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

Convolution of Sequences Formula

y_n = _{k= -ꝏ}∑^ꝏ (x_k) * (h_k)

• y_n = resulting sequence at the n^th index.
• X_k = First input sequence.
• h_k = 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 “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}