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From: fede@bernina.ethz.ch (Federico Bonzanigo)
Newsgroups: comp.dsp
Subject: Re: 48k to 44.1k sample rate conversion
Message-ID: <1991May15.105543.12165@bernina.ethz.ch>
Date: 15 May 91 10:55:43 GMT
References: <5826@media-lab.media.mit.edu.MEDIA.MIT.EDU> <1991May13.173129.18295@bernina.ethz.ch>
Reply-To: fede@bernina.UUCP (Federico Bonzanigo)
Organization: Swiss Federal Institute of Technology (ETH), Zuerich
Lines: 49

In article <1991May13.173129.18295@bernina.ethz.ch> hanke@nessie.cs.id.ethz.ch (Norbert Hanke) writes:
>
>Sample rate conversion is not that difficult: when done by a FIR filter
>the filter coefficients have to be calculated for the 7.056 MHz sampling
>frequency. But fortunately, 146 out of 147 input samples (at 7.056 MHz) are
>0 for 48 kHz input, and 159 out of 160 output samples don't have to be
>calculated. These two facts together make the computing power requirements
>reasonable for sampling rate converters. More difficult, however, is the
>calculation of about 10000 filter coefficients for a high quality sampling
>rate converter.
>
>Norbert Hanke
>ETH Zurich, Switzerland 

I have to add the following:

- It should be possible to design a FIR filter of such a length with a
suitable Remez algorithm and computer power. A filter of length up to
ca. 15000 has been designed on an Alliant FX80. A modified
Parks-McClellan program should do the job. The modifications should
reduce the arithmetic errors and use better initial values to ensure
the convergence of the Remez algorithm. Some of them are described in
the last two sections of a paper of mine "Some Improvements to the
Design Programs for Equiripple FIR Filters", Proc. ICASSP 82, pp.
274-277.  Other improvements aimed at reducing the computation time
will surely help, such as the ones described in: A. Antoniou, "New
Improved Method for the Design of Weighted-Chebyshev, Nonrecursive,
Digital Filters", IEEE Trans. on Circuits and Systems, Vol. CAS-10, pp.
740-750 (Oct.  1983).  Circuits and Systems, Vol. CAS-30, No. 10, pp.
740-750.  Obviously I claim to have a better suited program...

- A trick that has been used in this field to avoid the direct design
of such a long filter is to design a filter of length around 1000-2000
using the Remez algorithm and then to interpolate the coefficients to
the desired filter length. 


Federico Bonzanigo
  Electrical Engineering Dept.
  Swiss Federal Institute of Technology (ETH)
  ETH-Zentrum
  CH-8092 Zurich, Switzerland
E-mail:	      bonzanigo@nimbus.ethz.ch
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