# [music-dsp] "Factorization" of filter kernels

```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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```