A continuous-time signal (a square wave) is given by

$f_{step}$ (t) = u(t − T) − u(t − 3T) − [u(t − 5T) − u(t − 7T)]

This signal is applied to a system with a transfer function given by
$\frac{v_{ out}}{v_{in}} = \frac{1}{1-z^{-1} }$
Determine the time domain output of the system.

Question

A continuous-time signal (a square wave) is given by

[latex]f_{step}[/latex] (t) = u(t − T) − u(t − 3T) − [u(t − 5T) − u(t − 7T)]

This signal is applied to a system with a transfer function given by

[latex]\frac{v_{ out}}{v_{in}} = \frac{1}{1-z^{-1} }[/latex]

Determine the time domain output of the system.

Accepted Answer

First, we take the transfer function and cross-multiply so that

[latex]v_{ out}-v_{ out}z^{-1}= v_{ in}[/latex]

Noting that [latex]z^{-1}[/latex] is a unit delay means that, in the time domain, the previous equation can be rewritten as

[latex]v_{ out\_k}= v_{ in\_k}+ v_{ out\_k - 1}[/latex]

where k denotes the kth sampling instant. Figure A.12 shows a plot of the outputs noting that, at every sampling instant, the output is the sum of the last output plus the current input.

Question A.4: A continuous-time signal (a square wave) is given by fstep (...

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