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# Convolution calculator

Input comma separated values and press calculate button to find data sequence using convolution calculator

## Convolution calculator

Convolution calculator is used to find the convolution of two sequences.

## What is the Convolution of Two Sequences?

The convolution of two sequences is a mathematical operation that convolutes the two discrete sequences to generate a new resultant discrete sequence. It is denoted as **“(S _{1}) * (S_{2})”** and read as the convolution of S

_{1 }with S

_{2}.

## Convolution of Sequences Formula

**y _{n} = _{k=} _{-ꝏ}∑^{ꝏ} (x_{k}) * (h_{k})**

**y**= resulting sequence at the n_{n}^{th}index.**X**= First input sequence._{k}**h**= Second input sequence._{k}- “
**k**” is the index used for summation ranging from negative infinity to positive infinity.

And** “*” **denotes the convolution operation which involves multiplying the values of “x_{k}” and “h_{n-k}” at each value of “k” and summing all values to get the resultant “y_{n}”.

## How to find the Convolution of Two Sequences?

Here are a few examples of the convolution of two sequences.

**Example 1:**

If x = {6, 7, 1, 2}, h = {1, 3, 2} then find the Convolution sequence.

**Solution:**

**Step 1: **Write the given data.

x = {6, 7, 1, 2}

h = {1, 3, 2},

y_{n} =?.

**Step 2: **Write the Formula of Convolution.

y_{n} = _{k=} _{-ꝏ}∑^{ꝏ} (x_{k}) * (h_{k})

**Step 3:** Put the data in the above formula.

y_{n} = _{k=} _{-3}∑^{0} {6, 7, 1, 2}* {1, 3, 2}

**y _{n} = {6, 25, 34, 19, 8, 4}**

**Example 2:**

If x = {3, 6, 7, 8}, h = {0.1, 0.3, 0.2} then find the Convolution sequence.

**Solution:**

**Step 1: **Write the given data.

x = {3, 6, 7, 8}, h = {0.1, 0.3, 0.2}, y_{n} =?.

**Step 2: **Write the Formula of Convolution.

y_{n} = _{k=} _{-ꝏ}∑^{ꝏ} (x_{k}) * (h_{k})

**Step 3:** Put the data in the above formula.

y_{n} = ∑_{k=} _{--3}^{0} {3, 6, 7, 8}* {0.1, 0.3, 0.2},

**y _{n} = {0.3, 1.5, 3.1, 4.1, 3.8, 1.6}**