Z Transform 2Z Linear Phase
Cuthbert Nyack
A transfer function with only zeros is shown below. When
the zeros are on the unit circle then the phase of the
transfer function increases linearly with frequency.
and the result is a linear phase filter with constant group delay.
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.
A linear phase filter has the same time delay at all frequencies.
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Copyright 2000 © Cuthbert A. Nyack.