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Math Calculators ▶ Convolution Calculator

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**Table of Content**

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 â€‹â€‹to obtain the convolution function.

$$Â (a * b) (t)Â := âˆ«_-âˆž^âˆžb(r) a(t â€“ r) dr $$

**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

$$ (a * b) (t)Â := âˆ«_-âˆž^âˆžb(r) a(t â€“ r) dr $$

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

$$ (a * b) (t)Â := âˆ«_-âˆž^âˆžb(r) a(t â€“ r) dr $$

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:

- First, enter given data sequences in both boxes. Remember, sets are separated with a comma.
- Hit the calculate button to see the convolution function.

- The convolution calculator provides given data sequences and using the convolution formula for the result sequence.
- Click the recalculate button if you want to find more convolution functions of given datasets.

**Reference:**

From the source of Wikipedia: Notation, Derivations, Historical developments, Circular convolution, Discrete convolution, Circular discrete convolution.