Say I have an FIR filter with desired magnitude characteristics. I could imagine using an allpass IIR in series with the FIR to alter the group delay characteristic to provide both a 'magnitude equalization' and 'delay equalization' curve custom for the application.
I imagine this would be simpler in the frequency domain where the imaginary component of each slice of the FFT would adjust the group delay of a bandwidth corresponding to the nyquist frequency of the system divided by the FFT length, and then IFFT'ing to find the impulse response, windowing that impulse response to design the filter.
I see Matlab has an IIR feature for custom group delay in fdatool. Why does it have to be an IIR? Can an FIR have a custom group delay?
Thanks for any pointers!