12.3 TIME-DOMAIN CONVOLUTION INTEGRAL

We show in this section that the impulse response is a complete characterisation of a linear time-invariant circuit. It is a complete characterisation in the sense that the zero-state response of a linear time-invariant circuit to the application of any arbitrary input source function can be determined from the impulse response and the input source function.

We show this in three steps. In the first step, we show that the zero-state response of a linear time-invariant circuit to a narrow rectangular pulse input of unit area content can be approximated by its impulse response. In the second step, we show that any arbitrary input source function can be resolved into a stream of weighted impulses. In the third ...

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