Convolution of Fourier Series Coefficients

So I have generated the fourier series coefficients for x(t) and y(t). I know that if z(t) = x(t)y(t) then in the frequency domain the coefficients of x(T0 and y(t) would be convolved.

if x(t) -> ak and y(t) -> bk

then z(t) -> conv(ak,bk)

Right?

I used my own function to calculate ak and bk which all came out to be accurate. Then I used the function to calculate ck for z(t). Now when I convolved ak and bk in matlab it doesn't give me the result ck. WHY?

my function is coeffs which calculates N number of coefficients.

ak = coeffs(x,t,w0,N)

bk = coeffs(y,t,w0,N)

ck = coeffs(z,t,w0,N)

ckcalc = conv(ak,bk)

figure;
subplot(2,1,1)
stem(abs(ck))
subplot(2,1,2)
stem(abs(ckcalc))

Why don't the plots match?

Answer 1

[NN]

As far as I know the convolution theorem is only valid if you convolute the full time series with each other, else wise you will always run into trouble. And I would guess that ak, and yk did not cover the full spectral domain.