Z Transform 2P/2Z Impulse, Step and Ramp Response

Cuthbert Nyack
The transfer function of a system with 2 poles and 2 zeros is shown below:-
The corresponding difference equation is :-

Applet below show the impulse response of a 2 pole, 2 zero system and its dependence on the location of the poles and zeros. The unit circle is shown in magenta, the imaginary Z axis is in pink, the pole location is shown as a green "x" and the zero location as a green "o".

Parameters (0.97, 20.0, 0.0, 22.0, NA, NA, NA, 0, 0, 0.89)
The zeros are at the origin, the response is a discrete damped sinusoid.

Parameters (0.97, 20.0, 0.70, 22.0, NA, NA, NA, 0, 0, .5)
The zeros affect the initial behaviour.

Parameters (0.0, 20.0, 1.0, 22.0, NA, NA, NA, 0, 0, 1.0)
The poles are at the origin, the zeros are on the unit circle. The impulse response is finite and consists of 3 values. Moving the zeros to the left of the imaginary axis changes the 2nd value in the impulse response.

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Copyright 2000 © Cuthbert A. Nyack.