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.- 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.
Exam
In the academic year 2024-2025, this course is not taught. In the new BSc this course will reappear as EE3S1. Until then, there will be two final resits, 15 April 2025 13:30--16:30, and 16 July 2025 13:30--16:30.
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
- 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.
- 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.
All classes have been video-recorded in Collegerama in 2022.
Teachers
prof.dr.ir. Alle-Jan van der Veen (AJV), dr. Geethu Joseph (GJ), and dr. Borbala Hunyadi (BoH).
Program
The program for Spring 2024 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 2022 |
|||
|---|---|---|---|---|---|---|---|---|
| 1. | 22/4/2024 | 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_01 | |
| 2. | 23/4/2024 | GJ | DSP: Introduction and examples |
6.1, 6.2, 6.3, 6.4, 6.5 | DSP: Chs. 1, 6 |
DSP 1 |
EE2S31_02 | |
| 3. | 25/4/2024 |
AJV | Pairs of random vectors (cont'd) |
8.1.3, 8.2.3, 8.4.1, 8.4.3, 8.4.5 |
SP: Ch. 8 |
SP 2 | EE2S31_03 | |
| 4. | 29/4/2024 |
GJ | DSP: (Non-ideal) Sampling and Reconstruction |
6.6, 6.9, 6.10, 6.11, 6.12, 6.13, 6.14, 6.15, 6.24 |
DSP: 6.1 - 6.5 |
DSP 2 | EE2S31_04 | |
| 5. | 30/4/2024 |
AJV | 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 |
SP: Ch. 7 | SP 3 | EE2S31_05 | |
| 6. | 2/5/2024 |
AJV | Moment generating function, central limit theorem. |
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: | SP 3 | EE2S31_05 | |
| 7. | 6/5/2024 |
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: |
SP 4 | EE2S31_06 | |
| 8. | 7/5/2024 |
GJ | DSP: Sampling in frequency domain, Discrete Fourier Transform (DFT) |
7.1, 7.7, 7.11, 7.12, 7.13, 7.23 |
DSP: 7.1 - 7.2 |
DSP 3 | EE2S31_07 | |
| 9. | 13/5/2024 |
AJV | Exercise session |
|
SP |
SP Exercise | EE2S31_09 | |
| 10. | 14/5/2024 |
GJ | DSP: Spectral analysis and filtering using DFT |
7.2, 7.3, 7.6, 7.8, 7.9, 7.14, 7.15, 7.21 |
DSP: 7.3, 7.4, 10.2 |
DSP 4
|
EE2S31_08 | |
| 11. | 16/5/2024 | GJ | DSP: Efficient implementation of the DTF: FFT. Exercises |
8.1, 8.3, 8.4, 8.7, 8.8, 8.11, 8.19, 8.20 |
DSP: 8.1, 8.2 |
DSP 5
|
EE2S31_10 | |
| 22/5/2024 | Exam (part 1). Note: the FFT is examined in part 2. |
|||||||
| 12. | 27/5/2024 | 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_12 | |
| 13. | 28/5/2024 | AJV | 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_13 | |
| 14. | 30/5/2024 | BoH | DSP: Quantization and round-off effects |
6.18, 9.31, 9.32, 9.33, 9.34, 9.35, 9.38
|
DSP: 6.3, 9.4 - 9.6 |
DSP 6 | EE2S31_11 | |
| 15. | 3/6/2024 | AJV | The autocorrelation function & signal processing, PSD |
supplement: 5.1, 6.1 |
SP: supplement sections 5 and 6 |
SP 7 | EE2S31_14 | |
| 16. | 6/6/2024 | BoH | DSP: Sigma-delta modulation |
6.16, 6.18, 6.20 |
DSP: 6.6 |
DSP 7 | EE2S31_15 | |
| 17. | 10/6/2024 | AJV | PSD, CPSD, frequency domain relationships. |
supplement: 7.1, 8.1, 8.3, 8.5 |
SP: supplement sections 7 & 8 |
SP 8 | EE2S31_16 | |
| 18. | 13/6/2024 | BoH | DSP: Multi-rate signal processing |
11.1, 11.5, 11.9, 11.10, 11.11, 11.12 |
DSP: 11.1 - 11.8 |
DSP 8 |
EE2S31_17 | |
| 19. | 17/6/2024 | AJV | SP: Exercise session |
SP 9 |
EE2S31_18 | |||
| 20. | 20/6/2024 | BoH | DSP: Exercise session | DSP 9 | EE2S31_19 | |||
cancelled |
DSP: Lattice filter structures (not since 2022) |
9.12,9.13, 9.15 |
DSP: 9.2.4, 9.3.5 |
DSP 10 | ||||
| 28/6/2024 | Exam (part 2) | |||||||
| 17/7/2024 | Resit | |||||||
| 17/4/2025 | Resit | |||||||
| 16/7/2025 | Resit |
Past exams
Exam (complete) of July 2024, with Solutions.Exam (part 2) of June 2024, with Solutions.
Exam (part 1) of May 2024, with Solutions.
Exam (complete) of July 2023, with Solutions.
Exam (part 2) of June 2023, with Solutions.
Exam (part 1) of May 2023, with Solutions.
Exam (complete) of July 2022, with Solutions.
Exam (part 2) of June 2022, with Solutions.
Exam (part 1) of May 2022, with Solutions.
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.
