Discrete-time and Statistical Signal Processing

Fall Semester 2022

Prof. Hans-Andrea Loeliger

Location: HG F3, Zoom (meeting ID will be sent to the registered participants)
Lectures:­ Tuesdays, 14:15 – 16:00
Tutorial Sessions: HG F3, Zoom (time slots & meeting IDs will be announced to the registered participants)
Assistants: Guy Revach

Lecture Notes, Problems, and Solutions (login)


The course introduces some fundamental topics of digital signal processing with a bias towards applications in communications. The two main themes are linearity and probability. In the first part of the course, we deepen our understanding of discrete-time linear filters. In the second part of the course, we review the basics of probability theory and discrete-time stochastic processes. We then discuss some basic concepts of detection theory and estimation theory, as well as some practical methods including LMMSE estimation and LMMSE filtering, the LMS algorithm, and the Viterbi algorithm. A recurrent theme is the stable and robust "inversion" of a linear filter.


1. Discrete-time linear systems and filters:
state-space realizations, z-transform and spectrum,
decimation and interpolation, digital filter design,
stable realizations and robust inversion.

2. The discrete Fourier transform and its use for digital filtering.

3. The statistical perspective:
probability, random variables, discrete-time stochastic processes;
detection and estimation: MAP, ML, Bayesian MMSE, LMMSE;
Wiener filter, LMS adaptive filter, Viterbi algorithm.

Who should attend?

Students interested in signal processing – virtually every student of electrical engineering.

Lecture Notes

Complete lecture notes are available in electronic form.


180 minutes written examination.
Lecture Notes (not including problems and solutions) and personal notes (max. 4 pages). No electronic devices. (Pocket calculators will be handed out, if necessary.)

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