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Transitional Gaussian Filters

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

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  1. Jon

    Jon Guest

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

    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

  3. 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 Edwards

    Reg Edwards Guest


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