Fourier series – frequency shift of function


Let's say I represented some function $$f(t)$$ in terms of complex Fourier series. Then if I want to calculate complex Fourier series of frequency shifted function $$f(t),$$ can I use result I got for "non freq. shifted" $$f(t)$$ to get complex Fourier series for frequency shifted $$f(t),$$ or I have to start with calculations from beginning?

Best Answer

I believe its better to do the calculation again just to be safe.

But unlike in time shifting where the Fourier Coefficients are multiplied with a exp(-jkwo*to) the Coefficients in frequency shift remain the same but get shifted by the specific amount of shift. Suppose you are shifting the original signal by M then and the Fourier coefficients of the original signal is given by say Ak. Then in case of the shifted signal with coefficient Bn=Ak-M.

It would be helpful if you clarify and make the question more specific.