# Rectangular Pulse Response of 2 Pole System, Time and Frequency Domains.

Cuthbert Nyack

Consider a 2 pole system with poles at z = re^{±jq}. The transfer function of the system
is given by *Y*(*z*)/*X*(*z*) and the output can be determined for any
input by the difference equation for *y*(*n*).
Alternatively the DFT Xi(m) for the input can be calculated. The
DFT Xs(m) of the system can be calculated by sampling the DTFT. The
DFT of the output is now the product Xi(m)Xs(m) and taking the inverse of
this gives the output.

The applet below compares the output obtained both ways.
cyan
shows the output calculated from the difference equation and
violet
shows the output calculated from the inverse of the DFT of the output.

The input and its spectrum is shown in red and pink respectively.

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COPYRIGHT © 2007 Cuthbert Nyack.