# Frequency response of system with feedback and feedforward co-efficients?

For seismological application, I am playing with an elliptical filter, and once I have both sets of feedback and feedforward co-efficients, how do I make it so that I can plot the frequency response of the system? Can I also use the same technique to make the frequency response for a bessel?

I know that I can take the FFT for an FIR filter and I can get its transfer function, but for a non-FIR, is there a way also using the FFT?

$$H(z)=\frac{\sum_{m=0}^{M}b_mz^{-m}}{\sum_{n=0}^{N}a_nz^{-n}}\tag{1}$$
Usually, $a_0$ is normalized to 1. In order to evaluate $H(z)$ on the unit circle $z=e^{j\theta}$ you can compute the FFTs of the numerator and of the denominator of (1) separately and then divide to get the frequency response of the filter.
If you use Matlab or Octave, you can simply use the command $\tt{freqz}$.