Circular Convolution

Greetings,

I was wondering if there was a way to perform convolution without lengthening
the signal.  Can cirular convolution be used for this?  Everything I've
looked up so far only mentions graphics operations.  I am working with sound.
	

Hi,

you can certainly use circular convolution to prevent
signal expansion after filtering. say your input is of
length L = 5 and the filter is of length M = 3. Then
generate a new signal by perodically extending the
input by length M-1 = 2:

input: 1 2 3 4 5
periodically extended input : 4 5 1 2 3 4 5 1 2 
(length = 9)

now after doing convolution, you should ignore first
two values in the o/p. The next L values are your
filtered result, corresponding to the original input 1
2 3 4 5. 
 
instead of a mere periodic extension, you may want to
use symmetric peridoc extension of the form:
3 2 1 2 3 4 5 4 3

For further details, check the following paper:

B. Usevitch, A tutorial on Modern Lossy Wavelet Image
Compression: Foundations of JPEG 2000, IEEE Signal
Processing Magazine, Sep 2001, pp 22-35. 

hope that helps. 
regards,
Sameer
	---
"To know the road ahead, ask those coming back."
- Chinese proverb
	--- ShadowsEdge Admin <shadowsedge@shad...>
wrote:
> Greetings,
> 
> I was wondering if there was a way to perform
> convolution without lengthening the signal.  Can
> cirular convolution be used for this?  Everything
> I've looked up so far only mentions graphics
> operations.  I am working with sound.
> 
> 
> 
> 

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