---------------------------- Original Message ----------------------------
Subject: Re: [music-dsp] Recognizing Frequency Components
From: "Evan Balster" <e...@imitone.com>
Date: Thu, January 26, 2017 12:36 pm
To: music-dsp@music.columbia.edu
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> Philosophy rant: Frequency is a model. You can use tools that build on
> that model to describe your signal in terms of frequency, but none of them
> are going to be perfect. A pure 10hz tone is a mathematical abstraction
> which you'll not find in any digital signal or measurable phenomenon.
uhm, once a sinusoid is isolated (and in the OP's case there is only this
single sinusoid), frequency is not merely a mathematical abstraction. �it has a
definite mathematical definition and it is the time rate of
change of phase of that sinusoid.
> But, *ooh�boy!* is that abstraction useful for modeling real things.
>
> If you have an extremely clean signal and you want an extremely accurate
> measurement, my recommendation is to forgo fourier transforms (which
> introduce noise and resolution limits) and use optimization or measurement
> techniques in the time domain. In your example, *zero crossings are the
> easiest and best solution* as Steffan suggests.
certainly the easiest. �might have to do something in between samples at the
zero crossing.
i thought Steffan mentioned something about using a Gaussian window. �he
mentioned a paper he found but did not identify it. �i
am a little curious.
there were a few folks doing sinusoidal modeling, and folks in this group
probably don't think of sinusoids as static but with changing frequency and
changing amplitude. �turns out that windowing with Gaussian leads to some very
nice analytic results for obtaining
instantaneous frequency, sweep rate on the frequency, and ramp rate on the
amplitude (as well as the amplitude and phase of the sinusoid in the center of
the window).
> Another interesting approach, which I mention for scholarly purposes, would
> be to design a digital filter with a sloping magnitude response (even the
> simplest one-pole lowpass could do) and apply it across the signal. You
> can measure the change in the signal's power (toward the end, because the
> sudden beginning of a sine wave produces noise) and find the frequency for
> which the filter's transfer function produces that attenuation. This
> filter-based technique (and related ones) can generalize to other problems
> where zero-crossings are less useful.
>
*only* once (when i was sorta copying an idea patented in the AXON pitch
detector, which is really fast, like 12 or 13 ms) have i ever used
zero-crossing for any pitch or frequency measurement. �attacks are a problem,
but outside of the attack of a note, i can't think of
zero-crossings as useful for anything. �(some people have written that they
apply gain changes at zero-crossings to reduce the zipper. i don't think it's
such a good idea.)
�
--
r b-j � � � � � � � �
�r...@audioimagination.com
"Imagination is more important than knowledge."
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