[time-nuts] Generation of pulse train with 1/4 noise
I need to generate a sequence of pulses at around 1 Hz with a 1/f characteristic (human heartbeat, as it happens). I'd like to do this using software and a timer, so I'm looking for a clever algorithm using a random number generator to do it. I could take the phase noise spectrum and turn that into some form of cumulative probability distribution for the period, then generate a random number from 0-1 and use the inverse of the CPD to determine the period. But I was wondering if there's some clever way that just happens to generate what I'm looking for. Sort of like how you sum up 12 random numbers to generate a Gaussian with variance 1. and then, the Box-Muller algorithm as an alternate way. A generalized approach for the exponent between 0.5 and 1.5 would be useful. I found some techniques such as building a filter with the required power spectral density and then running white noise through it. There's a matlab ( C) package out there called cnoise, as well. cnoise builds an array of samples and uses a FFT to do the filtering efficiently. I'd rather have some sort of difference/recursion equation that I can just call each time I need the next interval. I did find some code based on a paper by Higham that does what's called the Ornstein-Uhlenbeck stochastic difference equation. dt = tmax / n; x(1) = x0; for j=1:n dw = sqrt ( dt ) * randn; x(j+1) = x(j) + dt*theta*(mu-x(j)) + sigma * dw But I don't trust it, because the matlab and c versions do not agree. 1/f^2 (brownian) is easy by taking the random number sequence and integrating. x(j+1) = x(j) + randn(1); ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
Re: [time-nuts] Generation of pulse train with 1/4 noise
Hi How much horsepower do you have on the gizmo that's doing the generation? For instance, is this coming out of an MSP-430 or a Core I-7? Bob On Feb 15, 2013, at 7:43 AM, Jim Lux jim...@earthlink.net wrote: I need to generate a sequence of pulses at around 1 Hz with a 1/f characteristic (human heartbeat, as it happens). I'd like to do this using software and a timer, so I'm looking for a clever algorithm using a random number generator to do it. I could take the phase noise spectrum and turn that into some form of cumulative probability distribution for the period, then generate a random number from 0-1 and use the inverse of the CPD to determine the period. But I was wondering if there's some clever way that just happens to generate what I'm looking for. Sort of like how you sum up 12 random numbers to generate a Gaussian with variance 1. and then, the Box-Muller algorithm as an alternate way. A generalized approach for the exponent between 0.5 and 1.5 would be useful. I found some techniques such as building a filter with the required power spectral density and then running white noise through it. There's a matlab ( C) package out there called cnoise, as well. cnoise builds an array of samples and uses a FFT to do the filtering efficiently. I'd rather have some sort of difference/recursion equation that I can just call each time I need the next interval. I did find some code based on a paper by Higham that does what's called the Ornstein-Uhlenbeck stochastic difference equation. dt = tmax / n; x(1) = x0; for j=1:n dw = sqrt ( dt ) * randn; x(j+1) = x(j) + dt*theta*(mu-x(j)) + sigma * dw But I don't trust it, because the matlab and c versions do not agree. 1/f^2 (brownian) is easy by taking the random number sequence and integrating. x(j+1) = x(j) + randn(1); ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there. ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
Re: [time-nuts] Generation of pulse train with 1/4 noise
On 2/15/13 4:52 AM, Bob Camp wrote: Hi How much horsepower do you have on the gizmo that's doing the generation? For instance, is this coming out of an MSP-430 or a Core I-7? Bob The mighty ArduinoUno... But it only has to generate one number every second: i.e. I'm simulating human heartbeats: I have a anthropomorphic dummy that has air bladders for lungs and heart that we use to simulate a human for radar testing. The Arduino just uses timers to open and close solenoid valves to create the right frequency and amplitude of motion. Right now it has a somewhat unrealistically uniform pulse rate. There's some faster cheap processors out there that I could drop in, as well: teensy3 with the 48MHz Cortex is pretty powerful. On Feb 15, 2013, at 7:43 AM, Jim Lux jim...@earthlink.net wrote: I need to generate a sequence of pulses at around 1 Hz with a 1/f characteristic (human heartbeat, as it happens). I'd like to do this using software and a timer, so I'm looking for a clever algorithm using a random number generator to do it. ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
Re: [time-nuts] Generation of pulse train with 1/4 noise
