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Introduction to DSP - IIR filters: the meaning of z

z is a complex number:

z equation

When drawn on the Argand diagram, z has the curious property that it can only have a magnitude of 1:

magnitude of z

So z, which is the variable used in our frequency response, traces a circle of radius 1 on the Argand diagram. This is called the unit circle.

The map of values in the z plane is called the transfer function H(z).

The frequency response is the transfer function H(z) evaluated around the unit circle on the Argand diagram of z:

Argand diagram of z

Note that in the sampled data z plane, frequency response maps onto a circle - which helps to visualise the effect of aliasing.

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