# EE2S31 Signal 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, EE1M31), and a first course on digital signal processing (following the course Signals and Systems, EE2S11).

For study guide information (teaching goals, etc.), see Study guide.

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.
1. Repetition: (discrete-time) signal processing, poles and zeros, filter functions
2. Non-ideal sampling and reconstruction
3. Sampling in the frequency domain, the Discrete Fourier Transform
4. Spectral analysis and filtering using the DFT
5. Efficient computation of the DFT: the FFT
6. Digital filter structures based on allpass filters
7. Quantization and rounding errors in filters
8. Analog-to-digital conversion using sigma-delta modulation
9. 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.
1. Pairs of random variables
2. Random vectors & conditional probability models
3. Sums of random variables,
4. Derived random variables
5. moment generating function
6. central limit theorem.
7. Deviation of RVs from its expected value:Markov ineq., Chebyshev ineq. and the Chernoff bound.
8. Sample mean, unbiased estimators, consistency.
9. Estimation of Random variables, blind estimation, conditional estimation, MMSE, MAP and ML estimators.
10. Stochastic processes.
11. Estimation of autocorrelation functions, ergodicity, the autocorrelation function & signal processing for WSS signals.
12. The autocorrelation function & signal processing, PSD, CPSD & frequency domain relationships.

### Exam

The examination of the course is conducted in two parts (in the middle and at the end of the quarter). Both partial exams contain a 50/50 distribution of questions on signal processing and stochastic processes.
The final grade is the average of the two partial exam results. This calculation is done with one decimal place, and the final grade will be rounded to half a digit. The re-examination is conducted in one part (over all lecture material). The result of the partial exams expires for re-examination and is not transferable to the next year.

Be sure to register for each partial exam on Osiris!

The exams are closed book. You are permitted to bring one A4-size page (2 sides) of HANDWRITTEN notes.

### Books

1. 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).
2. Signal Processing supplement, which belongs to Stochastic processes: R.D. Yates and D.J. Goodman,"Probability and Stochastic Processes", 3rd edition, 2014.
3. Digital Signal processing: J.G. Proakis and D.G. Manolakis, "Digital signal processing, principle, algorithms and applications", 4th edition (Pearson international edition).

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

Most classes have been video-recorded in Collegerama in 2016. However, since then the teachers have changed, so that the ordering of some of the lectures has been modified, and new slides with different emphasis on some of the topics are being introduced. So it merits to attend the lectures.

### Teachers

prof.dr.ir. Alle-Jan van der Veen (AJV) and dr. Borbala Hunyadi (BoH).

## Program

The program for Spring 2021 is as follows:

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

Date
Content Exercises Chapter Slides Collegerama
1. 21/4/2021 AJV

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

SP: Ch. 5

welcome SP 1 EE2S31_SP1
2. 23/4/2021 BoH

DSP: Introduction and examples

DSP: Ch. 1

DSP 1
EE2S31_DSP1
3.

28/4/2021

AJV

Random vectors & conditional probability models

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
8.1.3, 8.2.3, 8.4.1, 8.4.3, 8.4.5

SP:
Chs. 7, 8

SP 2

EE2S31_SP2

4.

30/4/2021

BoH

DSP: (Non-ideal) Sampling and Reconstruction

6.6, 6.10

DSP: 6.1 t/m 6.5

DSP 2 EE2S31_DSP2
5.

3/5/2021

AJV

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

6.2.1, 6.2.5, 6.2.7, 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

SP:
Ch. 6.2, 6.5, 9 and 10

SP 3 EE2S31_SP3
6.

7/5/2021

BoH

DSP: Sampling in frequency domain, Discrete Fourier Transform (DFT)

7.1, 7.21,7.23

DSP: 7.1 - 7.2

DSP 3 (from slide 31) EE2S31_DSP3 from 58:00
7.

10/5/2021

BoH

DSP: Spectral analysis and filtering using DFT

7.3, 7.14

DSP: 7.3, 7.4, 10.2

DSP 4
EE2S31_DSP4 (from 1:12:45)
8.

12/5/2021

AJV

Estimation of Random variables, blind estimation, conditional estimation, MMSE, MAP and ML estimators

12.1.312.1.5, 12.2.1, 12.2.3, 12.2.5, 12.3.3, 12.4.3

SP:
Ch. 12

SP 4 EE2S31_SP4
9.

19/5/2021

AJV

Exercise session

SP

SP Exercise
10. 21/5/2021 BoH

DSP: Efficient implementation of the DTF: FFT. Exercises

8.1, 8.3

DSP: 8.1, 8.2

DSP 5 (from slide 7)
EE2S31_DSP5 from 33:20 to 41:30
11. 28/5/2021 Exam (part 1)
12. 31/5/2021 BoH

DSP: Quantization and round-off effects

9.19, 9.34. 9.36

DSP: 6.3, 9.4 - 9.6

DSP 6 EE2S31_DSP7
13. 2/6/2021 AJV

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

SP: Ch. 13 (except 13.4- 13.6)

SP 5
EE2S31_SP5
14. 7/6/2021 BoH

DSP: Sigma-delta modulation

6.16, 6.18, 6.20

DSP: 6.6

DSP 7 EE2S31_DSP7
15. 9/6/2021 AJV

Example: the random telegraph signal, 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

SP: Supplement sections 1 and 2

SP 6 EE2S31_SP6
16. 14/6/2021 BoH

DSP: Multi-rate signal processing

11.1, 11.5, 11.9, 11.10, 11.11, 11.12

DSP: 11.1 t/m 11.8

DSP 8
EE2S31_DSP9
17. 16/6/2021 AJV

The autocorrelation function & signal processing, PSD

supplement: 5.1, 6.1

SP: supplement sections 5 and 6

SP 7 EE2S31_SP7
18. 21/6/2021 BoH

DSP: Exercise session

19. 23/6/2021 AJV

PSD, CPSD, frequency domain relationships.

supplement: 7.1, 8.1, 8.3, 8.5

SP: supplement sections 7 & 8

SP 8
EE2S31_SP8
20. cancelled AJV

SP: Exercise session

21.

cancelled

DSP: Lattice filter structures (not in 2021)

9.12,9.13, 9.15

DSP: 9.2.4, 9.3.5

DSP 9
22. 1/7/2021 Exam (part 2)
23. 27/7/2021 Resit

### Past exams

Exam (complete) of July 2021, with Solutions.
Exam (part 2) of July 2021, with Solutions.
Exam (part 1) of May 2021, with Solutions.
Exam (complete) of July 2020, with Solutions.
Part 2 exam of July 2020, with Solutions.
Part 1 exam of May 2020, with Solutions.
Exam (complete) of July 2019, with Solutions.
Part 2 exam of July 2019, with Solutions.
Part 1 exam of May 2019, with Solutions.
Exam (complete) of July 2018, with Solutions.
Part 2 exam of July 2018, with Solutions.
Part 1 exam of May 2018, with Solutions.
Part 2 exam of July 2017, with Solutions.
Part 1 exam of May 2017, with Solutions.
Exam (complete) of July 2016, with Solutions.
Part 2 exam of June 2016, with Solutions.
Part 1 exam of May 2016, with Solutions.