Hi Ok, how about a nice simple table? Something in the 500 to 4K entries shouldn't repeat often enough to be noticeable. Each entry probably can be a byte. Bob On Feb 15, 2013, at 8:09 AM, Jim Lux jim...@earthlink.net wrote: On 2/15/13 4:52 AM, Bob Camp wrote: Hi How much horsepower do you have on the gizmo that's doing the generation? For instance, is this coming out of an MSP-430 or a Core I-7? Bob The mighty ArduinoUno... But it only has to generate one number every second: i.e. I'm simulating human heartbeats: I have a anthropomorphic dummy that has air bladders for lungs and heart that we use to simulate a human for radar testing. The Arduino just uses timers to open and close solenoid valves to create the right frequency and amplitude of motion. Right now it has a somewhat unrealistically uniform pulse rate. There's some faster cheap processors out there that I could drop in, as well: teensy3 with the 48MHz Cortex is pretty powerful. On Feb 15, 2013, at 7:43 AM, Jim Lux jim...@earthlink.net wrote: I need to generate a sequence of pulses at around 1 Hz with a 1/f characteristic (human heartbeat, as it happens). I'd like to do this using software and a timer, so I'm looking for a clever algorithm using a random number generator to do it. ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there. ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
Re: [time-nuts] Generation of pulse train with 1/4 noise
On 2/15/13 5:37 AM, Bob Camp wrote: Hi Ok, how about a nice simple table? Something in the 500 to 4K entries shouldn't repeat often enough to be noticeable. Each entry probably can be a byte. Bob Yes.. that might work.. Or, for that matter, I believe you could do it by randomly selecting a time increment from a table with the right distribution. ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
Re: [time-nuts] Generation of pulse train with 1/4 noise
Hi I was going to suggest picking start and stop points in the table with your random number generator, but it's pretty much the same thing. If the base rate is 60 bpm, then each spacing is 16.666… ms. My *guess* would be that anything past 0.1 ms likely doesn't matter for the base rate. If that's all true, then a byte per entry is actually overkill. You might be able to get away with 4 bits per entry. There's also no absolute need for a linear coding scheme, you could get both good resolution and a small number of bits. That might make fiddling the entry points a bit tough though. The timing does relate to multiple valves, so it's not quite as simple as a single rate. The time delta's for the other stuff are all pretty short, so you may or may not be planing to randomly drive them as well. It all depends on how fanatic you get about the timing ... Bob On Feb 15, 2013, at 8:50 AM, Jim Lux jim...@earthlink.net wrote: On 2/15/13 5:37 AM, Bob Camp wrote: Hi Ok, how about a nice simple table? Something in the 500 to 4K entries shouldn't repeat often enough to be noticeable. Each entry probably can be a byte. Bob Yes.. that might work.. Or, for that matter, I believe you could do it by randomly selecting a time increment from a table with the right distribution. ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there. ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
Re: [time-nuts] Generation of pulse train with 1/4 noise
On 2/15/13 6:21 AM, Bob Camp wrote: The timing does relate to multiple valves, so it's not quite as simple as a single rate. The time delta's for the other stuff are all pretty short, so you may or may not be planing to randomly drive them as well. It all depends on how fanatic you get about the timing ... Not very.. The physical device being driven has one solenoid valve that fills and drains the heart bladder. The radar looks at the gross surface movement of the thorax (on the order of 1mm), and we want something that isn't perfectly regular and that has some variability (so that the algorithms used to detect the heartbeat don't wind up relying on heart rate being zero bandwidth). Rather than just implement something like interval = 60/bpm + 0.1*rand I figured if there was an easy way to generate something from a realistic distribution, it would be nice. ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
Re: [time-nuts] Generation of pulse train with 1/4 noise
Hi I think a simple table approach sounds like the quick / dirty way to go. Bob On Feb 15, 2013, at 9:56 AM, Jim Lux jim...@earthlink.net wrote: On 2/15/13 6:21 AM, Bob Camp wrote: The timing does relate to multiple valves, so it's not quite as simple as a single rate. The time delta's for the other stuff are all pretty short, so you may or may not be planing to randomly drive them as well. It all depends on how fanatic you get about the timing ... Not very.. The physical device being driven has one solenoid valve that fills and drains the heart bladder. The radar looks at the gross surface movement of the thorax (on the order of 1mm), and we want something that isn't perfectly regular and that has some variability (so that the algorithms used to detect the heartbeat don't wind up relying on heart rate being zero bandwidth). Rather than just implement something like interval = 60/bpm + 0.1*rand I figured if there was an easy way to generate something from a realistic distribution, it would be nice. ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there. ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
Re: [time-nuts] Generation of pulse train with 1/4 noise
