Hi Joe and all,

Thanks Joe for implementing the fft-based convolution. It makes a big 
difference in execution time. 

It might save even more time if we calculated the averaged complex amplitude 
at, say, 1/100’th or even 1/1000’th as many points enabling us to use a much 
smaller fft for the return to the time-domain. We could interpolate or even use 
a piece-wise constant approximation to the complex amplitude when calculating 
the reconstructed signal. Do you think that this is worth pursuing? 

Note that this idea, taken to the extreme of one sample of the complex 
amplitude per symbol, reduces to the original symbol-by-symbol approach that I 
tried first when we implemented two-pass decoding for wspr. Recall that the 
symbol-by-symbol approach worked pretty well - so it might take only a few 
samples per symbol to essentially get all of the available benefit...

FYI - when I ran the latest jt65 on my data just now I got significantly fewer 
decodes than I got last night before the fft-based-filter implementation. I 
traced the problem to a mis-print in the scaling factor “fac”. The incorrect 
scaling meant that only 78% of the signal was subtracted - giving a maximum 
suppression of about 13 dB. I’ve committed the fix. 

If you get a chance to run this latest version on your files, I expect that you 
should see a bigger improvement with the second pass.

Steve k9an

> Program                     Decodes  Time
> --------------------------------------------
> WSJT-X v1.6.0 v5636 (kvasd)  2270     230 s
> jt65 (1 pass, sfrsd2)        2296     767
> jt65 (2 passes, sfrsd2)      2819    2144
> 
> Note that although the 2-pass decoder is significantly slower than the 
> others, it still takes less than 5 s per .wav file, on average.  This is 
> perfectly acceptable performance -- especially since the all-important 
> decode at the QSO frequency always happens first, and will generally be 
> done in less than a second.
> 
>       -- Joe, K1JT
> 
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