Is there a relationship between amplitude and phase response of a realizable filter? For the purpose of ease, let us consider only a FIR digital filter. I would like to design a FIR digital filter with a given frequency response (amplitude and phase responses given as a function of frequency)? Non-causal filters are allowed. The amplitude and phase responses are continuous and absolute integrable. Theoretically, you can find the filter coefficients by taking the inverse fourier transform of the frequency response. So long as the Inverse Fourier Transform exists, you can choose amplitude and phase responses arbitrarily and independently. Is this understanding correct?