EE2S1 Signals and Systems
Introduction
Starting from complex function theory, this course develops the mathematical description of signals and linear time-invariant (LTI) systems by means of the Laplace and Fourier transforms. In this description, signals are represented by sums of complex exponentials, being the 'eigenfuctions' of LTI systems. It follows that the effect of an LTI system on a signal (convolution) can equivalently be described by a product in the Laplace or Fourier domain. The implications are profound and form the basis of a large part of electrical engineering (and other engineering studies). This course is the basis for follow-up courses sich as Digital Signal Processing.The course covers the Laplace, Fourier and z-transform, and presents the relations between signals in time domain and frequency domain, first for time-continuous (analog) signals, and then for time-discrete (digital) signals.
The course also covers the basics of analog filter design (analog filter functions, IIR filter design, Butterworth and Chebyshev filters), digital filter design via transformation of analog filters to digital filters (impulse invariance, bilinear transform, frequency transformations), and simple digital filter structures.
The course includes 3 lab sessions in the Tellegenhall, where you will apply and extend your knowledge on the course material. These take the form of Python programming exercises.
Exam
The exam is written and consists of two parts. The first part (week 5) covers time-continuous signals, the second part (week 10) time-discrete signals. The final grade is the average of the two parts. The resit exam covers the full course.The exams are closed book. You are permitted to bring one A4-size page (2 sides) of handwritten notes.
Each course lab exercise has to be signed off (pass/fail), and you need passes on all exercises to pass the course. These 3 passes are also an entry requirement for the EE2L1 IP3 practical in Q2.
Book
"Signals and Systems using MATLAB, Fourth Edition" by Aydin Akan and Luis Chaparro, Academic Press; 4rd edition (2024). ISBN: 978-0-443-15709-7.
You may also use "Signals and Systems using MATLAB, Third Edition" by Luis Chaparro and Aydin Akan, Academic Press; 3rd edition (2018). ISBN: 978-0128142042.
An electronic version of the 2nd edition of the book is available via the library: TU Delft Library. The differences with the newer editions are marginal.
We will make new Collegerama recordings in 2024. Most classes have also been video-recorded in 2021. There are earlier versions: 2015 available in dutch, and 2018 in english. Links are provided in the table below. For the english recordings, the links work only after logging in into Collegerama.
Teachers
dr.ir. Rob Remis (RR) and prof.dr.ir. Alle-Jan van der Veen (AJV).
Program
The program for Fall 2024 is as follows:
| Date | Content | Chaparro 3rd ed | Chaparro 4th ed | Slides | Collegerama 2015 (NL) | Collegerama 2018 (EN) | Collegerama 2021 (EN) | Collegerama 2024 (EN) | ||
|---|---|---|---|---|---|---|---|---|---|---|
| 1. | Mon 2 Sep | RR | Introduction. Continuous-time signals. Standard signals, Dirac impulse function. | Ch. 1 | Ch. 1 |
Ch.0 slides
Ch.1 slides | 01 | 11/13/2018 | EE2S11_01 | EE2S1_001 |
| 2. | Wed 4 Sep | RR | Dirac impulse function (cont'd). Exercises impulse function. LTI systems. | (see slides) | (see slides) | Exercises | 02 | 11/16/2018 | EE2S11_02 | EE2S1_002 |
| 3. | Mon 9 Sep | RR | Linear time-invariant (LTI) systems. Convolution integral. BIBO stability. The two-sided Laplace transform. | Ch. 2 | Ch. 2 | Ch.2 slides | 03 | 11/20/2018 | EE2S11_03 | EE2S1_003 |
| 4. | Wed 11 Sep | RR | Exercises convolution. The two-sided Laplace transform (cont'd). | Ch. 3 | Ch. 3 | Ch.3a slides | EE2S11_04 | 11/23/2018 | EE2S11_04 | EE2S1_004 |
| 5. | Fri 13 Sep | RR | Two-sided Laplace transform (cont'd), one-sided Laplace transform, circuits and differential equations | Ch. 3 (cont'd) | Ch. 3 (cont'd) skip 3.9 | Ch.3b slides | EE2S1_005 | |||
| 6. | Mon 16 Sep | RR | One-sided Laplace transform, circuits and differential equations (cont'd), Exercises Laplace transform and its applications | Ch. 3 (cont'd) | Ch. 3 (cont'd) skip 3.9 | Solutions | EE2S11_05 | 11/27/2018 | EE2S11_05 | EE2S1_006 |
| 7. | Wed 18 Sep | RR | Introduction to Fourier series analysis, eigenfunction property, Fourier series (complex and goniometric) of a periodic signal. Line spectrum. | Ch. 4 | Ch. 4 | Ch.4a slides | EE2S11_06 | 11/30/2018 | EE2S11_06 | EE2S1_007 |
| 8. | Mon 23 Sep | RR | Relation of Fourier series to the Laplace transform. Properties of Fourier series; convergence analysls (Gibbs phenomenon). | Ch. 4 (cont'd) | Ch. 4 (cont'd) | Ch.4b slides | EE2S11_07 | 12/4/2018 | EE2S11_07 | EE2S1_008 |
| 9. | Wed 25 Sep | RR |
Exercises; trial exam solutions
(Note: since 2020, Chapter 5 Fourier Transform is covered in the final exam.) | EE2S11_09 EE2S11_10 | 12/11/2018 (no mic) | EE2S11_08 | EE2S1_009 | |||
| 10. | Fri 27 Sep | RR | Exercises | EE2S1_010 | ||||||
| Mon 30 Sep | Exam (part 1) | |||||||||
| 11. | Wed 2 Oct | AJV | The Fourier Transform, spectral representation, Parseval, time-frequency duality. Properties of the Fourier transform. | Ch. 5 | Ch. 5 (skip 5.9) | Ch.5 slides Table w/properties Exercises | EE2S11_08 | 12/7/2018 | EE2S11_09 | EE2S1_011 |
| 12. | Fri 4 Oct | AJV |
Basics of filtering: phasors, relation poles/zeros to the frequency response.
