# DFT circular convolution

Started by October 11, 2007
```hello everybody!!
can anyone tell me in calculating circular convolution using DFT
what will happen if i use two different length signal?
suppose one is of 4 point and the other is of 3 point then what will be
the system?i have to do both 4 point DFT?or 4+3-1 or 6 point DFT as like
linear convolution...
plz help me out..
shatila

```
```shatila wrote:
> hello everybody!!
> can anyone tell me in calculating circular convolution using DFT
> what will happen if i use two different length signal?
> suppose one is of 4 point and the other is of 3 point then what will be
> the system?i have to do both 4 point DFT?or 4+3-1 or 6 point DFT as like
> linear convolution...
> plz help me out..
> shatila

Well, as you should know, convolution using a DFT is done by
multiplying the (complex) values of each DFTed signal. If you want to
do that with two signals of different length with no prior padding,
some values of your longer signals won't find any match for
multiplication.

I suggest you to read more about it on relevant chapters on
http://www.dspguide.com

```
```"Michel Rouzic" <Michel0528@yahoo.fr> wrote in message
>
> shatila wrote:
>> hello everybody!!
>> can anyone tell me in calculating circular convolution using DFT
>> what will happen if i use two different length signal?
>> suppose one is of 4 point and the other is of 3 point then what will be
>> the system?i have to do both 4 point DFT?or 4+3-1 or 6 point DFT as like
>> linear convolution...
>> plz help me out..
>> shatila
>
> Well, as you should know, convolution using a DFT is done by
> multiplying the (complex) values of each DFTed signal. If you want to
> do that with two signals of different length with no prior padding,
> some values of your longer signals won't find any match for
> multiplication.
>
> I suggest you to read more about it on relevant chapters on
> http://www.dspguide.com
>

Short answer: pad both sequences with zeros so the lengths are equal and
both have length >=6.

As an exercise, do the circular convolution in time as a "cartoon" on a
sheet of paper.
Or, if you like, assume that the sequences are periodic and do the same
thing.
It's then easy to visualize why you want the lengths >=6 then... because
otherwise there will be overlap.
Then, as mentioned in other responses, also understand that the lengths have
to be *equal* for the FFT/multiply/IFFT process to make any sense.

Fred

```