# DFT in IIR filters

To further summarize, I want to create a function in matlab that finds the time domain signal $y(n)$ and its $n$ time components ($n=0,1,2,...$) given the numerator and denominator of a transfer function (filter) and the input sequence. I want to know if you can use the DFT and circular convolution to convolve $H(\omega)$ and $X(\omega)$ if the former is an IIR filter (there's a feedback).

• Can you please edit the question for clarity? The series of operations mentioned in the post is not entirely clear and a few steps could be considered redundant. Would it be possible to describe what exactly are you trying to achieve?
– A_A
Nov 27 '16 at 14:00
• Done. Sorry for being a bit confusing. Nov 27 '16 at 14:27
• If you have the transfer function and the input sequence, if the filter is LTI, what is the issue here? You just have to convolve the two sequences. Nov 27 '16 at 14:38
• The catch is that I want the process to be done in the frequency domain, not in the time domain itself. So what should I do after using fourier transform on both the H(z) and x(n)? Nov 27 '16 at 14:44
• Thank you. There already is such a function in MATLAB. Can I please ask if this is some kind of homework where you have been asked to "emulate" the way that function operates?
– A_A
Nov 27 '16 at 14:55