I have a time varying discrete signal x(t) sampled at 5ms rate. I need to find the amplitude of the 20 Hz frequency component for each sample. What I do today is that for each sample I do a Short-time Fourier Transform of the data in a window around that sample. Then I read the amplitude for the 20 Hz frequency component off the amplitude spectrum. This seems to work fine, but it is slow.
How can I speed up this process? For instance I am only interested in the 20 Hz component. Is there some way I can avoid finding the complete amplitude spectrum (that is faster than FFT)?