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An online convolution calculator will combine two different data sequences into a single convolution data sequence quickly. This calculator does point to point multiplication of given functions.
In mathematics, convolution is the mathematical operation of two functions (a and b), which creates a third function (a * b) that represents how the shape of one function is modified by another function. It is also defined as the integral of the product of any two functions after one function is inverted and shifted. So, calculate the integral of all offset values to obtain the convolution function.
$$ (a * b) (t) := ∫_-∞^∞b(r) a(t – r) dr $$
Example 1:
Write first data sequence (A) = 1, 0, 1, 0, 0
Then, write second data sequence (B) = 0.2, 0.5, 0.6
By using convolution formula
$$ (a * b) (t) := ∫_-∞^∞b(r) a(t – r) dr $$
Thus, result data sequence (C) = 0.2, 0.5, 0.8, 0.5, 0.6, 0.0, 0.0
Example 2:
Put the first data sequence (A) = 1, 1, 1, 0, 0, 0
Now, put second data sequence (B) = 1, 1, 1, 0, 0, 0
With the help of convolution integral formula
$$ (a * b) (t) := ∫_-∞^∞b(r) a(t – r) dr $$
Hence, the result data sequence (C) = 1, 2, 3, 2, 1, 0, 0, 0, 0, 0, 0
Our Calculator helps you to compute the convolution function of given functions by following these steps:
Reference:
From the source of Wikipedia: Notation, Derivations, Historical developments, Circular convolution, Discrete convolution, Circular discrete convolution.