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

University of West Attica · Department of Computer Engineering and Informatics

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Signals and Systems

Constant Time Systems

Vasileios Evangelos Athanasiou
Student ID: 19390005

GitHub · LinkedIn

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Supervision

Supervisor: Adonis Bogris, Professor

UNIWA Profile · LinkedIn

Co-supervisor: Georgios Antoniou, Laboratory Teaching Staff

UNIWA Profile

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Athens, April 2021

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README

Constant Time Systems

This project was completed for the Signals and Systems Laboratory and focuses on the analysis and simulation of constant-time systems using MATLAB.

The repository includes documentation and MATLAB code for exercises examining system stability and system causality.

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Table of Contents

Section	Folder/File	Description
1	assign/	Assignment instructions and exercise description
1.1	assign/EXERCISE 3 - CONSTANT TIME SYSTEMS.pdf	Exercise instructions (English)
1.2	assign/ΑΣΚΗΣΗ 3 - ΣΥΣΤΗΜΑΤΑ ΣΥΝΕΧΟΥΣ ΧΡΟΝΟΥ.pdf	Exercise instructions (Greek)
2	docs/	Documentation related to constant time systems exercises
2.1	docs/Constant-Time-Systems.pdf	Constant time systems documentation (English)
2.2	docs/Συστήματα-Συνεχούς-Χρόνου.pdf	Constant time systems documentation (Greek)
3	src/	MATLAB source code files for constant time systems exercises
3.1	src/c1.m	MATLAB script file
3.2	src/c2.m	MATLAB script file
4	README.md	Project documentation
5	INSTALL.md	Usage instructions

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1. Exercises Summary

1.1 Exercise 2 — System Stability

This exercise evaluates the stability of a system defined by the relation:

$$ y(t) = e^{x(t)} $$

Input Signal

$$ x(t) = \cos(2\pi t) $$

Analysis

• The input signal is bounded since

$$ |x(t)| \le 1 $$

• The resulting output signal remains bounded, satisfying

$$ |y(t)| \le N $$

for some constant bound.

Conclusion

Since a bounded input produces a bounded output (BIBO condition), the system is considered stable.

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2. Exercise 3 — System Causality

This exercise studies system causality through time scaling.

Input Signal

$$ x(t) = u(t) - u(t-1) $$

Output Signal

$$ y(t) = x(t/4) $$

Analysis

• The output appears compressed or shifted relative to the input.
• The system output at time t depends on future input values.

Conclusion

The system is non-causal, since output depends on future input values.

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3. MATLAB Implementation

The implementation uses MATLAB tools for signal construction and visualization.

Key commands used

• Time vectors: Created using the colon operator

  t = 0:0.1:10;

• Signal construction: Uses functions such as:
  • cos
  • zeros
  • ones
• Visualization tools:
  • plot
  • subplot
  • title
  • ylim

These commands allow comparative visualization and analysis of system behavior.

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4. Summary

This laboratory task demonstrates the evaluation of system properties such as stability and causality, reinforcing theoretical concepts through MATLAB-based simulation and visualization.