Re: MUSIC Algorithm: Suitable for General Periodic Signals?

John O'Flaherty wrote:
On Wed, 03 Dec 2008 07:41:40 -0500, Randy Yates <yates@xxxxxxxx>
wrote:

Andor <andor.bariska@xxxxxxxxx> writes:

On 3 Dez., 12:45, Rune Allnor <all...@xxxxxxxxxxxx> wrote:
On 3 Des, 12:23, Andor <andor.bari...@xxxxxxxxx> wrote:





On 3 Dez., 11:04, Rune Allnor <all...@xxxxxxxxxxxx> wrote:
On 3 Des, 09:45, Andor <andor.bari...@xxxxxxxxx> wrote:
Randy Yates wrote:
It seems that the MUSIC algorithm is for estimation of sinusoids. Is
there an adaptation or other similar algorithm that can be applied to
estimate the fundamental frequencies of a mixture of periodic signals?
Hello Randy
In the presence of noise and with only finitely many samples of the
signal, I don't think your task is solvable, unless you can supply
some constraints.
you need very many samples (multiple periods) to determine the period.
Wrong. MUSIC can do that in very few samples, depending
on the SNR.
No, what I said is correct (and you are saying the same thing): in the
presence of noise, the number of samples required for determining the
frequencies of the summands depends on the width of the confidence
intervals and the SNR. In the examples I gave and that you snipped it
is clear why there are many samples required.
Sorry, I axed your first post too badly: While you are
right for general (quasi) periodic signals, you chose
an example that doesn't does not support your claim:
The sinusoidal is the one quasi-periodic signal where the
period can actually be determined with just a few samples.
You are forgetting the noise, Rune. Any noise, however small, will not
allow to determine the frequencies of two sinusoids accurate enough
(with finitely many samples) to exclude the possiblity that there is
no fundamental period.
I see your point, Andor.

Actually, what I'm trying to figure out how to do (as an academic
exercise at this point rather than a paying job) is estimate heart rate
R_H and respiratory rate R_R from a single microphone signal containing
both.

This is why I asked Randy if he could supply constraints. If we knew
that the frequencies of the sinusoids were selected from a finite set
of possible frequencies (eg DTMF tones), then, given some frequency
estimation method (MUSIC or any other) and the SNR, we can supply
bounds on the number of samples required to determine the fundamental
frequency with 1-eps chance for error (the value of eps will give a
lower bound on the number of required samples).
Generally R_H > R_R, but not necessarily so. And there's nothing that
would prevent R_H = M * R_R, either.

Sounds in general to me like MUSIC is a bad approach. Thank you both,
Rune/Andor, for your responses and guidance.

One aspect is that heart rate (and maybe respiration rate) isn't
really periodic*. Separating the signals by the spectra of the
impulses (for heart rate, at least), or the fact that heart sound is
double (lub-dub), and finding time intervals between beats would give
a series of instantaneous heart rates, which could be averaged
appropriately.

You will find that the only difference between the average of ten beat intervals and (time-between-first-beat-and-eleventh-beat)/10 is less accumulated round-off error in the second method.

Jerry
--
Engineering is the art of making what you want from things you can get.
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.

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