impulse response computing

jim skrev:
> Rune Allnor wrote:
> >
> > Martin Eisenberg skrev:
> > > Rune Allnor wrote:
> >
> > > > In some cases some severe simplifications and idealizations --
> > > > "severe" in the sense that they have introduced large errors --
> > > > have been used to obtain those separable functions.
> > >
> > > That's what I meant by the part of the sentence that you snipped, I
> > > guess. Out of interest, what systems did those functions describe?
> > > Did you choose separable approximations to simplify processing or for
> > > other reasons?
> >
> > There are mainly two areas of 2D z transforms I have worked with:
> > Images and Partial Differential Equations.
> >
> > Images are sampled on regular (n,m) points, so there separable
> > kernels are used by default.
>
> If you are saying that the regular sampling of an image precludes the
> use of filters that are not separable into 2 1d filters - that is
> incorrect.

I did not. I am saying that image filters that are to be expressed as
z transforms are expressed as at most two 1D transforms. Some are
expressed even simpler; as one cylinder symmetric 1D ZT.

> If you are saying that they are not commonly used - that is
> also incorrect. The commonly used implementation of a Sharpening filter
> would be one example of  a filter that can't be separated into two 1d
> filters.

And how often do you see a sharpening filter extressed as a z
transform?

Rune