 # Convolution calculator

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

Give Us Feedback

## 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 “(S1) * (S2)” and read as the convolution of S1 with S2.

## Convolution of Sequences Formula

yn = k= -ꝏ (xk) * (hk)

• yn = resulting sequence at the nth index.
• Xk = First input sequence.
• hk = Second input sequence.
• 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 “xk” and “hn-k” at each value of “k” and summing all values to get the resultant “yn”.

## 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},

yn =?.

Step 2: Write the Formula of Convolution.

yn = k= -ꝏ (xk) * (hk)

Step 3: Put the data in the above formula.

yn = k= -30 {6, 7, 1, 2}* {1, 3, 2}

yn = {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}, yn =?.

Step 2: Write the Formula of Convolution.

yn = k= -ꝏ (xk) * (hk)

Step 3: Put the data in the above formula.

yn = ∑k= --30 {3, 6, 7, 8}* {0.1, 0.3, 0.2},

yn = {0.3, 1.5, 3.1, 4.1, 3.8, 1.6}

### Math Tools 