18.3 IMPULSE RESPONSE

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If we put an impulse into a system the output will be an impulse response.

Figure 18.2 Response of the system to a single pulse

If we add all of the impulse responses together we will get a total system response. This operation is called convolution.

Figure 18.3 A set of pulses for a system gives summed responses to give the output

Consider the unit impulse of a system with the given differential equation. Note: This method is only valid for trivial differential equations with only one homogeneous term. The preferred method is shown later.

Note that the derivation of the unit impulse function assumed zero initial conditions, so the process of convolution must also assume systems start at rest and undeflected.