EE3S1 Signal Processing

This course was previously taught as EE2S31 Signals Processing.

Introduction

Signal processing plays an important role in many applications, such as consumer electronics (mp3 player, mobile phone, CD player, TV (HD)), radar and medical applications. This course covers two topics: an introduction into random signals (following the course Probability and Statistics, EE2M1), and a first course on digital signal processing (following the course Signals and Systems, EE2S1).

In this course the following topics are discussed:

Digital signal processing

The part on signal processing considers in particular one-dimensional signals and discusses digital filter design, filter structures, the DFT spectral analysis, filter implementation, and multirate filters.

Repetition: (discrete-time) signal processing, poles and zeros, filter functions
Non-ideal sampling and reconstruction
Sampling in the frequency domain, the Discrete Fourier Transform
Spectral analysis and filtering using the DFT
Efficient computation of the DFT: the FFT
Digital filter structures based on allpass filters
Quantization and rounding errors in filters
Analog-to-digital conversion using sigma-delta modulation
Multirate signal processing

Stochastic processes

The part on stochastic processes introduces the concept of stochastic models and random processes to describe systems and signals that are not deterministic in nature.

Pairs of random variables
Random vectors & conditional probability models
Sums of random variables,
Derived random variables
moment generating function
central limit theorem.
Deviation of RVs from its expected value:Markov ineq., Chebyshev ineq. and the Chernoff bound.
Sample mean, unbiased estimators, consistency.
Estimation of Random variables, blind estimation, conditional estimation, MMSE, MAP and ML estimators.
Stochastic processes.
Estimation of autocorrelation functions, ergodicity, the autocorrelation function & signal processing for WSS signals.
The autocorrelation function & signal processing, PSD, CPSD & frequency domain relationships.

Course labs

The course has 4 courselabs, in week 2, 4, 6, 8. The course labs are pass/fail; you need a pass on each of the labs. The labs use Jupyter Colab and Python programming. You work in groups of 2 (create your own groups in Brightspace). The labs take place in the Tellegenhall (presence required; some audio equipment is needed).

Exam

The written exam consists of exercises from both SSP and DSP (roughly 50/50). The exams are closed book. You are permitted to bring one A4-size page (2 sides) of handwritten notes.

The results of the courselabs are pass/fail; you need a pass to activate your final grade in Osiris.

Books

Stochastic processes: R.D. Yates and D.J. Goodman,"Probability and Stochastic Processes, A Friendly Introduction for Electrical and Computer Engineers", 3rd edition, 2014. The TU Delft Library has an e-book version that you can access online (you will need to login using your TU Delft email address).
Signal Processing supplement, which belongs to Stochastic processes: R.D. Yates and D.J. Goodman,"Probability and Stochastic Processes", 3rd edition, 2014.
Thomas Holton: "Digital Signal Processing". Cambridge Univ. Press, 2021

A solution manual including answers to some of the problems in "Probability and Stochastic Processes" can be downloaded from here.

All classes have been video-recorded in Collegerama in 2022. Since then the DSP material has changed, so the 2022 recordings for DSP are not recommended.

Teachers

prof.dr.ir. Alle-Jan van der Veen (AJV) and dr. Geethu Joseph (GJ).

Program

The program for Spring 2026 is as follows:

SSP refers to classes on stochastic signal processing, and DSP refers to classes on digital signal processing.

