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.