UNIVERSITY OF WEST ATTICA
SCHOOL OF ENGINEERING
DEPARTMENT OF COMPUTER ENGINEERING AND INFORMATICS

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Digital Signal Processing

Digital Signal Processing at Matlab

Vasileios Evangelos Athanasiou
Student ID: 19390005

GitHub · LinkedIn

Supervisor: Emmanouel Bratsolis, Special Technical Laboratory Staff

UNIWA Profile

Athens, January 2023

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Project Overview

The report consists of 30 laboratory exercises (as listed in the table of contents) centered on generating, transforming, and plotting discrete-time signals.
All exercises are implemented in MATLAB, with signal definitions influenced by the student’s registration number (AM), which determines specific constants and time intervals.

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Table of Contents

Section	Folder / File	Description
1	assign/	Assignment material
1.1	assign/ExersLabForDelivery22-23.pdf	Laboratory exercises for submission (English)
1.2	assign/ΑσκησειςΕργΓιαΠαράδοση22-23.pdf	Εργαστηριακές ασκήσεις προς παράδοση (Greek)
2	docs/	Theoretical documentation
2.1	docs/Digital-Signal-Processing-at-Matlab.pdf	Digital Signal Processing using MATLAB (English)
2.2	docs/Ψηφιακή-Επεξεργασία-Σήματος-στο-Matlab.pdf	Ψηφιακή Επεξεργασία Σήματος με MATLAB (Greek)
3	graphs/	Output graphs and figures
3.1	graphs/ex*.png	Plots generated from MATLAB exercises
4	src/	MATLAB source code
4.1	src/ex1.m	Exercise 1 implementation
4.2	src/ex2a.m, src/ex2b.m	Exercise 2 implementations
4.3	src/ex3*.m	Exercise 3 implementations (standard & repmat versions)
4.4	src/ex4.m	Exercise 4 implementation
4.5	src/ex5a.m, src/ex5b.m	Exercise 5 implementations
4.6	src/ex6.m – src/ex9b.m	Exercises 6–9 implementations
4.7	src/ex10.m – src/ex19.m	Exercises 10–19 implementations
4.8	src/ex22.m, src/ex25.m, src/ex26.m, src/ex29.m	Advanced exercise implementations
4.9	src/dft.m	Discrete Fourier Transform implementation
4.10	src/convall.m	Convolution utility function
4.11	src/stepseq.m	Step sequence generation
4.12	src/my_toeplitz.m	Custom Toeplitz matrix function
4.13	src/freq.m	Frequency analysis utility
4.14	src/transfer.m	Transfer function implementation
4.15	src/theory.m	Theoretical signal analysis script
5	README.md	Repository overview and usage instructions

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Exercise 1: Multi-Part Discrete Signal

The first exercise involves plotting a discrete-time signal ( x[n] ) defined over three distinct intervals:

$$ -2 \le n \le 4 $$

Constant value equal to the single-digit sum of the student’s ID
(calculated as 9)

$$ 4 < n \le 10 $$

Constant value of 0

$$ 10 < n \le 20 $$

Signal defined by:

$$ x[n] = \sqrt{2n} $$

MATLAB Implementation Highlights

• Uses stem(n, x) for discrete-time plotting
• Employs ones() and zeros() to construct constant signal segments
• Computes the single-digit sum of the student ID using a custom loop with modulo operations

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Exercise 2: Signal Transformations

The second exercise examines unit step and unit impulse signals.

Signal Definition

$$ y[n] = u(n - 3) - 6\delta(n - 1) $$

• Time Interval:

$$ n = -51 $$

to

$$ n = 51 $$

determined by the student’s ID

Key Implementation Details

• Uses a custom MATLAB function stepseq to generate the unit step sequence
• Combines step and impulse signals to form composite discrete-time signals

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Contents Summary

The complete laboratory report includes the following (partial overview):

• Exercise 1: Multi-part discrete signal plotting (Pages 4–7)
• Exercise 2: Unit step and impulse combinations (Pages 7–16)
• Exercises 3–30: Various DSP signal implementations and analyses (Pages 16–120)

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Technical Setup

• Software: MATLAB
• Primary Commands Used:
  stem, zeros, ones, sqrt, xlabel, ylabel, title

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This laboratory work demonstrates practical proficiency in discrete-time signal modeling, MATLAB-based visualization, and fundamental DSP concepts through structured and progressively complex exercises.

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Installation & Setup Guide

This repository contains a Digital Signal Processing (DSP) laboratory project implemented in MATLAB, consisting of 30 structured exercises focused on discrete-time signal generation, transformation, and visualization.
The project is intended for academic use in Digital Signal Processing courses.

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Prerequisites

1. Operating System

Supported platforms:

• Windows (recommended)
• macOS
• Linux

MATLAB scripts in this repository are platform-independent.

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2. MATLAB Environment

Required Software

• MATLAB 2023 (recommended)
  • Earlier versions (R2020b+) should also work, but MATLAB 2023 was used during development and testing.

Required Toolboxes

The project primarily uses core MATLAB functionality.
No specialized toolboxes are strictly required.

Optional (helpful but not mandatory):

• Signal Processing Toolbox

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3. Hardware Requirements

• Minimum 4 GB RAM (8 GB recommended)
• At least 2 GB of free disk space
• Audio playback support (for .WAV file experiments)

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4. Knowledge Prerequisites

Basic understanding of:

• Digital communications fundamentals
• Sampling theory
• Sinusoidal signals
• Fourier Transform & FFT
• MATLAB scripting (.m files, functions, plotting)

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Installation

1. Clone the Repository

Using Git:

git clone https://github.com/Digital-Signal-Processing-aka-Uniwa/Matlab.git

Alternative (Without Git)

• Open the repository URL in your browser
• Click Code → Download ZIP
• Extract the ZIP file to a local directory

2. Install MATLAB

1. Install MATLAB 2023 from MathWorks
2. Activate MATLAB using:
   • University license, or
   • Personal MathWorks account
3. Verify MATLAB launches correctly

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Project Setup in MATLAB

1. Set the Working Directory

1. Open MATLAB
2. Navigate to the cloned repository folder
3. Set it as the working directory:

cd path_to_repo/Matlab

Or:

• Use the Current Folder panel in MATLAB
• Right-click → Add to Path → Selected Folders and Subfolders

2. Verify Folder Structure

Ensure the following directories are visible:

• assign/
• docs/
• src/
• graphs/ MATLAB scripts are located in:

src/

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Running the Exercises

1. Execute an Exercise Script

From the MATLAB Command Window:

run('src/ex1.m')

Or:

• Open the script in the MATLAB Editor
• Press Run

Each exX.m file corresponds to a specific laboratory exercise.

2. Supporting Functions

Some exercises depend on custom utility functions located in src/, such as:

• stepseq.m – unit step sequence
• dft.m – Discrete Fourier Transform
• convall.m – convolution helper
• my_toeplitz.m – custom Toeplitz matrix
• freq.m – frequency analysis
• transfer.m – transfer function modeling

Ensure the entire src/ folder is on the MATLAB path.

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Output & Visualization

• Generated figures are displayed during script execution
• Saved plots are stored in:

graphs/

in .png format

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Open the Documentation

1. Navigate to the docs/ directory
2. Open the report corresponding to your preferred language:
   • English: Digital-Signal-Processing-at-Matlab.pdf
   • Greek: Ψηφιακή-Επεξεργασία-Σήματος-στο-Matlab.pdf