Mathematical and Technical Detail

Mathematical Aspects of *

Although the star notation is widely used, it must be remembered that convolution is an operator: At any t the value of y(t) depends on the entire signals x(t) and h(t). Thus, for example, operations such as time shift must be treated carefully, since h(t - 2) * x(t - 2) does NOT yield the signal y(t - 2).

Notice also that the mathematical operation *  has an identity operation, since

x(t) * d (t ) = x(t)

for any  (suitably continuous) signal  x(t).

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