Z Transform and System Identification.

Cuthbert Nyack
Given the input x(n) to a system and the output y(n) from the system, then it is possible to derive the Impulse Response I(n) of the system. This proceedure is called System Identification and the equation required is shown below.
The following applet illustrates the proceedure. x(n) is set by the first 12 scrollbars labelled in cyan and the output by the next 24 labelled in pink. Numerical values are shown in white. For verification, the output derived from the input and the calculated impulse response is also shown slightly shifted to the right. The Impulse Response may go on for a very long time and could be unstable depending on x(n) and y(n).

The image below shows the first 24 samples of the impulse response required to reshape a distorted pulse into a rectangular pulse.

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COPYRIGHT 2008 Cuthbert Nyack.