# Linear Frequency Dependent IQ Distortion

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 ?

• I'm having severe IQ distortion trying to read and understand that question... Different meaning of IQ though I guess... Abbreviations don't help on here. – Trevor_G Aug 11 '17 at 16:06
• I edited the question for that. I in IQ means In-Phase and Q means Quadrature. – math Aug 11 '17 at 16:09
• What are the degrees-of-freedom for your signal? and how can those be mapped into other signal domains? – analogsystemsrf Aug 11 '17 at 17:18
• @analogsystemsrf, what do you mean by degree of freedom in my signal? the input signal is OFDM signal passed through the channel. Assume it is y and I need to distort it by IQ mismatch such that phase is changing across subcarriers linearly and amplitude is just constant – math Aug 11 '17 at 17:23

• @math nonsense! usually, linear function has shape $f(x) = ax,\,a\in\mathbb R$; and your function is $Ae^{i f(x) } = A e^{iax}$, and that is a complex sinusoid, nothing else. Even if you say $f(x) = ax + b$ , then your function becomes $Ae^{iax + ib}$, and that is still a complex sinusoid! This does even hold true for any $a,b\in \mathbb C$!! – Marcus Müller Aug 11 '17 at 20:48