Transfer Functions 2 Poles Impulse, Step and Ramp Response
The Z transform of a 2 complex conjugate pole system is shown
n zeros at the origin are included in the transfer function.
and its difference equation is given by:-
y(k) = x(k + n - 2)
y(k - 1)
- p2y(k - 2)
The impulse response of a 2 pole system is shown in
red below and its dependence on the pole locations can be
seen by changing p and f.
The unit circle is shown in magenta, the imaginary Z axis is in pink and the pole
locations are shown as green "x"s. When the poles are off the
real +ve axis but inside the unit circle, the impulse response has the
characteristic of a
damped sinusoid as for a continuous system.
eg (0.96, 20.0, NA, NA, NA, NA, NA, 2, 0, 1.0) 18 (360/20)
samples per period.
eg (0.96, 90.0, NA, NA, NA, NA, NA, 2, 0, 2.0)
The response is still a damped sinusoid but at 0.25
ws ie 4 samples per period,
2 at the peaks and 2 at the zeros of the sinusoid.
eg (0.96, 180.0, NA, NA, NA, NA, NA, 2, 0, 0.3)
The response is a damped sinusoid at 0.5
ws ie 2 samples per period
at the peaks of the sinusoid.
The step and ramp response can be seen by changing Fn.
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Copyright 2000 © Cuthbert A. Nyack.