Convolution of Fourier Series Coefficients

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ha9981
ha9981 2012-11-8
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?

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回答（1 个）

NN
NN 2012-11-8
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.

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