The transfer function of the inverse (also called just comb without inverse) comb combined with 2 pairs of complex conjugate pairs is shown below.

In the applet below the gray curve above the magenta lines show the response between 0 and ½ w

In the applet the number of zeros is kept fixed at 36 spaced 10º apart. The 2 pairs of complex conjugate poles can be used to cancel 2 adjacent zeros producing a simple bandpass filter. The passband of the filter can be "shaped" by using many more zeros and cancelling several of them. This is one way of implementing frequency sampling filters.

If one zero at z = 1 is cancelled, the transfer function is shown in the following equation. The result is an averaging filter(lowpass characteristic) which in this case averages N samples.

Copyright 2000 © Cuthbert A. Nyack.