Randy Yates <yates@ieee.org> writes:> [...] > 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 one of those relatively simple exercises for the human ear/mind, but getting an algorithm to do it seems almost intractable... I wish these two domains could be cross-correlated a little better! -- % Randy Yates % "...the answer lies within your soul %% Fuquay-Varina, NC % 'cause no one knows which side %%% 919-577-9882 % the coin will fall." %%%% <yates@ieee.org> % 'Big Wheels', *Out of the Blue*, ELO http://www.digitalsignallabs.com
MUSIC Algorithm: Suitable for General Periodic Signals?
Started by ●December 2, 2008
Reply by ●December 3, 20082008-12-03
Reply by ●December 3, 20082008-12-03
I wonder if using two microphone signals and applying blind source separation would help separate the two signals. -- % Randy Yates % "Maybe one day I'll feel her cold embrace, %% Fuquay-Varina, NC % and kiss her interface, %%% 919-577-9882 % til then, I'll leave her alone." %%%% <yates@ieee.org> % 'Yours Truly, 2095', *Time*, ELO http://www.digitalsignallabs.com
Reply by ●December 3, 20082008-12-03
On 3 Dez., 13:18, Rune Allnor <all...@tele.ntnu.no> wrote:> On 3 Des, 12:54, Andor <andor.bari...@gmail.com> wrote: > > > > > > > On 3 Dez., 12:45, Rune Allnor <all...@tele.ntnu.no> wrote: > > > > On 3 Des, 12:23, Andor <andor.bari...@gmail.com> wrote: > > > > > On 3 Dez., 11:04, Rune Allnor <all...@tele.ntnu.no> wrote: > > > > > > On 3 Des, 09:45, Andor <andor.bari...@gmail.com> 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. > > No, I'm not. > > > 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. > > Now we are moving into hair-splitting. Randy asked about > "general periodic" signals. I interpret that as "general > signals of quasi-periodic nature". It seems you interpret > something else.I was considering the following task: assume that x1(t) and x2(t) are two sinusoids (simplest case for periodic signals) at different frequencies. One has the measurement y[n] = x1(nT) + x2(nT) + e_n where T is the known sampling period and e_n is measurement noise. Determine if y[n] has a fundamental period, and if so, find the fundamental period. My answer is: if e_n = 0 for all n, then the task is solvable, else it is not solvable. Regards, Andor
Reply by ●December 3, 20082008-12-03
On 3 Des, 14:12, Andor <andor.bari...@gmail.com> wrote:> I was considering the following task: assume that x1(t) and x2(t) are > two sinusoids (simplest case for periodic signals) at different > frequencies. One has the measurement > > y[n] = x1(nT) + x2(nT) + e_n > > where T is the known sampling period and e_n is measurement noise. > Determine if y[n] has a fundamental period, and if so, find the > fundamental period.That's a different question than I considered.> My answer is: if e_n = 0 for all n, then the task is solvable, else it > is not solvable.I don't think it is solvable at all, unless you have infinite amounts of data. With finite amounts of data you can always generate a periodic signal by repeating the sequence you already have ad infinitum. Which brings us straight into the quagmire with the periodicty of the DFT and all that. Not my favourite neck o'the woods. Rune
Reply by ●December 3, 20082008-12-03
Randy Yates wrote:> Randy Yates <yates@ieee.org> writes: > >>[...] >>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 one of those relatively simple exercises for the human ear/mind, > but getting an algorithm to do it seems almost intractable... I wish > these two domains could be cross-correlated a little better!The phrase "relatively simple exercises for the human ..." brings to mind speech recognition. Would some techniques from that field be productive? As I type I can't recall its name, but basically taking the fft of a power spectrum. Might not one rate be more prominent than the other? Are there sample recordings available on the web? I recall some time back when a physiologist was asking questions about extracting specific information from either an EEG or EKG, I ran across a university site that collected copies of the raw data used by research papers. Never bookmarked it.
