The Fourier spectrum exponential Fourier series coefficients

The Fourier spectrum (exponential Fourier series coefficients) of a certain periodic waveform is given by alpha_n = {(-1)^n/n^2, n = plusminus 1, plusminus 2, ... 0, n = 0 Write the trigonometric Fourier series for the corresponding function x(t). Use a computer program to calculate and plot an approximation to the function x(t). Use as many terms of the series as seems necessary.

Solution

(a) The fourier series is a sum of sine and cosine functions in which it is represented in trigonometric form. so for the given function the trigonometric fourier series is

X(t) = sin (-t) + (sin (-3t)/3)+ (sin (-5t)/5)

so by substituting in the given function it gives -1 so by applying in sin we get this trigonometric fourier form.

(b)

n= input(\'enter n value:\');

alphvale = zeros(n);

for i = 1:n

if n==0

alphvale(i)=0;

else

alphvale(i)=power((-1),n)/power((n),2);

end

end

plot(alphvale);