FFT for a specific frequency range.

I would like to convert a signal to frequency domain. The desired frequency range is 0.1 Hz to 1 Hz and the frequency resolution is 0.01 Hz.

With the sampling rate of 30 Hz, FFT gives the frequency components up to 15 Hz. Raising the sampling rate gives better frequency resolution. However, FFT gives wider frequency range. In my case, I just want 0.1 Hz to 1 Hz, FFT gives up to 15 Hz ( Extra computation ).

My question is, is there anyway standard way I can compute a frequency domain of a signal with specific frequency range and high resolution?

Answer

I think the best solution to your problem is to use the chirp-DFT. It's like a magnifying glass for a certain frequency range. It is more efficient than the direct implementation of the DFT (without FFT), because an FFT algorithm can be used with some appropriate pre- and post-processing. You basically need to modulate your signal with a chirp signal, then filter using an FFT, and then again chirp-modulate your signal to get the desired frequency response. See here and here for details on how to implement the chirp-DFT.