Signals & Communication Systems Project: SIMULINK Analysis

Signals and Communication Systems
EECN 302
Course
Project

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EECN302: Course Project
Project Title:
Systems Analysis using
SIMULINK

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EECN302: Course Project
Table of Contents
Introduction: .................................................................................................................................... 3
Objectives: ...................................................................................................................................... 3
Results: ............................................................................................................................................ 4
Part 1: Frequency Response Analysis using SIMULINK........................................................... 4
Part 2: Time-Domain Analysis using SIMULINK ................................................................... 19
a. Impulse Response:.......................................................................................................... 19
b. Step Response ............................................................................................................. 20
Time-Domain Analysis of 3rd order system .............................................................................. 21
System Specifications for unit step input.............................................................................. 21
Final values for impulse & unit step input ............................................................................ 22
Stability ................................................................................................................................. 23
Discussion & Conclusion .............................................................................................................. 23

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EECN302: Course Project
Introduction:
Linear Time-Invariant (LTI) systems form the backbone of modern signal processing and
communication engineering. Analyzing their behavior in both time and a frequency domain is
critical for designing efficient systems, optimizing performance, and troubleshooting real-world
applications. This project influences MATLAB and Simulink to simulate and investigate LTI
systems, focusing on first-order and higher-order dynamics, frequency response, and time-
domain characteristics such as impulse and step responses.
Beyond basic simulations, the implementation of this project explores advanced signal
processing concepts, including:
 Convolution: How LTI systems transform input signals in the time domain.
 Autocorrelation: Measuring signal self-similarity over time delays.
 Cross-correlation: Quantifying similarity between two signals with time shifts.
 Power Spectral Density (PSD): Analyzing frequency-domain power distribution.
A key emphasis is placed on first-order systems, where the interplay between time and frequency
responses reveals fundamental principles of signal processing. By combining theoretical
analysis with interactive Simulink modeling, this project bridges abstract concepts with practical
validation.
Objectives:
The primary goals of this project include:
 Designing a SIMULINK model to simulate Linear Time-Invariant (LTI) systems.
 Gaining proficiency in MATLAB and SIMULINK for computational analysis and
graphical visualization.
 Evaluating system performance through time-domain and frequency-domain
simulations in MATLAB.
 Analyzing frequency response, autocorrelation, cross-correlation, and power spectral
density (PSD) of basic LTI systems.
 Examining time-domain responses of LTI systems under different conditions.

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EECN302: Course Project
Results:
Part 1: Frequency Response Analysis using SIMULINK
The frequency response of an LTI system is defined by the relationship:
Y(jω)=H(jω)X(jω)
Where:
 Y(jω) = System output
 X(jω) = System input
 H(jω) = Transfer function
To simulate this in SIMULINK, a sinusoidal input signal is applied, and the output is compared
to the input. Key observations include:
1. Linearity & Time-Invariance: For a sinusoidal input x(t)=sin(ωt), the output y(t) remains
sinusoidal at the same frequency.
2. Amplitude & Phase Shift: The output differs from the input by:
A scaling factor equal to the magnitude of H(jω). A phase shift determined by arg (H(jω))=ϕ
y(t) = |H(jw)|.|X(w)|(cos(t + ФH )
We constructed the following SIMULINK model as shown in Figure 1.
Figure 1: Simulink Model of given system