The given input
x(t) is approximated with narrow rectangular pulses, each scaled to the appropriate value of
x(t) at the corresponding t (which lies at the midpoint of the base of width
d). This is called the staircase approximation of
x(t).
By merely knowing the impulse response one can predict the response of the signal
x(t) by using the given formula for convolution.
If we are given unit-step response, we can calculate unit-impulse response by
differentiating the unit-step response .
If we are given unit-impulse response, we can calculate unit-step response by taking running integral of unit-impulse response .
The convolution
(x*h)(t) is the common (shaded) area enclosed under the curves x(v) and h(t-v)as v varies over the entire real axis.
As t increases,
h(t-v) can be considered to be a train moving towards the right and at each point on the v -axis the common area under the product x(v) and h(t-v) is the value of y(t) at that t.
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