Transitional Gaussian Filters

• posted

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?
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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

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I read in sci.electronics.design that Jon wrote (in ) about 'Transitional Gaussian Filters', on Mon, 3 Jan 2005:

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'.

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

• posted

Reg,

Thanks for your interest. I'm interested in applying the algorithm to the design of other transitional or "compromise" filters, e.g., Gaussian in the passband, Chebyschev in the stopband, etc. I don't want to reinvent the wheel if I don't have to.

Regards, Jon

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