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

[Magnus Danielson]

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