cascade and summation process in frequency domain using overlap and save method

Question

hello i'm doing signal processing like this

S : FFT of input signal from microphone

Exp : just gain

1/(Q*J) : include frequency component, I convert this equation to frequency domain digital filter using frequency sampling method

and similar process are conducted several time

and i'am doing overlap and save method like this

1. zero padding input signal -> fft
2. zero padding filter.1 -> fft
3. multiplication -> ifft -> discard first block -> y1
4. zero padding y1 -> fft
5. zero padding filter.2 -> fft
6. multiplication -> ifft -> discard first block -> y2
7. So on....

my question is if it is impossible to combine all filter to one (cascaded filter) every time fft and ifft and discard process will be conducted that is very inefficient. is there efficient method to filter signal several time in frequency domain?

Answer 1

Your process may wrong. With Overlap-save you typically don NOT zero pad the input, but time shift it. You only pre-pend the first frame with zeros.

my question is if it is impossible to combine all filter to one (cascaded filter)

Yes, of course. To cascade two impulse responses, simply convolve the impulse responses. You can also just multiply the transfer functions in the frequency domain, you just need to make sure that the FFT length is more than twice the sum of the length of all impulse responses.