Convolution Calculator

Enter the values of both data sets, and the calculator will compute their convolution to generate a single convolved data set.

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An online Convolution Calculator allows you to combine two sequences of data into a single convolution sequence efficiently. This tool performs element-wise multiplication and summation of the provided sequences step by step.

What is Convolution?

In mathematics, convolution is an operation between two functions f(t) and g(t) that produces a new function (f * g)(t). The resulting function describes how the shape of one function is influenced by the other. Convolution can also be expressed as the integral of the product of the two functions after one is flipped and shifted:

$$ (f * g)(t) := \int_{-\infty}^{\infty} f(\tau) \, g(t - \tau) \, d\tau $$

How to Compute Convolution?

Example 1:

First sequence (F): 1, 0, 2, 0, 0
Second sequence (G): 0.5, 0.3, 0.2
Apply the convolution formula:

$$ (f * g)(t) := \sum f(k) \, g(t - k) $$

Resulting convolution sequence (H): 0.5, 0.3, 1.1, 0.6, 0.4, 0.0, 0.0

Example 2:

First sequence (F): 1, 2, 1, 0, 0
Second sequence (G): 1, 0, 1, 0, 0
Using the convolution formula:

$$ (f * g)(t) := \sum f(k) \, g(t - k) $$

Resulting convolution sequence (H): 1, 2, 2, 2, 1, 0, 0, 0, 0

How Our Convolution Calculator Works

Input:

Enter both sequences in the input fields, separated by commas.
Press the Calculate button to generate the convolution sequence.

Output:

The calculator outputs the resulting convolution sequence based on the entered data.
You can press Recalculate to compute convolutions for new sequences.

Reference:

Source: Wikipedia: Convolution – Definitions, Derivations, Circular and Discrete Convolutions

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