From: "Klaus von der Heide" <v.d.heide@on-line.de>
To: rsgb_lf_group@blacksheep.org
Date: Sat, 24 Jun 2000 12:23:09 +0200
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Subject: Re: LF: Re: Shrinking sounds - fiasco
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From:           	Paul Keinanen <keinanen@sci.fi>
To:             	rsgb_lf_group@blacksheep.org
Subject:        	LF: Re: Shrinking sounds - fiasco
Date sent:      	Fri, 23 Jun 2000 15:48:12 +0300
Send reply to:  	rsgb_lf_group@blacksheep.org

> On Fri, 23 Jun 2000 10:27:59 +0100, Talbot Andrew
> <ACTALBOT@dera.gov.uk> wrote:
> 
> 
> >1)	Take the off air signal recording at (say) 8000 Hz sampling rate
> 
> >2)	Digitally mix down to some arbitrarily low frequency 
> 
> >3)	Filter to the necessary sub-Hz bandwidth centred on the signal
> 
> >4)	Decimate this filtered data to a much lower sampling rate by
> >just taking one sample out of every (say) 256 . 
> 
> >For anyone contemplating writing software to do this, note that stages
> >3) and 4) can be taken together - if using an FIR filter, the filtering
> >process needs to be done for each decimated sample only - this saves
> >considerable processing overhead for the long filter tap lengths
> >necessary
> 
> 
> If you plan to combine steps 3) and 4) by doing first decimating and
> then narrow band (sub-Hz) filtering, shouldn't you low pass filter the
> signal produced by the mixdown at 2) to have a bandwidth less than 15
> Hz for the final 31.25 Hz sample rate to meet the Nyquist criteria ?
> 
> Paul OH3LWR
>
 
Yes, a decimation must be preceded by a decimation filter. The output 
of this filter is only needed at the decimated rate. So, you will 
compute the FIR algorithm at the decimated rate. But the input buffer 
is at the full sample rate. And this full rate is the design rate of 
the filter. Since the pass band and the stop band are very narrow 
only very few coefficients are necessary. Usually halfband filters 
are used with less than 10 non vanishing coefficients.

Interpolation filters have to run at the up-sampled output rate. 
If the alias-suppression must be the same as with the decimation 
then the interpolation is the most costly operation of the filter. 

I made a universal multirate filter for adjustable bandwidth 
0.01 Hz ... 3kHz at -130 dB and adjustable input and output 
frequencies running on the DSP56002EVM in real time. This filter 
uses a very efficient bandpass decimation and interpolation with 
halfband filters. It is available on request.

If you have MATLAB (Student Edition or full, Ver. 5.0 or higher) 
an interactive DSP-Lecture including multirate filter design 
(Chapter 13) is available on request. 

73 de Klaus, DJ5HG