Signals and Systems Laboratory Coursework

Introductory Video

Introduction

This lab will teach you some fundamentals of Digital Signal Processing (DSP), and introduce you to Python and Jupyter Notebooks, mathematical tools that integrate numerical analysis, matrix computation and graphics in an easy-to-use environment. Jupyter Notebooks are highly interactive; their interpretative nature allows you to explore mathematical concepts in signal processing without tedious programming. Once grasped, the same tool can be used for other subjects such as circuit analysis, communications, and control engineering.

Learning Outcomes

At the end of this lab you will be able to:

1. Generate and analyse discrete-time signals using Python
2. Analyse signals by applying Fourier transforms and window functions
3. Analyse digital filters and their responses
4. Demonstrate conceptual understanding of discrete signal processing
5. Evaluate your work and your results

Objectives

1. Derive equations for the 3 types of Discrete Fourier Transforms.
2. Generate sinusoidal signals in Python as vectors and investigate the effects of DFT and Windowing. You will then use these techniques to investigate an unknown signal (provided).
3. Filter noise from the unknown signal by removing unwanted frequencies in the frequency domain.
4. Investigate the effects of passing Pulse and Impulse signals through a digital filter.
5. Investigate simple digital filter and their responses (FIR and IIR).

Requirements

To complete this lab you will need to install and run jupyter notebooks on you personal laptop.

Recommended Textbooks

This experiment is designed to support the second year Signals and Systems course. Since the laboratory and the lectures may not be synchronised, you may need to learn certain aspects of signal processing ahead of the lectures. While the notes provided in this experiment attempt to explain certain basic concepts, they are far from complete. You will likely find the recommended textbook helpful when studying this experiment as well as the lecture course: S. Haykin and B. Van Veen, 'Signals and Systems,' 2nd Ed., Wiley, 2003.

Timetable

There are 7 exercises in this coursework; Exercises 1 to 4 are compulsory and you should aim to complete all of them in approximately 4 hours. Exercises 5 to 7 (plus part of Exercise 3) are optional and should take about 4 hours to complete. Lab sessions for this module are also provided (see timetable).

Assessment

This coursework is not assessed separately but is assessed as part of the exam. Normally, some of the parts of Question 1 of the exam will ask questions on the material covered in the coursework. The nominal weighting of the coursework-related questions in the exam amounts to 10% of the course total. Given that the material covered in the coursework is also covered in lectures and tutorial questions, coursework-related questions will not be labelled as such on the exam paper, and may be embedded in other questions. The coursework-related questions in the exam will specifically assess understanding of the theoretical concepts and the methods for signal analysis and processing covered in the coursework. The optional exercises in the coursework will not be assessed in the exam in a coursework-specific manner.

Contact

This laboratory coursework was developed and designed by Aidan O. T. Hogg and Patrick A. Naylor (with help from Vincent W. Neo and Emilie d'Olne). Please post on the course Forum (or email p.naylor@imperial.ac.uk) if you have any suggestions or comments about this document as this will help future year groups.

Getting started with Jupiter Notebooks

Linux or MAC setup

Video of setup:

1. Download this Git repository
2. Install Python 3.9 (or any version from 3.6 to 3.9) from https://www.python.org/downloads/macos/
3. Install the required Python packages

python -m pip install numpy matplotlib scipy soundfile jupyter

Note: you may need to replace python with python3

4. Go to the SS_LAB_2021 folder and run the Jupyter Notebook

python -m jupyter notebook

Note: you may need to use python -m notebook instead

Windows setup

Video of setup:

1. Download this Git repository
2. Install Python 3.9 (or any version from 3.6 to 3.10) from https://www.python.org/downloads/
3. Download the get-pip.py (https://bootstrap.pypa.io/get-pip.py) file and store it in the same directory as python is installed. Run the command given below:

python get-pip.py
python -m pip install --upgrade pip

Note: you may need to replace python with python3

4. Install the required Python packages

python -m pip install numpy matplotlib scipy soundfile jupyter

5. Go to the SS_LAB_2021 folder and run the Jupyter Notebook

jupyter notebook

Note: you may need to use python -m notebook instead