Fast convolution algorithm

Question

I need to convolve two one dimensional signals, one has on average 500 points (This one is a Hanning window function), the other 125000. Per run, I need to apply three times

Answer 1

Fast convolution can be carried out using FFTs. Take the FFT of both input signals (with appropriate zero padding), multiply in the frequency domain, then do an inverse FFT. For large N (typically N > 100) this is faster than the direct method.