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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 ?

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    \$\begingroup\$ 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. \$\endgroup\$ – Trevor_G Aug 11 '17 at 16:06
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    \$\begingroup\$ I edited the question for that. I in IQ means In-Phase and Q means Quadrature. \$\endgroup\$ – math Aug 11 '17 at 16:09
  • \$\begingroup\$ What are the degrees-of-freedom for your signal? and how can those be mapped into other signal domains? \$\endgroup\$ – analogsystemsrf Aug 11 '17 at 17:18
  • \$\begingroup\$ @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 \$\endgroup\$ – math Aug 11 '17 at 17:23
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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.

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  • \$\begingroup\$ What I was asking is that is my original approach correct to take the inverse IFFT of H and convolve with my signal (Is H all pass filter)? Can I model an all pass filter as constantexp(1iLinear function) \$\endgroup\$ – math Aug 11 '17 at 18:52
  • \$\begingroup\$ no, because that is a complex sinusoid, and that transforms to a single impulse! \$\endgroup\$ – Marcus Müller Aug 11 '17 at 20:35
  • \$\begingroup\$ This is not a complex exponential since K is changing from 1:64 so it is group of 64 exponential function and also H is in Frequency domain the phase is a+bK so it is H= Aexp(1i*(a+b*K)). \$\endgroup\$ – math Aug 11 '17 at 20:39
  • \$\begingroup\$ @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\$!! \$\endgroup\$ – Marcus Müller Aug 11 '17 at 20:48

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