Fourier Series representation for signals

[d2009]

Homework Statement

a) Write a Matlab function, which accepts the following inputs

-a finite set of Fourier series coefficients

-the fundamental period T of the signal to be reconstructed

-a vector t representing the times for which the signal will be reconstructed

Homework Equations

The Attempt at a Solution

function fourier1=f(a,T,t)
fourier1=zeros(length(a),1);
for n=1:length(a)
fourier1(n)=(a(n)*exp((i*(2*pi/T)*n*t)));
end;

 

[mighty2000]

Explanation:

This function, named "fourier1", takes in three inputs: a finite set of Fourier series coefficients, the fundamental period T, and a vector t representing the times for which the signal will be reconstructed. It first initializes a vector called "fourier1" with the same length as the input coefficients. Then, using a for loop, it calculates each term of the Fourier series using the formula a(n)*exp((i*(2*pi/T)*n*t)), where n is the index of the current coefficient and t is the time vector. Finally, it returns the reconstructed signal in the form of the vector "fourier1".