Squares) algorithms, performance analysis. Tracking time-varying parameters, applications.
  • Sinusoids in Noise : Maximum likelihood estimation, Cramer-Rao bounds, IQML algorithm and variations, subspace techniques, moment matching, MVDR filtering, Prony and Pisarenko techniques, Capon method, adaptive notch filtering.
Nb hours: 42.00
Nb hours per week: 3.00
Control form: examen écrit