Sampling, Nyquist-Shannon theorem, reconstruction using sinc interpolation. |
Ch. 5.7 Ch. 8 (skip 8.3, 8.4) |
Ch. 5.7 Ch. 6 (skip 6.3, 6.4) |
Ch.5.7 slides
Ch.8 slides Exercises | EE2S11_11 | 12/14/2018 | EE2S11_10 | EE2S1_012 |
| 13. | Mon 7 Oct | AJV | Discrete-time LTI systems, convolution. | Ch. 9 (skip 9.4) | Ch. 7 (skip 7.4) | Ch.9 slides | EE2S11_12 | 12/18/2018 | EE2S11_11 | EE2S1_013 |
| P1 | Wed 9 Oct | AJV | Course Lab 1: Convolution | (Brightspace) | ||||||
| 14. | Fri 11 Oct | AJV | Z-transform, convolution, stability | Ch. 10 (skip 10.5.3, 10.6 and 10.7) | Ch. 8 (skip 8.5.3, 8.6 and 8.7) |
Ch. 10 slides
| EE2S11_13 | 1/8/2019 | Bongo | EE2S1_014 |
| 15. | Mon 14 Oct | AJV | Discrete-time Fourier transform (DTFT); inverse DTFT. | Ch. 11.2 (skip 11.2.5) | Ch. 9.2 (skip 9.2.5) | Ch. 11 slides | EE2S11_14 | 1/11/2019 | Bongo | EE2S1_001 (first half no audio) |
| P2 | Wed 16 Oct | AJV | Course Lab 2: Frequency domain | (Brightspace) | ||||||
| 16. | Fri 18 Oct | AJV | Analog filter design: analog filter functions, IIR filter design; Butterworth, Chebyshev. Frequency transformations. | Ch. 7.3 | Ch. 5.9.2 | Ch.7.3 slides | EE2S11_15 | 1/15/2019 | Bongo | EE2S1_001 |
| 17. | Mon 21 Oct | AJV | Digital filter design using the truncated impulse response design technique. Windows. Transformation of analog filters to digital filters (impulse invariance, bilinear transform). | Ch. 12 t/m 12.5 (skip 12.4.4, 12.4.5) | Ch. 10 t/m 10.5 (skip 10.4.4, 10.4.5) |
Ch.12 slides
Exercises | EE2S11_16 | 1/18/2019 | EE2S11_12 | EE2S1_015 |
| P3 | Wed 23 Oct | AJV | Course Lab 3: Filter design | (Brightspace) | ||||||
| 18. | Fri 25 Oct | AJV |
Inverse z-transform.
Canonical realizations (FIR, IIR, transposition). |
Ch.10.5.1, 10.5.2, 10.5.5. Ch.12.6 |
Ch. 8.5.1, 8.5.2, 8.5.5. Ch.10.6 |
Ch. 10.5 slides Ch. 12.6 slides Exercises | EE2S11_17 | 1/22/2019 | EE2S11_13 | EE2S1_016 |
| 19. | Mon 28 Oct |
Exercises convolution, filter design and realisations.
Exercises sampling, z-transform, DTFT. |
ex.Ch.8 sampling ex.Ch.9 LTI ex.Ch.10 Z-transf. ex.Ch.11 DTFT |
Exam Jan 2024 Slides a Slides b | EE2S1_017 | |||||
| 20. | Wed 30 Oct | AJV |
Trial exam LECTURE CANCELLED | Trial exam | Trial exam |
Solutions | EE2S11_18 | 1/25/2019 | ||
| Thu 7 Nov | Exam (part 2) | |||||||||
| Tue 17 Dec | Resit |
Past exams
Before September 2024, the course was called EE2S11. The content of the course has not changed; the old exams of EE2S11 are also representative for the current exams.