	Date		Content	Exercises	Chapter	Slides	Collegerama 2022
1.	Tue 10 Feb	AJV	DSP: General intro to the course. Recap: Dig signals, z-transform, DTFT, realizations		DSP: Ch. 2, 3, 4, 5	DSP 1
2.	Thu 12 Feb	AJV	DSP: Recap sampling; non-ideal sampling, bandpass sampling (not in book)		DSP: Ch. 6.1-6.4	DSP 2
3.	Fri 13 Feb	GJ	SSP: Introduction. Pairs of random variables	5.1.1, 5.2.1, 5.2.2, 5.3.2, 5.4.1, 5.5.3, 5.5.8, 5.5.9, 5.7.9, 5.7.13, 5.8.3, 5.9.2	SSP: Ch. 5	SSP 1	EE2S31_01
P1	Tue 17 Feb	AJV	Course Lab 1: Aliasing; down and upsampling	(Brightspace)
4.	Thu 19 Feb	AJV	DSP: Down and upsampling; multistage resampling		DSP: Ch. 6.5; 13.5	DSP 3	EE2S31_07
5.	Fri 20 Feb	GJ	SSP: Pairs of random variables (cont'd) Random vectors	8.1.3, 8.2.3, 8.4.1, 8.4.3, 8.4.5	SSP: Ch. 8	SSP 2	EE2S31_03
6.	Tue 24 Feb	GJ	SSP: Conditional probability models Sums of random variables, derived random variables	7.1.1, 7.2.3, 7.2.9, 7.3.1, 7.3.3, 7.3.5, 7.3.9, 7.5.1, 7.5.3, 7.5.5 6.2.1, 6.2.5, 6.2.7	SSP: Ch. 7 Ch. 6.2, 6.5	SSP 3	EE2S31_05
7.	Thu 26 Feb	AJV	DSP: Discrete Fourier Transform (DFT); circular convolution		DSP: Ch. 10.1--10.3 (skip 10.2.5, 10.2.6)	DSP 4
8.	Fri 27 Feb	GJ	SSP: Moment generating function, central limit theorem. Deviation of RVs from its expected value: Markov ineq., Chebyshev ineq. and the Chernoff bound. Sample mean, unbiased estimators, consistency	9.2.1, 9.2.3, 9.3.3, 9.3.5, 9.3.7 10.2.1, 10.2.3, 10.2.5, 10.3.1	SSP: Ch. 9 and 10	SSP 3	EE2S31_05
P2	Tue 3 Mar	AJV	Course Lab 2: random vars: histogram pdf fitting; sum of two rv; autocorrelation	(Brightspace)
9.	Thu 5 Mar	AJV	DSP: Spectral analysis; matrix representation, zero padding, STFT, spectrograms		DSP: Ch. 10.2.5, 10.2.6, 10.4, 10.5; (Ch. 14.1, 14.2?)	DSP 5
10.	Fri 6 Mar	GJ	SSP: Estimation of random variables, blind estimation, conditional estimation, MMSE, MAP and ML estimators [Note errata on slides]	12.1.312.1.5, 12.2.1, 12.2.3, 12.2.5, 12.3.3, 12.4.3	SSP: Ch. 12	SSP 4	EE2S31_06
11.	Tue 10 Mar	GJ	SSP: Exercises		SSP	SSP Exercise	EE2S31_09
12.	Thu 12 Mar	AJV	DSP: Sigma-Delta quantizer		DSP: Ch. 6.7	DSP 6
13.	Fri 13 Mar	GJ	SSP: Stochastic processes	13.1.1, 13.3.1, 13.7.1, 13.7.3, 13.7.5, 13.9.3, 13.9.5, 13.9.7, 13.10.1, 13.10.3	SSP: Ch. 13 (except 13.4- 13.6)	SSP 5	EE2S31_12
P3	Tue 17 Mar	AJV	Course Lab 3: sigma-delta ADC	(Brightspace)
14.	Thu 19 Mar	AJV	DSP: Efficient implementation of the DTF: FFT. Overlap-add method		DSP: Ch. 11	DSP 7
15.	Fri 20 Mar	GJ	SSP: Estimation of autocorrelation functions, ergodicity, the autocorrelation function & signal processing for WSS signals.	Supplement: 1.1, 1.3, 2.1, 2.3, 2.5, 2.7	SSP: Supplement sections 1 and 2	SSP 6	EE2S31_13
16.	Tue 24 Mar	GJ	SSP: The autocorrelation function & signal processing, PSD	supplement: 5.1, 6.1	SSP: supplement sections 5 and 6	SSP 7	EE2S31_14
17.	Thu 26 Mar	AJV	DSP: Extra topics: option A: realizations (ladder, lattice; quantization), option B: multirate		DSP: A: Chapter 9; B: Chapter 13	DSP 6	EE2S31_11
18.	Fri 27 Mar	GJ	SSP: PSD, CPSD, frequency domain relationships	supplement: 7.1, 8.1, 8.3, 8.5	SSP: supplement sections 7 & 8	SSP 8	EE2S31_16
19.	Mon 30 Mar	GJ	SSP: Exercises			SSP 9	EE2S31_18
P4	Tue 31 Mar	AJV	Course Lab 4: 2-microphone adaptive noise cancellation	(Brightspace)
20.	Thu 2 Apr	AJV	DSP: Exercises
	Thu 16 Apr		Exam
	Thu 16 Jul		Resit

Past exams

Prior to 2025, this course was taught as EE2S31 Signal Processing. Most of the course content has not changed, so you can use old exams as study material. However, for the DSP part a new book is used, the slides have been reorganized and updated, and some material is dropped/added. The new course does not have midterm exams.