Signals and System

Signals and System 1
Signals and System
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Signals and System 2
Introduction
A signal is an explanation of how one constraint differs with another constraint. For example,
voltage shifting over time in an electronic circuit, or lustre varying with distance in an image
(Armstrong & Feldberg, 2015). A system is any procedure that yields an output signal in
reply to an input signal. Continuous systems input and output continuous signals, for instance
in analog electronics. Discrete systems input and output discrete signals, for instance
computer programs that control the values stored in arrays Godfrey, (2016).
Convolution describes the process of a signal passing through a linear, time-invariant system
defined by an impulse response (Lawson & Uhlenbeck, 2017). Convolution is a central
concept that describes every linear, time-invariant system that we create and use. Convolution
describes how the circuits affect a given voltage input, how radio waves travel through the
atmosphere, how to blur and sharpen images, how to recognize images/faces videos, etc.
While many of these systems do not use convolution directly (we often use faster algorithms
that indirectly perform convolution), understanding how and why convolution works is
essential to all of them (Pierce & Noll, 2015).
In this lab assignment, we will focus on understanding convolution and how to use it to
design and analyze systems. We will create several system impulse responses and study how
each system affects a given signal. We then study a widely used application of convolution,
known as “template matching” or “matched filtering,” that is often used to locate images,
radar or sonar signals, and musical segments in noisy data sets.
Objectives
This lab assignment has three learning objectives:
1. To improve your understanding of convolution.
2. To introduce you to the concept of correlation and template matching.

Signals and System 3
3. To design your own “Name that tune” algorithm
Methodology
The MATLAB program was used to create the convolution for signal manipulation and the
program is shown below.
On completion of manipulation, the program was later used to find convolution of the the
signals.
Results and Discussions
Part A: Convolution for Signal Manipulation........................................................................1
Part B: Convolution for Finding Signals................................................................................8
Part three...............................................................................................................................15
Functions..............................................................................................................................16
clear;
clc;
close all;
Part A: Convolution for Signal Manipulation
part one: Signal creation
x=stepseq(3,0,20)-stepseq(8,0,20)-imseq(17,0,20);
n = 0:20;
stem(n,x);
xlabel('Samples');
ylabel('Amplitude');
grid on;
%part two: Convolve with a Delta Function
h=imseq(0,0,20);
y = conv(x,h);
length_of_y=length(y)
a = 0:length(y)-1;
figure;
stem(a,y);
xlabel('Samples');
ylabel('Amplitude');
grid on;
%part three: Convolve with a Shifted Delta Function
k=[5 6 10 19];

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for i=1:4
s=k(i);
h=imseq(s,0,20);
y = conv(x,h);
a = 0:length(y)-1;
figure;
stem(a,y);
xlabel('Samples');
ylabel('Amplitude');
grid on;
end
% Part four: Convolve with Two Delta Function
k2=[19 17 14 11];
for i=1:4
s=k2(i);
h=imseq(0,0,20)-imseq(s,0,20);
y = conv(x,h);
a = 0:length(y)-1;
figure;
stem(a,y);
xlabel('Samples');
ylabel('Amplitude');
grid on;
end
% Part five: Convolve with a Box (Running Averaging)
h=(1/3).*stepseq(0,0,20)-stepseq(3,0,20);
y = conv(x,h);
a = 0:length(y)-1;
figure;
stem(a,y);
xlabel('Samples');
ylabel('Amplitude');
grid on;
% Part six: Convolve with a Di?erence (Edge Detection)
h=-imseq(0,0,20)+2.*stepseq(1,0,20)-imseq(2,0,20);
y = conv(x,h);
a = 0:length(y)-1;
figure;
stem(a,y);
xlabel('Samples');
ylabel('Amplitude');
grid on;