Re: Best way to measure precise harmonics?
- From: Tom Bruhns <k7itm@xxxxxxx>
- Date: Sat, 20 Oct 2007 13:30:52 -0700
On Oct 19, 9:05 pm, "Ken S. Tucker" <dynam...@xxxxxxxxxxxx> wrote:
On Oct 19, 11:29 am, Tom Bruhns <k7...@xxxxxxx> wrote:
On Oct 19, 9:00 am, Martin Brown <|||newspam...@xxxxxxxxxxxxxxxxxx>
wrote:
On Oct 19, 4:32 pm, "Ken S. Tucker" <dynam...@xxxxxxxxxxxx> wrote:
On Oct 19, 1:37 am, Martin Brown <|||newspam...@xxxxxxxxxxxxxxxxxx>
wrote:
On Oct 18, 2:22 pm, eromlignod <eromlig...@xxxxxxx> wrote:
I need to find the component harmonic frequencies of an AF wave and I
need for it to be pretty precise (+/- .001 Hz or so). I have access
to a spectrum analyzer, but it just doesn't seem to be precise enough
(or I'm using it wrong). It gives me peaks in a frequency domain, but
they are not pinpoint lines, ostensibly due to a limited-sample FFT.
That goes with the territory. To obtain a +/- 0.001 Hz frequency
resolution you would have to measure the signal for ~1000 seconds
Are there any other devices or methods to obtain accurate frequencies
of each harmonic to three decimal places? Thanks for any suggestions
you might have.
FFT will do it if you can supply enough data in the time domain
(choose a 2^N FFT). Practical implementations will require potentially
anti-alias regridding and a few other tweaks to sort out boundary
conditions.
Some hardware FFT based analysers can zoom in on a region of interest,
but non of them can get around the uncertainty principle. A short
burst of pure tone decaying in amplitude always contains a range of
frequencies around the fundamental.
Question: How good are todays A to D Converters?
Good enough for studio quality digital audio to have taken over from
analogue.
Will the conversion introduce serious artifacts?
Shouldn't do if it is done correctly. The most important thing is to
have an analogue brick wall filter to ensure that no out of band
frequencies reach the input to the ADC. Any timing phase jitter in the
converter will also hurt.
I'm thinking that once the wave form is in digital
form it's just software to compare that to a perfect
sine wave at various frequencies. I'm sure that's
be done.
Just a SMOP... But for these volumes of data it requires some skill to
obtain the optimum results for a high dynamic range spectrum
containing a fundamental and a bunch of its near harmonics.
FFT is just a quick way to decompose a signal into its frequency
components. Classical slow DFT would be glacially slow on large
datasets unless you were only looking at a handful of likely
frequencies.
Regards,
Martin Brown
We've been building FFT analyzers for many years; I can assure you
that ADCs that are very linear do a great job in these analyzers. The
advent of delta-sigma converters made life a lot easier, and of course
for audio they are pretty much universal now. Obviously, if you are
looking for overtones in the spectrum of an excited string, and those
overtones are very close to the frequency of harmonics of the
fundamental, you'll want to know just how much harmonic distortion is
being introduced in the signal path. It can come from the transducer
that goes from acoustic to electrical, and in the amplifiers ahead of
the ADC, and in the ADC itself. It's quite possible to get distortion
in the electrical path lower than -100dBc in the audio range, but it's
also pretty difficult (in my experience) to find hard specs on the
distortion introduced by the acoustic to electrical transducer:
microphone or other pickup. If the overtone and fundamental are both
pure enough tones, and if the harmonics are enough different in
frequency from the overtones, the analyzer can resolve them.
Given a stream of samples from a good audio "card" (or external USB
audio port or whatever), the processor in a modern PC should have no
trouble at all keeping up doing "zooming" and decimating. That makes
the display of the results somewhat easier and the FFT processing can
be done real-time, since you're doing FFTs on relatively small blocks
of data at a slow data rate (after decimation). Does anyone sell
software that actually does all this (nearly) real-time? We used to
do it for audio-range analyzers using a custom ASIC chip set, but
these days, there's certainly plenty of processing power in a typical
PC. We still do it with an ASIC, but now much, much faster.
