Question

Matlab Problem: please use matlab format, thank you in advance!!

Problem 6 (1 point. Instructor's Initials This is Problem 5.20 in the text, with the following corrections and additions: 1) There is an error in the formula for f(x). The correct formula is saies seroatmation dfs ea ee witn m 1,3. 1 2??? -sin 4 /A f(x) = Write a program that accepts as user input the number of terms in the sum. For example, if the user requests 3 terms in the sum, the program should compute the sum for n- 1, 3, and 5. The program should then plot the approximate waveform, from x0 to 2L. This should show 2 cycles of the square wave as displayed in the figure. Let L- 1 for this problem. 2) 0.5 Demonstrate operation to the instructor, and print a copy of the program to attach to the lab.

Answer 1

Matlab code for square wave approximation

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L=1; % defining L
x=0:0.001:2*L; % generating vector x
n=input('number of terms: '); % accepting no of terms as user input
f=zeros(1,length(x)); % initializing vector to store the approximation
for i=1:length(x) % for all values of x=0,0.001,...2
sum=0; % initializing sum to 0
for j=1:2:2*n-1 % for n =1,3,5..
sum=sum+(1/j)*sin((2*j*pi*x(i))/L); % evaluating the summation part
end
f(i)=(4/pi)*sum; % multiplying summation with the constant
end
plot(x,f) % plotting the approximation of square wave
title('fourier series approximation of square wave')

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Output

G: Program Files* MATLAB R2017a» Editor - GProgram Files MATLABR2017asquareFourAppx.nm X Command Window calcAnalyze.m Х gibbsPhen.m fourierSeries.m fourierplot.m x square ourAppx.m >C+ quareFourAppx mumber of terms: 3 x > L-l; $ detining L x=0:0.001:2*L; 8 qene rating n-input ('number of terms: '); f_ze ro3 (1, length (x)); vector x 3- accepting no of terma aa uger input Figures-Figure 1 Figure 1 X initializing vector to atore the approximation for all values f x-0 , 0.001, initializing 311m t 0 for n -1,3,5.. 5for i-1:length (x) 2 sum- for J-1:2:24n-1 fourier series approximation of square wave sum-sum-(1/j)"sin {(2+5 pi#x(1))/L); evaluating the summation end f(1)-(4/pi)*sum; 릅 multiplying summation with the 10- 11end 12-lot (x,) 13title'ourier series approxinalion of square wave constant plotting the approximation of square wave 0.5 0 -0.5 1.5 0 0.5 2 script Ln13 Col 34