Reply by ●December 3, 20082008-12-03
On Wed, 03 Dec 2008 07:41:40 -0500, Randy Yates <yates@ieee.org> wrote:>Andor <andor.bariska@gmail.com> writes: > >> On 3 Dez., 12:45, Rune Allnor <all...@tele.ntnu.no> wrote: >>> On 3 Des, 12:23, Andor <andor.bari...@gmail.com> wrote: >>> >>> >>> >>> >>> >>> > On 3 Dez., 11:04, Rune Allnor <all...@tele.ntnu.no> wrote: >>> >>> > > On 3 Des, 09:45, Andor <andor.bari...@gmail.com> 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. -- John * The first graph on this page shows a time series of heart rate measurements on a healthy subject: http://www.physionet.org/tutorials/ndc/
Reply by ●December 3, 20082008-12-03
John O'Flaherty <quiasmox@yeeha.com> writes:> 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.Hi John, True it's not strictly periodic. But I was hoping it's close enough... and that there was a more robust method than bone-headed peak detection. Where are you going to set the threshold? This is an algorithm that has to run unattended on a platform over multiple subjects, multiple signal strength scenarios, multiple SNR scenarios, etc. -- % Randy Yates % "She's sweet on Wagner-I think she'd die for Beethoven. %% Fuquay-Varina, NC % She love the way Puccini lays down a tune, and %%% 919-577-9882 % Verdi's always creepin' from her room." %%%% <yates@ieee.org> % "Rockaria", *A New World Record*, ELO http://www.digitalsignallabs.com
Reply by ●December 3, 20082008-12-03
On 3 Des, 19:56, Randy Yates <ya...@ieee.org> wrote:> John O'Flaherty <quias...@yeeha.com> writes: > > 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. > > Hi John, > > True it's not strictly periodic. But I was hoping it's close > enough... and that there was a more robust method than bone-headed peak > detection. Where are you going to set the threshold? This is an > algorithm that has to run unattended on a platform over multiple > subjects, multiple signal strength scenarios, multiple SNR scenarios, > etc.Do you have an example data set you can post? Rune
Reply by ●December 3, 20082008-12-03
On Wed, 03 Dec 2008 13:56:55 -0500, Randy Yates <yates@ieee.org> wrote:>John O'Flaherty <quiasmox@yeeha.com> writes: > >> 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. > >Hi John, > >True it's not strictly periodic. But I was hoping it's close >enough... and that there was a more robust method than bone-headed peak >detection. Where are you going to set the threshold? This is an >algorithm that has to run unattended on a platform over multiple >subjects, multiple signal strength scenarios, multiple SNR scenarios, >etc.ECG and plethysmograph heartrate detection systems face all those problems; there's AGC for threshold control. At any rate, googling around idly, I found this, using the "blind source" thingy you mentioned up-thread, for separation of fetal from mother's heartbeat in ECGs. Maybe it could be adapted to microphone signals and heart vs. respiration- http://www.comp.nus.edu.sg/~changec/publications/P0861.pdf -- John
Reply by ●December 3, 20082008-12-03
Rune Allnor <allnor@tele.ntnu.no> writes:> On 3 Des, 19:56, Randy Yates <ya...@ieee.org> wrote: >> John O'Flaherty <quias...@yeeha.com> writes: >> > 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. >> >> Hi John, >> >> True it's not strictly periodic. But I was hoping it's close >> enough... and that there was a more robust method than bone-headed peak >> detection. Where are you going to set the threshold? This is an >> algorithm that has to run unattended on a platform over multiple >> subjects, multiple signal strength scenarios, multiple SNR scenarios, >> etc. > > Do you have an example data set you can post?Hi Rune, Sure - try these: http://www.digitalsignallabs.com/signals Thanks. --Randy -- % Randy Yates % "And all that I can do %% Fuquay-Varina, NC % is say I'm sorry, %%% 919-577-9882 % that's the way it goes..." %%%% <yates@ieee.org> % Getting To The Point', *Balance of Power*, ELO http://www.digitalsignallabs.com
