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Discrete-Time and Statistical Signal Processing
Last Updated: 2026-02-05 15:48:05
Abstract
The course introduces some fundamental topics of digital signal processing with a bias towards applications in communications: discrete-time linear filters, inverse filters and equalization, DFT, discrete-time stochastic processes, elements of detection theory and estimation theory, LMMSE estimation and LMMSE filtering, LMS algorithm, Viterbi algorithm.
Objective
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 throughout the course is the stable and robust "inversion" of a linear filter.
Content
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.
Resources
Lecture Notes
Lecture Notes
General Information
- Language
- English
- Levels
- BSC , MSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- written 180 minutes
- Aids
- Lecture Notes (not including problems and solutions) and personal notes (max. 4 pages). No electronic devices. (Pocket calculators will be handed out, if necessary.)
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise | Discrete-Time and Statistical Signal Processing |
|
4 h weekly |
Offered In
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5th Semester: Third Year Core Courses (Can be freely combined, a list of recommendations is available under )
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Application Area (Only necessary and eligible for the Master degree in Applied Mathematics. One of the application areas specified must be selected for the category Application Area for the Master degree in Applied Mathematics. At least 8 credits are required in the chosen application area.)
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Computers and Networks (The core courses and specialisation courses below are a selection for students who wish to specialise in the area of "Computers and Networks", see . The individual study plan is subject to the tutor's approval.)
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Specialisation Courses (These specialisation courses are particularly recommended for the area of "Computers and Networks", but you are free to choose courses from any other field in agreement with your tutor. A minimum of 40 credits must be obtained from specialisation courses during the Master's Programme.)
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Energy and Power Electronics (The core courses and specialisation courses below are a selection for students who wish to specialise in the area of "Energy and Power Electronics", see . The individual study plan is subject to the tutor's approval.)
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Specialisation Courses (These specialisation courses are particularly recommended for the area of "Energy and Power Electronics", but you are free to choose courses from any other field in agreement with your tutor. A minimum of 40 credits must be obtained from specialisation courses during the Master's Programme.)
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Signal Processing and Machine Learning (The core courses and specialisation courses below are a selection for students who wish to specialise in the area of "Signal Processing and Machine Learning ", see . The individual study plan is subject to the tutor's approval.)
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Core Courses (These core courses are particularly recommended for the field of "Signal Processing and Machine Learning". You may choose core courses form other fields in agreement with your tutor. A minimum of 24 credits must be obtained from core courses during the MSc EEIT.)
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Foundation Core Courses (Fundamentals at bachelor level, for master students who need to strengthen or refresh their background in the area.)
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Communication (The core courses and specialisation courses below are a selection for students who wish to specialise in the area of "Communication", see . The individual study plan is subject to the tutor's approval.)
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Core Courses (These core courses are particularly recommended for the field of "Communication". You may choose core courses form other fields in agreement with your tutor. A minimum of 24 credits must be obtained from core courses during the MSc EEIT.)
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Foundation Core Courses (Fundamentals at bachelor level, for master students who need to strengthen or refresh their background in the area.)
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Major Courses (A total of 42 CP must be achieved during the Master Programme. The individual study plan is subject to the tutor's approval.)
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Recommended Subjects (These courses are recommended, but you are free to choose courses from any other special field. Please consult your tutor.)
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Recommended Subjects (These courses are recommended, but you are free to choose courses from any other special field. Please consult your tutor.)
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Electives (This is a selection of courses particularly suitable for the MSc QE. In agreement with the tutor, students may choose other courses from the ETH course catalogue.)
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