# Z Transform
Inverse Comb Filter.

Cuthbert Nyack

The transfer function below has zeros linearly spaced along the
unit circle and poles at the origin. This filter is referred
to as an inverse comb filter
response. Some books refer to this transfer function as the
comb filter.

In the applet below,
the gray curve above the magenta lines show the response between 0 and
½ w_{s} while the
gray curve above the green lines
show the response between ½ w_{s}
and w_{s}. 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.

When the zeros are on the unit circle, the response goes to
zero at the zero locations and rising in between. Increasing
the number of zeros reduces the height of the peaks between
the zeros.

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Copyright 2000 © Cuthbert A. Nyack.