At this assignment, we want to implement the trigonometric Fourier series in MAT

Question

At this assignment, we want to implement the trigonometric Fourier series in MATLAB. The goal is to write a function which calculates the trigonometric Fourier series coefficients of a given periodic function. a. Write a MATLAB function, [ao a, bl- FSLTN), which gets the input function x(t) as a vector x, the vector of time positions (t in sec), the period (T in sec), and N (number of coefficients) as the input arguments so as to calculate and return the trigonometric Fourier series coefficients (aoanabn) @m = Sto+7 f(t)cos (na,t)dt 2 cto+T Here, ao is a scalar and a and b are two vectors of length N. For integration purposes, use trapz in MATLAB

Explanation / Answer

function [a0,a,b]=FS(x,t,T,N)
n=1:N;
a=zeros(1,N);
b=a;
w=2*pi/T;
a0=trapz(x)/T;
for i=1:N
    a(i)=(2/T)*trapz(x.*cos(n(i)*w*t));
    b(i)=(2/T)*trapz(x.*sin(n(i)*w*t));
end

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