Environmental Engineering Reference
In-Depth Information
A given input waveform can be represented by the linear combination
of a set of basic functions, possibly infinite, that are linearly indepen-
dent. The response of the circuits to each of these basis functions is
first computed separately and the complete response of the circuit is
then obtained by summing up its response to the basis functions.
As an illustration, consider a linear circuit. The input waveform
is shown in Fig.4.8. The input waveform is approximated with a
piecewise-liner input waveform shown in Fig.4.8.
The input in the interval
is represented by
where is the unit step function. Note that the time origin of
(4.54) is at It can be shown that under the condition
the response is obtained from
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