How can I plot the fourier series of a rectangular pulse by calculating the coefficients?

Question

Niloufar 2022-10-6

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1818795-how-can-i-plot-the-fourier-series-of-a-rectangular-pulse-by-calculating-the-coefficients

评论： VBBV 2022-10-8

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I want to find the fourier series of this recangular pulse shown in the code until N by using this formula

but I don't get the desired output.here is my code.could anyone tell what is the problem of my code?

here is the output I want to get

close all; clear; clc;
N = 2;
f = @(x) rectangularPulse(-1,1,x);
x = -2:0.01:2;
%2*p is the period
p = 1;
% the main function
plot(x,f(x),'LineWidth',2);
grid;
hold on;
grid minor;
xlim([-2 2]);
ylim([-0.1 1.1]);
x = linspace(-2,2,9).';
y = linspace(0,1,0.2);
a0 = (1/(2*p))*integral(f,-p,p);
an = zeros(1,N);
bn = zeros(1,N);
for n=1:N
    fan = @(x) rectangularPulse(-1,1,x).*cos((n*pi/p)*x);
    an(1,n) = (1/p)*integral(fan,-p,p);
    fbn = @(x) rectangularPulse(-1,1,x).*sin((n*pi/p)*x);
    bn(1,n) = (1/p)*integral(fbn,-p,p);
end
fs = a0 + sum(an.*cos((1:N).*x) + bn.*sin((1:N).*x),2);
plot(x,fs,'LineWidth',2);

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Answer 1

VBBV 2022-10-6

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1818795-how-can-i-plot-the-fourier-series-of-a-rectangular-pulse-by-calculating-the-coefficients#answer_1068030

在 MATLAB Online 中打开

close all; clear; clc;

N = 2;

f = @(x) rectangularPulse(-1,1,x);

x = -2:0.001:2;

%2*p is the period

p = pi;

% the main function

plot(x,f(x),'LineWidth',2);

grid;

hold on;

grid minor;

xlim([-2 2]);

ylim([-0.1 1.1]);

x = linspace(-2,2,9).';

y = linspace(0,1,0.2);

a0 = (1/(2*p))*integral(f,-p,p);

an = zeros(1,N);

bn = zeros(1,N);

for n=1:N

fan = @(x) rectangularPulse(-1,1,x).*cos((n*pi/p)*x);

an(1,n) = (1/p)*integral(fan,-p,p);

fbn = @(x) rectangularPulse(-1,1,x).*sin((n*pi/p)*x);

bn(1,n) = (1/p)*integral(fbn,-p,p);

end

fs = a0 + sum(an.*cos((1:N).*x) + bn.*sin((1:N).*x),2);

plot(x,fs,'LineWidth',2);

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VBBV 2022-10-6

If you try with N = 10 or higher it looks similar and closely approximates the rectangular pulse

VBBV 2022-10-8

Note that if you are comparing waveforms for N = 6 with other results as you shown, it may give different results. The output which you shown may have been obtained with a different upper limit summation for coefficients in the series.

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