With respect to determining frequencies, _IF_ I know a priori that I'm
dealing with a pure tone (and therefore stable in phase and
amplitude), and the signal-to-noise ratio is good, I can determine the
frequency to within 0.001Hz with well under 100 seconds of data. The
reason is that I know exactly the response of each FFT point to any
frequency, and the response of a set of FFT points to the waveform can
only have happened with a particular input. It's equivalent, I guess,
to fitting a sinusoid to the digitized points; if I am quite sure the
input is a sinusoid with unknown frequency, phase, amplitude and
perhaps DC offset, I don't need very many samples to nail down those
four unknowns. Of course, the difficulty is that I almost never can
be really SURE that my input is a pure sinusoid. I must also have
enough data points to sufficiently average out whatever noise there
is; thus, a really good SNR allows fewer points to determine the
sinusoid.
You mentioned filtering to avoid aliasing. That's something else that
has been aided a whole lot by the delta sigma converters, since the
sample rate is much higher than the highest input frequency of
interest. The analog filter can be relatively gentle, and the
filtering becomes mainly a digital process; it can be linear phase FIR
filters, which makes corrections somewhat easier, too.
Even when you don't know what the input waveform really is, or when
you know it contains harmonics and overtones and the like, maybe even
multiple "fundamentals," an FFT analyzer can give you a very good
picture of what your signal looks like, spectrally. You do need to
understand things like "windowing" and what happens if your input
frequencies are not integer multiples of 1/(time record length)
though.
Cheers,
Tom
Interesting, I'll pull this quote,
" hard specs on the distortion introduced
by the acoustic to electrical transducer:"
Just so you guys know I'm serious about this
subject, I/we designed this unit,
http://www.trak4.com/earco/index.html
and I respect the problem of acoustic transducers.
At that site are recorded wave forms of Loons,
(let me know if you have any problems getting
their call, my current system hasn't got audio).
I'd get the Loons to yell by recording them and
then replaying their call over the lake. They'd
show at my dock yelling back. So I relied on
my "tin ear" (and others) to inform me of distortion.
I wasn't crazy about the science of the test but
what choice did I have?
Regards
Ken S. Tucker
No problem getting the loon sounds to play, though there's a
tremendous amount of echo in them, it seems like!
I hadn't directly addressed your original posting where you asked how
good modern ADCs are, and about analyzing the digitized sounds. The
best off-the-shelf audio converters I know about are 24 bit, can
digitize with output rate of 96k and 192k samples/second in addition
to the old 48k, and have distortion products typically at the part per
million level. The noise is pretty darned good too. I suspect it's
unlikely that you'll find a transducer that linear, at least not with
loud sounds, and it's not trivial by any means to make a preamp with
such low distortion (though some of the modern op amps have helped a
lot with that).
One way to view an FFT is that it compares the input signal with sines
and cosines at the frequencies corresponding to the FFT points (also
commonly called "bins"). An advantage of the DFT is that you can do
that comparison for any spot frequency, and you're not limited to the
linear frequency spacing of the FFT; but of course, it's much slower
if you want to do a LOT of points. On the other hand, there's a DFT
algorithm that lets you calculate as the data comes in, and as soon as
you've finished collecting the data, just a very few operations gives
you the final answer from the DFT -- you can run several of those in
parallel if you want.
And of course, you can design a filter or detector that is "optimal"
in some sense, using things you know about the waveform you're
analyzing. An FFT is a good general-purpose spectral analysis tool,
but it likely won't be the _best_ tool for some specific application.
Cheers,
Tom
Cheers,
Tom
.
- References:
- Best way to measure precise harmonics?
- From: eromlignod
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- From: Martin Brown
- Re: Best way to measure precise harmonics?
- From: Ken S. Tucker
- Re: Best way to measure precise harmonics?
- From: Martin Brown
- Re: Best way to measure precise harmonics?
- From: Tom Bruhns
- Re: Best way to measure precise harmonics?
- From: Ken S. Tucker
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