# How to perform Convolution in excel?

Started by December 19, 2005
```Hi all,

As the subject suggest, I would like to know if anyone know how to
perform convolution in excel?

In excel only have the Fourier analysis, but no convolution Function.

Sulphox

```
```sulphox wrote:
> Hi all,
>
> As the subject suggest, I would like to know if anyone know how to
> perform convolution in excel?
>
> In excel only have the Fourier analysis, but no convolution Function.

You can use the convolution theorem:

where * denotes the point-wise multiplication of complex vectors.

```
```<abariska@student.ethz.ch> wrote in message
> sulphox wrote:
>> Hi all,
>>
>> As the subject suggest, I would like to know if anyone know how to
>> perform convolution in excel?
>>
>> In excel only have the Fourier analysis, but no convolution Function.
>
> You can use the convolution theorem:
>
>
> where * denotes the point-wise multiplication of complex vectors.

In Excel:

"Signal1" in column A

"Filter" or reversed "Signal2" in column B

Column C filled with SUMPRODUCT(\$nonzero range of cells in Column A (\$ for
unchanging), running range of cells in Column B of same length as range in
Column A)

Example:
The fixed-length function is in Column D
The longer function is in Column C.
The convolution is in Column E.

E51=SUMPRODUCT(D\$4:D\$54,C1:C51)
where
the shortest array "D" is of length 51 and
"C" can be of any length.
C starts with 51 zeros so the leading transient can be computed.

Not fancy but it works.

Fred

```
```Hi,

Do you mean that convolution is the multiplication of 2 complex
number?
let's say if i have S(f) which is FFT of s(n),
also i have Y(f) which is the FFT of y(t).

Do you mean the convolution of S(f) and Y(f) is the Product of the
Multiplication of S(f) and Y(f)?

Sulphox

```
```sulphox wrote:
> Hi,
>
> Do you mean that convolution is the multiplication of 2 complex
> number?
> let's say if i have S(f) which is FFT of s(n),
> also i have Y(f) which is the FFT of y(t).
>
> Do you mean the convolution of S(f) and Y(f) is the Product of the
> Multiplication of S(f) and Y(f)?

Almost. The convolution of s(n) with y(t) is the inverse FT of the
(point-wise) product of S(f) with Y(f)!

```
```abariska@student.ethz.ch wrote:
> Almost. The convolution of s(n) with y(t) is the inverse FT of the
> (point-wise) product of S(f) with Y(f)!

With appropriate zeropadding (otherise, this describes circular
convolution).

```