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becomes an integral, and the representation of the output of a linear, time-in-variant system as a linear combination of delayed impulse responses also be-comes an integral. The resulting integral is referred to as the convolution in-tegral and is similar in its properties to the convolution sum for discrete-time signals and systems.

### Lyman 313226

Evaluating Convolution Integrals A way of rearranging the convolution integral is de-scribed and illustrated. The differencesbetween convolutionin timeand space are discussed and the concept of causality is intro-duced. The section ends with an example of spatial convolu-tion. 42

Ch. 3: Forced Vibration of 1-DOF System 3.1 Harmonic Excitation Force input function of the harmonic excitation is the harmonic function, i.e. functions of sines and cosines. This type of excitation is common to many system involving rotating and reciprocating motion. Moreover, many other forces can be represented as an infinite

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Evaluation of the convolution integral using graphical methods is also presented and illustrated with several examples. 6.1 The Impulse Response in Time Domain In this section we will discuss the impulse response of a network, that is, the output (voltage or current) of a network when the input is the delta function.

Now let's convolute the two functions. So the convolution of f with g, and this is going to be a function of t, it equals this. I'm just going to show you how to apply this integral. So it equals the integral-- I'll do it in purple-- the integral from 0 to t of f of t minus tau. This is my f of t.