Hi,

Maybe this can be of help.

http://www.musicdsp.org/archive.php?classid=3#65

All the best
Massimiliano

Il 19/01/2011 15.56, Uli Brueggemann ha scritto:
Hi,

thanks for the answer so far.
A polyphase filter is a nice idea but it does not answer the problem.
The signal has to be demultiplexed (decimated), the different streams
have to be filtered, the results must be added to get the final output
signal.

My question has a different target.
Imagine you have two system (e.g. some convolution  boards with DSP).
Each system can just run a 512 tap filter. Now I like to connect the
two systems in series to mimic a desired 1024 tap filter. The 1024
kernel is known and shall be generated by the two 512 tap filters.
So what's a best way to decompose the known kernel into two parts ? Is
there any method described somewhere?

Uli


2011/1/19 João Felipe Santos<joao....@gmail.com>:
Hello,

a technique that allows something similar to what you are suggesting
is to use polyphase filters. The difference is that you will not
process contiguous vectors, but (for a 2-phase decomposition example)
process the even samples with one stage of the filter and the odd
samples with another stage. It is generally used for multirate filter
design, but it makes sense to use this kind of decomposition if you
can process the stages in parallel... or at least it is what I think
makes sense.

You can search for references to this technique here [1] and here [2].
A full section on how to perform the decomposition is presented on
"Digital Signal Processing: a Computer-based approach" by Sanjit K.
Mitra.

[1] 
http://www.ws.binghamton.edu/fowler/fowler%20personal%20page/EE521_files/IV-05%20Polyphase%20FIlters%20Revised.pdf
[2] https://ccrma.stanford.edu/~jos/sasp/Multirate_Filter_Banks.html

--
João Felipe Santos



On Tue, Jan 18, 2011 at 5:46 AM, Uli Brueggemann
<uli.brueggem...@gmail.com>  wrote:
Hi,

a convolution of two vectors with length size n and m gives a result
of length n+m-1.
So e.g. two vectors of length 512 with result in a vector of length 1023.

Now let's assume we have a vector (or signal or filter kernel) of size
1024, the last taps is 0.
How to decompose it to two vectors of half length? The smaller vectors
can be of any arbitrary contents but their convolution must result
must be equal to the original vector.

It would be even interesting to "factorize"  given kernel into n
smaller kernels. Again the smaller kernels may have any arbitrary but
senseful contents, they can be identical but this is not a must.

Is there a good method to carry out the kernel decomposition? (e.g.
like calculating n identical factors x of a number y by x =
Exp(Log(y)/n) with x^n = x*x*...*x = y)

Uli
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