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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?

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Yes, you can always use the FFT to compute the frequency response of a discrete-time system at discrete frequencies. For an IIR filter you get the following transfer function:

$$H(z)=\frac{\sum_{m=0}^{M}b_mz^{-m}}{\sum_{n=0}^{N}a_nz^{-n}}\tag{1}$$

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 $\tt{freqz}$.

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  • $\begingroup$ Many thanks, also, if I have elliptical second order sections, then simply multiply the transfer functions of each section together? $\endgroup$ – TheGrapeBeyond Jun 4 '13 at 13:42
  • $\begingroup$ Yes, transfer functions of second-order sections can be multiplied to get the total transfer function. Please don't forget to accept the answer by clicking on the check-mark if it was useful for you. $\endgroup$ – Matt L. Jun 4 '13 at 14:27
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This is covered in pretty much every text book on digital signal processing. Try https://ccrma.stanford.edu/~jos/filters/ or http://www.eas.uccs.edu/wickert/ece2610/lecture_notes/ece2610_chap8.pdf for starters.

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