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Results tagged with convolution
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user 55461
Convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions.
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Initial rest condition applied on $x(t)$ vs $h(t)$
Define the LTI system $\mathcal{H} : x\mapsto y$
Define the convolution for continuous-time system :
$$
(x*h)(t)=\int_{-\infty}^{\infty}x(\tau)h(t-\tau)\;\text{d}\tau
$$
The initial rest condition states … that :
An LTI system with an input signal $x(t)$ is causal if and only if $x(t)=0$, $\forall t<0$
Now I have noticed that in some textbooks, the definition of convolution would have $h(\tau)$ instead …
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