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Date: Wed, 13 Dec 2006 11:55:08 +0100
From: Wolf DL4YHF <dl4yhf@freenet.de>
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Subject: Re: LF: RE: SAQ Receiver for Window$
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Status: O

Hi Johan and group,

You wrote..

>
> Yes, but SAQrx uses a complex FIR filter for the main
> selectivity so it will take some CPU power if you want:
>
> 1. narrow passband width AND...
> 2. small ripple in the passband AND...
> 3. steep skirts AND...
> 4. large stopband attenuation
>
> i.e. a "brickwall" response.
>
> A complex FIR with, for example:
>
>   Passband width = 100 Hz
>   Passband ripple <= 0.1 dB
>   Stopband width = 150 Hz
>   Stopband attenuation = 80 dB (either side of +/-75 Hz)
>
> designed with Parks-McClellan requires 2 * 1526 = 3052 taps.
> The main filter in SAQrx is run at Fs = 11025 Hz.
> I think ~3000 taps would work OK on a fast machine although
> I haven't checked it. The existing 1000Hz filter has 2*206 taps.
>
As an alternative (since you already have the forward and inverse FFT in 
your C-library) you could use FFT convolution for the filter, which 
*greatly* speeds up large filter kernels. The basic principle is to 
split up the incoming signal into overlapping FFTs (with say 4096 to 
16384 points), preferably using 50 % overlap and a raised cosine window, 
then do the filtering by multiplying the spectra with the filter's 
amplitude, and finally transform back to the time domain using the 
'inverse' FFT.
Because (sin(x)^2) + (cos(x)^2) = 1, there is no unwanted amplitude 
modulation caused by the FFT windowing if a 50 % overlap is used. I use 
this method in my own application, and it allows to run filters in 'real 
time' which are impossible with the classic FIR implementation (with 
convolution in the time domain). You don't even need to design the 
filter coefficients; all the algorithm needs is the filter's frequency 
response.
A similar method is described in 'The Scientist's Guide to Digital 
Signal Processing" (look for the overlap/add method in chapter 18; it's 
available online for free ).

Cheers,
  Wolf DL4YHF

(happy to be back from hospital)