If we have a set of time series data, y, consisting of 100 data points. One can apply a N (odd) Hamming window as a weighted moving average to decrease the noise. Say, if we choose 7 point Hamming window, H, [0.0800 0.3100 0.7700 1.0000 0.7700 0.3100 0.0800], and perform a weighted moving average on y. In Matlab, I am doing conv(y, H./sum(H), 'same').
Since this is a convolution, I am wondering that by convolution theorem, one should be able to obtain identical results in Fourier domain, because convolution should become multiplication in the Fourier domain.
However, the FFT of y will have 100 complex numbers, and Hamming window will also have 7 complex numbers. What would be an equivalent operation of a weighted moving average in the Fourier domain?