Z Transform Transfer Functions 1P 1Z Impulse, Step and Ramp Response

Cuthbert Nyack
The Z transform of the 1 pole, 1 zero system is shown below.
This Z transform can also be represented by the following difference equation from which the impulse response can be derived.
or y(n) = x(n) - z1x(n - 1) + p1y(n - 1). Zeros can be added to the transfer function by changing n in the applet below.
The applet below shows the impulse response in red for the system as the pole and zero locations are changed. The unit circle is shown in magenta, the real Z axis is in black, the imaginary Z axis is in orange, the pole location is shown as a green "x" and the zero location as a green "o".
Changing Fn shows the step and ramp response and their numerical values.

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Copyright 2000 © Cuthbert A. Nyack.