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Reply-To: "fred bartoli"
From: "fred bartoli"
References: <email@example.com> <firstname.lastname@example.org>
Subject: Re: Audio Phase meter cct wanted
Date: Tue, 19 Nov 2002 13:40:04 +0100
X-Newsreader: Microsoft Outlook Express 5.00.2314.1300
Organization: Guest of ProXad - France
NNTP-Posting-Date: 19 Nov 2002 13:37:20 MET
John Jardine a écrit dans le message :
> Tom Bruhns wrote in message
> > "John Jardine" wrote in message
> > > Tom Bruhns wrote in message
> > > news:email@example.com...
> > > > Very simple circuit: digitizer, feeding a processor. In the
> > > > processor, do a DFT (e.g. Goertzel algorithm) on the frequency
> > > > interested in. If you run the algorithm on two inputs at the same
> > > > time, you can easily get the (apparent) phase difference; you can
> > > > pretty easily account for non-simultaneous sampling if you want.
> > > > guess pretty much any processor with a hardware multiply could do
> > > > task for audio frequencies, one freq at a time. If you do an FFT
> > > > instead of DFT, you can have a whole band of freqs. Depending on
> > > > accuracy you need and the speed, even a built-in 8-bit ADC could be
> > > > enough, making for very few parts. Lots of options for the display.
> > ...
> > > Looks interesting. I'd seen (a suggestion of) Goertzel's use wrt
> > > LRC meters final phase extraction but had thought the Goertel was just
> > > sharp bandpass filter?. Using say alternate, 'zig zag' sampled
> > > does the phase info' present itself?.
> > So...there are several questions in there, I guess. First off: you
> > can think of the DFT as a filter, and the FFT as a bank of those
> > filters at evenly spaced center frequencies. The Goertzel algorithm
> > is simply a way to do a DFT which divides the processing up so that
> > it's easy to do incrementally as the samples come in; it can look just
> > like an IIR biquad section that starts with zero initial conditions.
> > So, they are filters that implement a single complex pole pair. The
> > poles happen to be exactly on the z-domain unit circle...so they
> > effectively have infinite Q. They start at zero energy in the filter,
> > and after the appropriate number of samples, you look at the filter
> > state and from that you can get an amplitude and phase. Just how you
> > interpret the filter state depends on the exact configuration of the
> > filter biquad; you could use a "canonical" biquad, but I've found that
> > other configurations work better if the input frequency is a small
> > fraction of the sample rate. If you have two input waveforms and you
> > use a ping-pong sampler, you just need to account for the phase
> > difference between samples, in addition to the indicated phase
> > difference from the DFT output.
> > The "infinite Q" thing is a bit misleading, perhaps. Because you're
> > dealing with an input waveform which might be sinusoidal, but is
> > chopped off before sample 0 and after sample n-1, the filter has
> > effectively added a modulation and thus responds significantly to a
> > range of input frequencies, and in fact will have a sin(x)/x spectral
> > behavior: the transform of the rectangular modulation.
> > I realize there are a lot of details left out. If you do a bit of
> > reading about the Goertzel algorithm, you should find that you can
> > implement one in a few minutes in a spreadsheet like Excel, to play
> > with, so you can test your math. That's what I did before I tried to
> > program one in DSP assembly language. Rapidly learned that I needed
> > to be sure the filter state variables could hold large enough values!
> > Cheers,
> > Tom
> Tom, thanks for the supporting info.
> Just recently I've tried a number of methods for the (precise) extraction
> the phase difference between two signals and from what you have said I
> it's worth giving the Goertzel a 'go'. Yes, the Goertzel routine looks
> small and it's going to be easy enough to simply programme the thing in
> Basic (floating point to start with) and trying out some different
> implementations and variables (data sets, sample rates etc) and simply
> examine the ensuing numbers.
> I've generally found that most of the digital methods out there all seem
> offer some kind of theoretical perfection but when it gets down to the
> gritty they start falling apart at the seams due to bedevilment by non
> infinite sample rates, imperfect S/N ratios or as you mention, sensitivity
> to sample set start/stop points.
> I have though had results far better better using digital methods than
> anything in the analogue area. I've also found no outright digital winner
> it's simply?! a question of finding an optimum (whole system) method that
> does not break my bank.
> I've seen the algorithm used in commercial phase modulated modems so in
> sense it has proved itself to be quite effective. The Goertzel may be the
> Thanks again
Also see the recent thread "A Little Goertzel Puzzle" in comp.dsp
Some small interesting additionnal points for you, I guess.
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