Re: Right function for Discrete Convolution

[Quentin Spencer]

NZG wrote:

> > Convolution returns an output longer than its inputs by definition.
> >    
> Does it? Perhaps I am misunderstanding convolution altogether.
> I have always learned it from the control standpoint, as being 
> x(n)*y(n) =
> the infinite summation of x(k)y(n-k) from k=-infy to k=infy for all n.
>
> This would imply the same dimension, n, would it not?
> Am I missing something?
> Does anyone have any links that explain why the dimension changes? 
>
> thx,
> NZG. 
>  
That is correct--if the signal is infinite in length, then any 
convolution involving the signal is also infinite in length, so you 
could argue that they are the same length (inf + N = inf). However, 
since practical application demands that we make our signals finite in 
length, then the convolution will be longer than the inputs. This is 
important in many signal processing applications where the signal is in 
some sense infinite--we are dealing with a small chunk of an ongoing 
signal. If I am filtering a signal in chunks of 1024 samples and my 
filter has length 100, the convolution of one chunk with the filter will 
have length 1123. The residual 99-point output must be saved and added 
to the first 99 points of the next output when I filter the next chunk.

-Quentin



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