Is there a relationship between amplitude response and phase?

[manjuvenamma]

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?

 

[Jediknight]

I don't think I'm on your level, but just in case it helps Ill tell you I just did experiments and reading on the fact that (at least with simple harmonic, which I am sure yours isn't so I should probably just stop typing now but what the hell) Amplitutude and frequency-and therefore?Amplitude and phase are independent.
Which seems to support your conclusion, sorry if I wasted your time