The Z transform of a system with 2 poles and 2 zeros is given below.

The variation of the frequency response of a system with the above transfer function is shown by the applet below. The gray curve above the magenta lines show the response between 0 and ½ w

Note that having a pole near the unit circle produces a peak in the response while having a zero on the unit circle produces a zero in the response. The location of the poles therefore determine the frequency of the peak response. Having zeros in the transfer function means that the response can be set to zero at certain frequencies by placing zeros at those frequencies.

Digital filters can be designed using poles, zeros or a combination of both.

Parameters (0.8, 15.0, 1.0, 90.0, 375, NA, 10.0, 1.5, 1, 0.14) show a low pass configuration.

Parameters (0.8, 165.0, 1.0, 0.0, 188, NA, 10.0, 1.5, 1, 0.07) show a high pass configuration.

Copyright 2000 © Cuthbert A. Nyack.