I am trying to find a way to shift the outputs of the FFT (any algorithm implementation, currently using radix-2) by half a bin with the same bandwidth. To put it another way, say you have a 512pt FFT sampling data for a bandwidth of 100 kHz. The frequency bins are going to fall ~390 Hz apart (bandwidth) For example 195 to 585 is effectively the band pass range for bin 2 which happens to fall at the center frequency of 390 Hz. Bin 3 is from 585 to 975 with Fc being 790 Hz. Say I want Fc to be 585 instead of 790. This represents a shift of all the FFT outputs by half a band.
I do not want to double the size of the FFT to get the result. I do not want to multiply the signal in time domain prior to FFT by an offset frequency as I don’t want to deal with extra products within bandwidth of the overall FFT.
Is there a way through modification of the twiddle factors to get the desired effect?