# Transitional Gaussian Filters

Discussion in 'Electronic Design' started by Jon, Jan 3, 2005.

1. ### JonGuest

I'm interested in an algorithm, or general approach, to the calculation
of pole locations for transitional Gaussian filters, e.g., Gaussian to
6db, Gaussian to 12 db, etc. I have references that have tables of
pole locations (Zverev, Williams), but no algorithms. Does anyone have
suggestions for good references?

2. ### Jens TingleffGuest

I haven't seen anything which suggest that you can do better than pure numerical
optimisation.

Some Spice-like packages (e.g. HSpice, Eldo) allow you to do optimisation with
multiple cost functions (e.g. minimise difference to pure Gaussian filter below
a certain frequency and minimise level in stop-band) where you can weigh the
costs functions to get the desired result. Another approach is to quickly write
a couple of cost-functions in Matlab and use the optimisation toolbox.

I know of one dedicated package for fitting poles and zeros given a requested
transfer function, but it was written such a long time ago that it might as well
not be there :-(.

This way you can also make your own filter type, e.g. 5th order LP filter with
one transmission zero (I have had joy with putting one transmission zero near
the DAC image frecuency in a reconstruction filter and optimsing for a flat
amplitude and group delay in the passband).

Hope this helps a little

Jens

3. ### John WoodgateGuest

The first edition of Williams says (2.7) 'The transitional filters
tabulated in chapter 12 were generated by mathematical techniques which
involve interpolation of pole locations.' No reference is given, but the
associated figures credit Zverev, so may be there is a reference in
Zverev to the source of these 'mathematical techniques'.

4. ### Reg EdwardsGuest

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Just interested - for practical reasons, why would you wish to know?