Inverse Comb with cancelled Zero
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 ws while the
gray curve above the green lines
show the response between ½ ws
and ws. Orange lines show
the phase variation. White disc shows the unit circle, black line
is the real z axis and orange line is the imaginary z axis. Pole is
shown by the "x" and the zero by an "o". When the "Theta" parameter is
zero the view is along the imaginary axis from the top. -90° corresponds
to a view along the real z axis from the left and +90° represents
a view along the real z axis from the right.
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
If one zero at z = 1 is cancelled, the transfer function is shown in the following
The result is an averaging filter(lowpass characteristic) which
in this case averages N samples.
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Copyright 2000 © Cuthbert A. Nyack.