🚀 go-pugleaf

In article <3504@radio.oakhill.UUCP> you write:
>
>I would like to use an IIR filter in a particular application.  I 
>also need linear phase response.  Does anyone have any good references
>to papers/books/chapters concerning digital phase correction for
>IIR filters.  I can't use an FIR in place of the IIR because it is
>a switched capacitor design and must be kept simple.  I CAN however
>use a small FIR or an IIR to digitally correct the phase...additionally,
>the phase ripple can be as high as +-10 degrees and still be considered
>acceptable correction. Any help would be apprieciated.
> 
> -Charlie Thompson

A solution to your problem could be Allpass Filters. With Allpass' you
can design approximately linear phase filters. Some good references :

S.K.Mitra,K. Hirano : Digital All-Pass Networks, IEEE Trans. on
Circuits and Systems, Vol. Cas-21, pp. 688-700, No.5, September 1974.

M.Renfors, T.Saram{ki : A Class of Approximately Linear Phase Digital
Filters Composed of Allpass Subfilters. Was presented at IEEE Int.
Symp. Circuits Syst. (San Jose, CA), May 1986.

# Risto Kotalampi rk76073@tut.fi   # Phones :                           #
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In article <1990Jul10.122121.28209@funet.fi> rk76073@naakka.tut.fi (Risto Kotalampi) writes:
>In article <3504@radio.oakhill.UUCP> you write:
>>
>>I would like to use an IIR filter in a particular application.  I 
...
>>the phase ripple can be as high as +-10 degrees and still be considered
>>acceptable correction. Any help would be apprieciated.
...
>> -Charlie Thompson
>
>A solution to your problem could be Allpass Filters. With Allpass' you
...
># Risto Kotalampi rk76073@tut.fi   # Phones :                           #

If you have the luxury of redesigning your IIR filter, I have had very good
results designing filters using Yule-Walker type techniques, certainly producing
+- 10 degrees in the passband, even for fairly funny filters (ie. low pass things
with integral 50Hz notches, notch just outside the pasband).
Reference:
Roberts and Mullis, Digital Signal Processing, Addison-Wesley, 1987

Although I used the functions delivered with Pro-Matlab from The Math Works to
do the design.

Also interesting (and of no personal design experience) is an article:
Clements, "On Causal Linear Phase IIR Digital Filters",
	IEEE Trans. ASSP, Vol 37, No. 4, Apr 1989

Good stuff -

James Taylor

In article <3187@phred.UUCP> james@phred.UUCP (JAMES Taylor) writes:
>
>Also interesting (and of no personal design experience) is an article:
>Clements (and Pease), "On Causal Linear Phase IIR Digital Filters",
>	IEEE Trans. ASSP, Vol 37, No. 4, Apr 1989

From the Summary (on p. 483) of the above paper:

"The main focus of this paper has been of a theoretical nature.
(Although) the nonrationality of the system described render them
unrealizable,..."

Before someone tries again to invent the perpetuum mobile, it has been
shown long ago that a causal and stable IIR filter with a rational (and
therefore realizable) transfer function cannot have a (exactly) linear
phase. A linear phase IIR filter should have its poles in reciprocal
pairs and therefore cannot be stable. The original proof can be found
in: A.G. Deczky, "General Expression for the Group Delay of Digital
Filters", Electronics Letters, Vol.5, No. 25, Dec. 11, 1969.


Federico Bonzanigo
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  Swiss Federal Institute of Technology (ETH)
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