Transfer Function Analysis by Manipulation of Poles and Zeros

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0.1

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25

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BilinearTransform

init

This Demonstration shows how the locations of poles and zeros of the system transfer function affect the system properties. Drag a pole or a zero of a discrete system transfer function

H(z)

to a different location and observe the effect on the system.

H(z)=

Y(z)

X(z)

represents the transfer function of a discrete time system, where

Y(z)

is the

Z

-transform of the output signal and

X(z)

is the

Z

-transform of the input signal. Writing

H(z)

as a ratio of two polynomials in

z

, the poles of

H(z)

are the roots of the denominator and the zeros are the roots of the numerator.

The continuous time transfer function approximation

H(s)

is generated using all supported

H(z)

to

H(s)

mapping methods in Mathematica 8. The mapping of the

z

plane to the

s

plane is also generated. A total of 12 different plots can be generated as you move the poles and zeros to different locations.