Exam (part 2)
of November 2024, with
Solutions.
Exam (part 1)
of September 2024, with
Solutions.
Exam (complete)
of July 2024, with
Solutions.
Exam (part 2)
of January 2024, with
Solutions.
Exam (part 1)
of December 2023, with
Solutions.
Exam (complete)
of July 2023, with
Solutions.
Exam (part 2)
of January 2023, with
Solutions.
Exam (part 1)
of December 2022, with
Solutions.
Exam (complete)
of July 2022, with
Solutions.
Exam (part 2)
of January 2022, with
Solutions.
Exam (part 1)
of December 2021, with
Solutions.
Exam (complete)
of July 2021, with
Solutions.
Exam (part 2)
of January 2021, with
Solutions.
Exam (part 1)
of December 2020, with
Solutions.
Exam (complete)
of July 2020, with
Solutions.
Exam (part 2)
of Jan 2020, with
Solutions.
Exam (part 1)
of December 2019, with
Solutions.
Exercises
The book by Chaparro contains many exercises; for some you will need Matlab. Here are some representative exercises.Regarding the 4th edition (but the numbering of the Solutions refers to the 2nd edition):
| Chapter 1: | 1, 2, 3, 4, 5, 7, 9, 12, 14, 15, 16 | Solutions |
| Chapter 2: | 1, 2, 3, 5, 6, 7, 10, 12, 13, 16 | Solutions |
| Chapter 3: | 1, 2, 5, 6, 8, 9, 10, 11, 17, 19, 21, 24, 25 | Solutions |
| Chapter 4: | 2,4, 6, 7, 9, 10, 14, 15, 18 | Solutions |
| Chapter 5: | 1, 2, 3, 4, 5, 12, 15, 16, 19 | Solutions |
| Chapter 5.9.2: | 26, 38 | Solutions |
| Chapter 6: | 2, 3, 4, 6, 7, 8, 11 | Solutions |
| Chapter 7: | 1, 3, 4, 6, 9, 10, 11, 13, 14, 16, 17, 23, 23 | Solutions |
| Chapter 8: | 1, 2, 3, 5, 7, 9, 12, 13, 14, 15, 17, 21 | Solutions |
| Chapter 9: | 1, 2, 3, 4, 5, 7, 8, 9 | Solutions |
| Chapter 10: | 11, 14, 15, 16 | Solutions |
Regarding the 3rd edition (but the numbering of the Solutions refers to the 2nd edition):
| Chapter 1: | 1, 2, 3, 4, 6, 8, 9, 11, 12, 13 | Solutions |
| Chapter 2: | 1, 2, 3, 4, 5, 8, 9, 11 | Solutions |
| Chapter 3: | 1, 3, 4, 6, 7, 8, 13, 15, 17, 20, 21 | Solutions |
| Chapter 4: | 2, 3, 4, 5, 7, 8, 10, 11, 12 | Solutions |
| Chapter 5: | 1, 2, 3, 4, 5, 13, 14, 16 | Solutions |
| Chapter 7: | 9 | Solutions |
| Chapter 8: | 2, 3, 4, 5, 8 | Solutions |
| Chapter 9: | 1, 2, 3, 5, 7, 8, 9, 11, 12, 14, 15, 20, 21 | Solutions |
| Chapter 10: | 1, 2, 3, 6, 8, 9, 14 | Solutions |
| Chapter 11: | 1, 2, 3, 4, 5, 7, 8, 9 | Solutions |
| Chapter 12: | 7, 9, 10 | Solutions |
Regarding the 2nd edition (refer to the online copy of the book):
| Chapter 1: | 1, 2, 3, 4, 6, 8, 10, 13, 15, 16, 17 | Solutions |
| Chapter 2: | 1, 2, 4, 5, 7, 8, 9, 12, 14, 15, 18 | Solutions |
| Chapter 3: | 1, 2, 4, 5, 7, 9, 10, 11, 12, 13, 18, 20, 22, 25, 29, 30 | Solutions |
| Chapter 4: | 2, 4, 6, 7, 9, 10, 12, 13, 17, 18, 21 | Solutions |
| Chapter 5: | 1, 2, 3, 5, 6, 7, 14, 17, 18, 19, 22 | Solutions |
| Chapter 7: | 9, 11, 12 (skip 12.b) | Solutions |
| Chapter 8: | 2, 3, 5, 8, 9, 10, 13, 15 | Solutions |
| Chapter 9: | 1, 2, 3, 6, 9, 10, 11, 13, 14, 15, 17, 18, 19, 25, 27 | Solutions |
| Chapter 10: | 1, 2, 3, 5, 7, 10, 13, 14, 15, 16, 18, 24 | Solutions |
| Chapter 11: | 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12 | Solutions |
| Chapter 12: | 11, 14, 15, 16 | Solutions |
