[time-nuts] Generation of pulse train with 1/4 noise

Bob Camp lists at rtty.us
Fri Feb 15 07:52:22 EST 2013


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 <jimlux at 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);
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