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From: "Peter O. Brackett"
Subject: Re: What filer has equal ripple phase response, and where can I find the pole positions for a 4th order filter?
Date: Sat, 18 Jan 2003 17:17:44 -0500
Organization: MindSpring Enterprises
X-Server-Date: 18 Jan 2003 22:17:29 GMT
X-Newsreader: Microsoft Outlook Express 5.00.2919.6600
> Bessel filters have maximally-flat phase response, but what filter is a
> general case, with equi-ripple phase response.
> I'm asking because I would need to use an all pass network based on 6th
> Bessel poles (plus the 6 matching zeros of course) whereas I would hope I
> get by with 4th order if I relax the spec to equi-ripple phase (say +/-3
> Tony (remove "_" from email address to reply)
Although such filters are indeed feasible [low pass with equiripple group
are no "standard" approximations or common tabulations of such filters.
Your only practical recourse is to select or design an appropriate low pass
then to approximate and synthesize an all-pass delay equalizer to place in
with the filter. The all-pass delay equalizer would be designed, say using
exchange algorithm, to equalize the group delay of the filter-equalizer
cascade to be
a prescribed constant plus or minus the prescribed equiripple amount.
Many years ago I was once in the business of designing, building and selling
"custom" all-pass equaizers commercially. There was a *big* market for them
the telecom wireline carrier system business. Back then we designed those
products with a set of specially developed approximation and synthesis
programs which I developed for the purpose. I still have such general
programs available for my own private use in my consulting practice, but my
for generating such designs are likely too high for "one-off" designs.
Lacking access to such custom programs, your best bet is to try to get by
Bessel filter that is "close" to what you want.
Indialantic By-the-Sea, FL.
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