I want to design FD (frequency dependent ) IQ (In-phase,Quadrature) distortion that changes the phase mismatch linearly like a+b*K ( where K is 1 to 64) and amplitude remains constant to test my estimation algorithm against it. I need this filter to be in time domain before FFT but changes the IQ imbalance parameters across different subcarriers(hence the name FD) .I wonder how to achieve this ? I was thinking something like H = alpha *exp(2*pi*1i*(a+b*K)) as the frequency response and just take the IFFT of this and convolve with the signal. Do you think this is correct , any help will be appreciated ?
What you describe, phase being linear to frequency, is just a linear-phase system.
We usually design FIR filters that way, because it leads to constant group delay and hence, a lack of dispersion.
Anyway, any FIR filter that has symmetrical (complex case: hermitian symmetry) in its taps does that.
The flat response in amplitude means you're looking for an all-pass filter. There's plenty literature out there on the design of FIRs.