[ntp:questions] measuring frequency

Robert Scott no-one at notreal.invalid
Mon Feb 11 16:11:39 UTC 2013

On Sat, 09 Feb 2013 17:18:25 GMT, unruh <unruh at invalid.ca> wrote:

>On 2013-02-08, Ivan Shmakov <oneingray at gmail.com> wrote:
>>>>>>> David Woolley <david at ex.djwhome.demon.invalid> writes:
>> 	[Cross-posting, and setting Followup-To:, to news:comp.dsp.]
>> [...]
>> > In Fourier terms, the spectral width of a piano note is going to be
>> > more than 12ppm and depend on the exact interval over which you
>> > measure it.  I would also suspect that the zero crossing interval
>> > changes significantly during the note, particularly at the start.
>> 	As per my experience with guitar signals, such a waveform is
>> 	likely to cross zero more than once per period.  Hence, by
>> 	counting such crossings one typically gets the frequency of one
>> 	of the note's harmonics, and not that of the pure tone.
>> 	BTW, is there a kind of overview of a method that could allow
>> 	for frequency measurement for such a signal?  (Preferably one
>> 	oriented to the uninitiated.  I can probably handle complex
>> 	math, though.)
>Use the fourier transform to get the rought freq. Then use zero
>crossings at around that period to narrow in on the freq. Of course if
>the harmonics are not exact (see piano) then those sero crossings will
>not give the freq of the fundamantal. You could filter the intput around
>that rough frequency of the fundamental, but that mightgive you very
>little signal ( the ear hears the fundamental pitch even if there is no
>fundamental i n the note )

You are refering to what is called "inharmonicity" in the piano.  The
effect is that the overtones are not locked to the fundamental.
Therefore when they are added on to the fundamental the effect they
will have on the zero crossings has a good deal of randomness from
cycle to cycle.  Whereas if they were locked to the fundamental (as in
a pipe organ) then they will still have an effect on the timing of the
zero crossings but at least that effect will be the same from cycle to
cycle, so the timing of the zero crossings will be a relatively good
measure of the fundamental frequency.

However even in the case of a pipe organ there can be problems with
this technique.  It is possible to imagine an overtone riding on a
lower frequency sine wave where the cusp of the overtone sine wave is
almost causing a zero crossing.  In that case the detection of the
zero crossing in the presence of a small amount of noise could
sometimes count that cusp and sometimes be delayed until the next
overtone cusp.  So the measurement of frequency could be unreliable
because of an arbitrarily small amount of noise or irregularity in

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