**Robotronicdiagram**. - In the first Matlab lesson programming, we will give you listing program for convolution function or we will guide you to make convolution function that based on Matlab software version R2009a.

Figure 1. Convolution using Matlab Toolbox and Own Function |

In here we will give you firstly description about what is convolution from Matlab toolbox and then we will give you listing program that we programmed with our self logical and give the same result with we using the Matlab toolbox.

Let we begin our lesson about convolution function from Matlab function toolbox.

# convolution

Convolution and polynomial multiplication

## Syntax

w = conv(u,v)

`C = conv(...,'shape')`

## Description

`w = conv(u,v)`convolves vectors

`u`and

`v`. Algebraically, convolution is the same operation as multiplying the polynomials whose coefficients are the elements of

`u`and

`v`.

`C = conv(...,'shape')`returns a subsection of the two-dimensional convolution, as specified by the

`shape`parameter:

## Definition

Let

`m = length(u)`and`n = length(v)`. Then`w`is the vector of length`m+n-1`whose`k`th element is
The sum is over all the values of

`j`which lead to legal subscripts for`u(j)`and`v(k+1-j)`, specifically`j``=``max(1,k+1-n)`:`min(k,m)`. When`m``=``n`, this givesw(1) = u(1)*v(1)w(2) = u(1)*v(2)+u(2)*v(1)w(3) = u(1)*v(3)+u(2)*v(2)+u(3)*v(1)...w(n) = u(1)*v(n)+u(2)*v(n-1)+ ... +u(n)*v(1)...w(2*n-1) = u(n)*v(n)

## Algorithm

The convolution theorem says, roughly, that convolving two sequences
is the same as multiplying their Fourier transforms. In order to make
this precise, it is necessary to pad the two vectors with zeros and
ignore roundoff error. Thus, if

`X = fft([x zeros(1,length(y)-1)])`

and

`Y = fft([y zeros(1,length(x)-1)])`

then

`conv(x,y) = ifft(X.*Y)`
According the concept of convolution above you can easily use function convolution using syntax "conv" for example:

And now you can try to use our convolution function that we arrange with the function name "konvolusi" like example below and see the result.

We know that our function and Matlab toolbox function give result same. And to test the result you can use the others input x and h.

And here are the listing program that we make for convolution function as follow:

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