tThe difference between the circular and regular convolution

I could not understand the difference between the circular and regular convolution can somebody ellobrate it.

Re: circular convolution

circular convolution is defined for convolving two periodic signals.
because to signals are infinite energy signals their convolution is either zero or infinite so regular convolution is not definable for this signal.
otherwise regular convolution is defined as one of or both of signals is/are nonperiodic.
regards

Re: circular convolution

This is example I wrote in Matlab
I think, you can analyze this and answer to your question by yourself

>> a=1:4
a =
1 2 3 4
>> b=5:8
b =
5 6 7 8

Linear convolution
>> conv(a,b)
ans =
5 16 34 60 61 52 32

circullar convolution
>> real(ifft(fft(a).*fft(b)))
ans =
66 68 66 60

linear convolution with periodic signal
>> conv([a a a a],b)
ans =
Columns 1 through 11
5 16 34 60 66 68 66 60 66 68 66
Columns 12 through 19
60 66 68 66 60 61 52 32
>>

Re: circular convolution

then is it that we will not be able to get back the original signal by taking the ifft of the product of fft of the 2 signals????? then how will we be able to get back the original signal?

thanking you,
AMRITH.S.

vadkudr said:

This is example I wrote in Matlab
I think, you can analyze this and answer to your question by yourself

>> a=1:4
a =
1 2 3 4
>> b=5:8
b =
5 6 7 8

Linear convolution
>> conv(a,b)
ans =
5 16 34 60 61 52 32

circullar convolution
>> real(ifft(fft(a).*fft(b)))
ans =
66 68 66 60

linear convolution with periodic signal
>> conv([a a a a],b)
ans =
Columns 1 through 11
5 16 34 60 66 68 66 60 66 68 66
Columns 12 through 19
60 66 68 66 60 61 52 32
>>

Click to expand...

Re: circular convolution

Circular Convolution: here take 2 inputs with same length or different length, if different length, then output will be bigger length, because the smaller length signal is padded with zeros. Now take DFT of the two input signals,

x[n]---->DFT----->X[K]----------|
X----X[k].Y[k]--------->IDFT------->>x[n]*Ny[n]
y[n]---->DFT----->Y[k]-----------|


where *N=cirularly convoluted with Mod N

Regular Convolution: Here the 2 signals may be periodic or aperiodic, also in this the period goes into negative domain, by mirroring either the input or impulse response. hence the length after convolution will be N1 + N2 - 1.

Added after 1 minutes:

in the above equation for circular convolution the second line is not appeared properly, hence to read it carefully, the second line is shifted towards right.

sorry for the inconvenience

Re: circular convolution

thanks

vadkudr said:

This is example I wrote in Matlab
I think, you can analyze this and answer to your question by yourself

>> a=1:4
a =
1 2 3 4
>> b=5:8
b =
5 6 7 8

Linear convolution
>> conv(a,b)
ans =
5 16 34 60 61 52 32

circullar convolution
>> real(ifft(fft(a).*fft(b)))
ans =
66 68 66 60

linear convolution with periodic signal
>> conv([a a a a],b)
ans =
Columns 1 through 11
5 16 34 60 66 68 66 60 66 68 66
Columns 12 through 19
60 66 68 66 60 61 52 32
>>

Click to expand...

thanks