# 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 were video-recorded in Collegerama in 2015 (available in dutch). We recorded them again in 2018 (in english); unfortunately the blackboard notes are missing in about half of the recordings. 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 2021 is as follows:

Date | Content | Chaparro | Slides | Collegerama 2015 (NL) | Collegerama 2018 (EN) | Collegerama 2021 (EN) | ||
---|---|---|---|---|---|---|---|---|

1. | Wed 10 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. | Fri 12 Nov | RR | Properties of elementary signals (cont'd). Dirac distribution + exercises. | (see slides) | Exercises | 02 | 11/16/2018 | EE2S11_02 |

3. | Wed 17 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. | Fri 19 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. | Wed 24 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 |

6. | Fri 26 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 |

7. | Wed 1 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 |

8. | Fri 3 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 | ||

Wed 8 Dec | Exam (part 1) | |||||||

9. | Fri 10 Dec | AJV | The Fourier Transform, spectral representation, Parseval, time-frequency duality. Properties of the Fourier transform, filtering. Relation poles/zeros and the frequency response. | Ch. 5 | Ch.5 slides Table w/properties | EE2S11_08 | 12/7/2018 | EE2S11_09 |

10. | Wed 15 Dec | AJV | Sampling, Nyquist-Shannon theorem, reconstruction using sinc interpolation. | Ch. 8 (skip 8.3, 8.4) |
Ch.8 slides
| EE2S11_11 | 12/14/2018 | EE2S11_10 |

11. | Fri 17 Dec | AJV | Discrete-time LTI systems, convolution. | Ch 9 (skip 9.4) | Ch.9 slides | EE2S11_12 | 12/18/2018 | EE2S11_11 |

12. | Wed 22 Dec | 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 |

13. | Wed 12 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 |

Exercises sampling, z-transform, DTFT. |
ex.Ch.8 sampling ex.Ch.9 LTI ex.Ch.10 Z-transf. ex.Ch.11 DTFT | |||||||

14. | Fri 14 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 |

15. | Wed 19 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 |

16. | Fri 21 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 |

Trial exam solutions | Trial exam |
Solutions | EE2S11_18 | 1/25/2019 | ||||

Thu 27 Jan | Exam (part 2) | |||||||

July | Resit |

### Past exams

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.

Exam (complete) of July 2018, with Solutions.

Part 2 exam of February 2018, with Solutions.

Part 1 exam of December 2017, with Solutions.

Exam (complete) of July 2017, with Solutions.

Part 2 exam of February 2017, with Solutions.

Part 1 exam of December 2016, 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 |