EE2S11 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.

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.

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.

Book

"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 3rd edition are marginal.

For this book, there is an Elsevier website with additional resources.

Most classes have been video-recorded in Collegerama 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 2023 is as follows:


Date
Content Chaparro Slides Collegerama 2015 (NL) Collegerama 2018 (EN) Collegerama 2021 (EN)
1. Mon 13 Nov RR Introduction. Continuous-time signals, elementary signals and operations. Rectangle function, sinc function, sign function. Properties of elementary signals. Ch. 1 Ch.0 slides
Ch.1 slides
01 11/13/2018 EE2S11_01
2. Wed 15 Nov RR Properties of elementary signals (cont'd). Dirac distribution + exercises. (see slides) Exercises 02 11/16/2018 EE2S11_02
3. Mon 20 Nov RR Continuous-time systems: Linear time-invariant systems. Convolution integral. BIBO stability. Ch. 2 Ch.2 slides 03 11/20/2018 EE2S11_03
4. Wed 22 Nov RR Eigenfunctions and eigenvalues of LTI systems. Introduction of the Laplace transform. ROC of the Laplace transform. Properties of the Laplace transform. Ch. 3 Ch.3a slides EE2S11_04 11/23/2018 EE2S11_04
5. Fri 24 Nov RR Exercises
6. Mon 27 Nov RR Inverse Laplace transform using partial fraction expansion; contour integral and residues. Ch. 3 (cont'd) Ch.3b slides Solutions EE2S11_05 11/27/2018 EE2S11_05
7. Wed 29 Nov RR Introduction to Fourier series analysis, eigenfunction property, Fourier series (complex and goniometric) of a periodic signal. Line spectrum. Ch. 4 Ch.4 slides
(old slides)
EE2S11_06 11/30/2018 EE2S11_06
8. Mon 4 Dec RR Relation of Fourier series to the Laplace transform. Properties of Fourier series; convergence analysls (Gibbs phenomenon). Ch. 4 (cont'd) Ch.4 slides (cont'd) (not on collegerama) EE2S11_07 12/4/2018 EE2S11_07
9. Wed 6 Dec RR Exercises; trial exam solutions
(Note: since 2020 the midterm exam is earlier than in previous years, and Chapter 5 Fourier Transform is now covered in the final exam.)
EE2S11_09 EE2S11_10 12/11/2018 (no mic) EE2S11_08
10. Fri 8 Dec RR Exercises
Wed 13 Dec Exam (part 1)
11. Fri 15 Dec AJV The Fourier Transform, spectral representation, Parseval, time-frequency duality. Properties of the Fourier transform. Ch. 5 Ch.5 slides Table w/properties Exercises EE2S11_08 12/7/2018 EE2S11_09
12. Mon 18 Dec 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 slides

Ch.8 slides
Exercises
EE2S11_11 12/14/2018 EE2S11_10
13. Wed 20 Dec AJV Discrete-time LTI systems, convolution. Ch 9 (skip 9.4) Ch.9 slides EE2S11_12 12/18/2018 EE2S11_11
14. Mon 8 Jan AJV Z-transform, convolution, stability, inverse z-transform. Ch. 10 (skip 10.5.3, 10.6 and 10.7) Ch. 10 slides
EE2S11_13 1/8/2019 Bongo
15. Wed 10 Jan AJV Discrete-time Fourier transform (DTFT); inverse DTFT.
(Note erratum mentioned on slide 26, related to the 2nd edition)
Ch. 11.2 (skip 11.2.5) Ch. 11 slides EE2S11_14 1/11/2019 Bongo
16. Fri 12 Jan Exercises sampling, z-transform, DTFT. ex.Ch.8 sampling
ex.Ch.9 LTI
ex.Ch.10 Z-transf.
ex.Ch.11 DTFT
17. Mon 15 Jan AJV Analog filter design: analog filter functions, IIR filter design; Butterworth, Chebyshev. Frequency transformations. Ch. 7.3 Ch.7.3 slides EE2S11_15 1/15/2019 Bongo
18. Wed 17 Jan 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.12 slides EE2S11_16 1/18/2019 EE2S11_12
19. Fri 19 Jan AJV Canonical realizations (FIR, IIR, transposition).
Exercises convolution, filter design and realisations.
Ch.12.6
Filter design
Realizations
Ch. 12.6 slides
Slides a
Slides b
EE2S11_17 1/22/2019 EE2S11_13
20. Mon 22 Jan AJV Trial exam solutions Trial exam Solutions
EE2S11_18 1/25/2019
21. Wed 24 Jan AJ --
Tue 30 Jan Exam (part 2)
July Resit

Past exams

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.
Exam (complete) of July 2019, with Solutions.
Part 2 exam of February 2019, with Solutions.
Part 1 exam of December 2018, with Solutions.

Exercises

The book by Chaparro contains many exercises; for some you will need Matlab. Here are some representative exercises.

Regarding the 3rd edition (but the numbering of the Solutions refers to the 2nd edition):

Chapter 1: 1, 2, 3, 4, 6, 9, 12 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: 9, 10 Solutions

Regarding the 2nd edition (refer to the online copy of the book):

Chapter 1: 1, 2, 3, 4, 6, 8, 11, 12, 13, 16 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: 14, 15, 16 Solutions