Definition
The convolution of f and g is written f∗g, using an asterisk or star. It is defined as the integral of the product of the two functions after one is reversed and shifted. As such, it is a particular kind of integral transform:
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(commutativity)
While the symbol t is used above, it need not represent the time domain. But in that context, the convolution formula can be described as a weighted average of the function f(τ) at the moment t where the weighting is given by g(−τ) simply shifted by amount t. As t changes, the weighting function emphasizes different parts of the input function.
More generally, if f and g are complex-valued functions on Rd, then their convolution may be defined as the integral:
Visual explanation of convolution. |
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Read more about this topic: Convolution
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