Z Transform 4 Poles 4 Zeros Frequency Response

Cuthbert Nyack
The Z transform of a 4 pole, 4 zero (2 complex conjugate pairs) system is shown below:-

The frequency response of the 4 pole, 4 zero system is shown 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. Poles are shown by the "x"s. 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.

Parameters (0.66, 14.0, 1.0, 87.0, 0.87, 32.0, 1.0, 180.0, 0, 0.02) a Basic low pass filter.
Parameters (0.64, 165.0, 1.0, 100.0, 0.87, 146.0, 1.0, 0.0, 188, 0.03) a Basic high pass filter.
Parameters (0.86, 35.0, 1.0, 129.0, 0.81, 59.0, 1.0, 0.0, 49, 0.2) a Basic band pass filter.




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Copyright 2000 © Cuthbert A. Nyack.