infinite impulse response - 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).