Hi Jim: Music synthesizers now use sounds recorded from real instruments and play them back. Why not record a real heart beat, maybe different ones from children, men, women, etc.? Have Fun, Brooke Clarke http://www.PRC68.com http://www.end2partygovernment.com/2012Issues.html Jim Lux wrote: I need to generate a sequence of pulses at around 1 Hz with a 1/f characteristic (human heartbeat, as it happens). I'd like to do this using software and a timer, so I'm looking for a clever algorithm using a random number generator to do it. I could take the phase noise spectrum and turn that into some form of cumulative probability distribution for the period, then generate a random number from 0-1 and use the inverse of the CPD to determine the period. But I was wondering if there's some clever way that just happens to generate what I'm looking for. Sort of like how you sum up 12 random numbers to generate a Gaussian with variance 1. and then, the Box-Muller algorithm as an alternate way. A generalized approach for the exponent between 0.5 and 1.5 would be useful. I found some techniques such as building a filter with the required power spectral density and then running white noise through it. There's a matlab ( C) package out there called cnoise, as well. cnoise builds an array of samples and uses a FFT to do the filtering efficiently. I'd rather have some sort of difference/recursion equation that I can just call each time I need the next interval. I did find some code based on a paper by Higham that does what's called the Ornstein-Uhlenbeck stochastic difference equation. dt = tmax / n; x(1) = x0; for j=1:n dw = sqrt ( dt ) * randn; x(j+1) = x(j) + dt*theta*(mu-x(j)) + sigma * dw But I don't trust it, because the matlab and c versions do not agree. 1/f^2 (brownian) is easy by taking the random number sequence and integrating. x(j+1) = x(j) + randn(1); ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there. ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
Re: [time-nuts] Generation of pulse train with 1/4 noise
I have found this: 1/f noise can be created using random noise generators but it can also be producted using deterministic functions. One such method is a finite difference equation proposed by I. Procaccia and H. Schuster at http://paulbourke.net/fractals/noise/ On Fri, Feb 15, 2013 at 4:05 PM, Bob Camp li...@rtty.us wrote: Hi I think a simple table approach sounds like the quick / dirty way to go. Bob On Feb 15, 2013, at 9:56 AM, Jim Lux jim...@earthlink.net wrote: On 2/15/13 6:21 AM, Bob Camp wrote: The timing does relate to multiple valves, so it's not quite as simple as a single rate. The time delta's for the other stuff are all pretty short, so you may or may not be planing to randomly drive them as well. It all depends on how fanatic you get about the timing ... Not very.. The physical device being driven has one solenoid valve that fills and drains the heart bladder. The radar looks at the gross surface movement of the thorax (on the order of 1mm), and we want something that isn't perfectly regular and that has some variability (so that the algorithms used to detect the heartbeat don't wind up relying on heart rate being zero bandwidth). Rather than just implement something like interval = 60/bpm + 0.1*rand I figured if there was an easy way to generate something from a realistic distribution, it would be nice. ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there. ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there. ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
[time-nuts] source for new Resolution T
I'd like to buy a new Resolution T and I'm not having a great deal of success getting a retail (quantity one) vendor from Trimble. Anyone have a typical on-line source (e.g. Diamond Point) in the US? -- Paul ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
Re: [time-nuts] Generation of pulse train with 1/4 noise
Jim, On 02/15/2013 03:56 PM, Jim Lux wrote: On 2/15/13 6:21 AM, Bob Camp wrote: The timing does relate to multiple valves, so it's not quite as simple as a single rate. The time delta's for the other stuff are all pretty short, so you may or may not be planing to randomly drive them as well. It all depends on how fanatic you get about the timing ... Not very.. The physical device being driven has one solenoid valve that fills and drains the heart bladder. The radar looks at the gross surface movement of the thorax (on the order of 1mm), and we want something that isn't perfectly regular and that has some variability (so that the algorithms used to detect the heartbeat don't wind up relying on heart rate being zero bandwidth). Rather than just implement something like interval = 60/bpm + 0.1*rand I figured if there was an easy way to generate something from a realistic distribution, it would be nice. There is several ways to produce 1/f noise. It seems like the option that best fits your needs is the lead/lag filtering option, which is covered in a few articles from NIST. A fellow JPL colleague of yours then worked on it to set it up properly, so the starting state is good. I'm sure you want to convert the BASIC code into something somewhat more modern, but if worse comes to worse, I could probably do that in C for you, as I have been thinking about doing it anyways. It's fairly trivial stuff. The key design issue is that you will need to decide how wide range of frequencies needs to fit the 1/f slope. Turns out that the need to simulate this both in digital and analogue domain have been a topic since the early 60thies at NBS (now NIST) and Jim Barnes did his PhD on it. They then improved on it further. Much of that was then used in musical designs for pink noise filtering. Let me know if you can't find the articles, and I will dig them up for you. I should be able to find them for you before I get to LA. Cheers, Magnus ___ time-nuts mailing list -- time-nuts@febo.com To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
