# Re: Robust method of fundamental frequency estimation.

```Some of the inexpensive tuners measure the zero crossing rate (time domain)
of the fundamental.  In other words, they measure the waveform period
directly.  PC software tuners often use the same approach.

Even with a relatively low digital sampling rate (e.g., 44100 Hz) the number
of samples per half-cycle for guitar string frequencies (~80 - ~300 Hz) is
more than 100 samples, and this is large enough that reasonably good tuning
can be accomplished.  Averaging over several cycles gives a bit of
improvement, too.

Regarding the use of FFT-based fundamental frequency estimation:  one of the
advantages of using higher frequency harmonics in the estimation process,
rather than just the fundamental, is that the uniform frequency resolution
(call it dX) of the DFT can be exploited.

For example, if the frequency of the third partial of a harmonic waveform is
found to be (X +/- dX) Hz using an interpolated FFT (where dX represents the
error in estimating the frequency) the fundamental estimate is thus X/3 +/-
dX/3, which is improved in resolution.

Note:  this requires figuring out which partial represents which harmonic
(see the Two-Way Mismatch article), and doesn't help if the waveform is
actually aperiodic (such as the piano).  There are some ways to take into
account the stretched partial frequencies due to string stiffness, but it is
pretty empirical.

Rob Maher

-----Original Message-----
From: AUDITORY - Research in Auditory Perception
[mailto:AUDITORY@xxxxxxxxxxxxxxx] On Behalf Of Bob Masta
Sent: Friday, February 02, 2007 7:14 AM
To: AUDITORY@xxxxxxxxxxxxxxx
Subject: Re: Robust method of fundamental frequency estimation.

Dear list:

As long as we are on this topic, does anyone know
what method those \$20 guitar tuner devices use?
I
n my limited experience (observing others) they seem
to work pretty well for guitars.  In fact, I'd have to say
"amazingly well", based upon my pre-computer
attempts at pitch extraction for stringed instruments.  <g>

Has anyone tried one on low piano notes?

Best regards,

Bob Masta

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