Table of Contents:
1. Assigned time function and MatLab Plot.......................................…………3
2. Script file of Laplace Transform, F(s), for the time function f(t)…...……... 3
3. Step Response example………………………………………………..…….4
4. Convolution example………………………………………………..…...….6
5. Appendix and References...………………………………………………….8
a. Source Code……………………………………………………...…...8
Antoaneta Mutafchieva
I.
Assigned time function:
f(t) = tsin(bt) +cos(at)
A = 4; B = 10; C = 2.4; D = 2;
Plot 1
II.
Script file that returns the Laplace Transform, F(s), for the time function f(t).
%%%%% Laplace Transform F(s) Partition %%%%%
syms f t s
f = t*sin(B*t) + cos(A*t);
laplace(f)
ans =
s/(s^2 + 16) + (20*s)/(s^2 + 100)^2
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Fig 1 - Screenshot of the source code and Laplace Transform return
III.
Step Response example - Describe briefly what the following code does
>> plant_controller = tf([24], [1 3 24])
>> impulse(plant_controller)
>> step(plant_controller)
The first line of the code above creates a 2nd order transfer function assigned to the name
plant_controller.
24
------------------ Continuous time transfer function
s^2 + 3s + 24
The following two lines are the impulse response and the step response of the system as
shown in the plots below.
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Antoaneta Mutafchieva
Plot 2 – Impulse Response
Polt 3 – Step response
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Antoaneta Mutafchieva
IV.
Convolution example
Describe briefly what the following command does (you can type “help ones” at the
i.
prompt):
>> x = ones(1,5);
The command above creates a matrix of ones with size 1x5 (1 row/ 5 columns).
ii.
Execute these commands and copy the plot into your Word document
>> x = ones(1,10);
>> h = ones(1,5);
>> y = conv(x,h);
>> plot(y);
>> pause
>> stem(y)
Plot 4 - Convolution plot
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Plot 5 - Stem plot
1) Explain what the code does
The code above creates matrix x of ones with size 1x10, x = [1 1 1 1 1 1 1 1 1 1] and
matrix h of ones with size 1x5, h = [1 1 1 1 1]. Then plot(y) represent the convolution of the two
matrices, Execution is paused until a key is entered and the stem plot(y) is shown.
2) and Determine whether or not the results, specifically the horizontal axis values, are
what you
expected them to be. Explain why or why not.
The x-axis of the convolution plot represent the length of the two matrices convolved.
Length(l) = length(x) + length(h) – 1, in this case 10 + 5 – 1 = 14.
The y-axis represents the highest coefficient of the convolution, in this case 5.
x = [1 1 1 1 1 1 1 1 1 1]
x9 + x8 + x7 + x6 + x5 + x4 + x3 + x2 + x + 1
h = [1 1 1 1 1]
x4 + x3 + x2 + x + 1
Convolution y = (x*h) contains the coefficients of the polynomial multiplication
y = [1 2 3 4 5 5 5 5 5 5 4 3 2 1]
3) Which, in your opinion, is better, the “plot” function or the “stem” function?
I like both “plot” and “stem” functions. Depending on assignment, and more important
number of plots to be generated and observed, maybe I would choose plot. I prefer continuous
values of curves rather than the discrete points.
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Antoaneta Mutafchieva
Appendix A: Source Code
% Source code written by Antoaneta Mutafchieva
% 03/27/2021
clf
clc
clear all
%%%%% Wave Transformations Partition %%%%%
A = 4; B = 10; C = 2.4; D = 2;
t = 1:1000;
% time array
g = @(t) sin(t/30);
% original sine wave
g1(t) = A*g(t+10);
% 1st transformation
g2(t) = C*g(2*t);
% 2nd transformation
plot(t(1:500),g(1:500),'b', t(1:500),g1(1:500),'g',
t(1:500),g2(1:500),'r')
%%%%% Laplace Transform F(s) Partition %%%%%
syms f t s
f = t*sin(B*t) + cos(A*t);
laplace(f)
%expected ans = (2*B*s)/(s^2 + B^2)^2 + s/(s^2 + A^2);
legend('g(t) = sin(t/30)', 'g1(t) = A*g(t + B)', 'g2(t) =
C*g(D*t)')
figure (gcf)
title ('Scaled and Translated Waves - AM');
% pause
- execution pauses until key is entered
xlabel('Time');
ylabel('Value');
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