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.