What is (f*g)(x)
multiplying inputs
The expression (f*g)(x) represents the convolution of two functions f(x) and g(x). The expression (f*g)(x) is defined as:
(f*g)(x) = integral from negative infinity to infinity of f(x-t) * g(t) dt
where * denotes multiplication and t is a variable of integration.
In simpler terms, (f*g)(x) is obtained by taking one of the functions (let’s say g(x)), flipping it horizontally, and then sliding it across the other function (f(x)) while multiplying the two functions point by point and adding up the results.
The resulting function (f*g)(x) is a new function that takes in the input variable x and gives back a value that represents the blending of the two original functions f(x) and g(x). The convolution operation has many applications in signal processing, image analysis, and other areas of mathematics and engineering.
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