[time-nuts] Re: Simple simulation model for an OCXO?

[Magnus Danielson]

Hi Jim,

Thanks for the corrections. Was way to tired to get the uniform and 
normal distributions right.

rand() is then by classical UNIX tradition is generated as a unsigned 
integer divided by the suitable (32th) power of two, so the maximum 
value will not be there, and this is why a small bias is introduced, 
since 0 can be reached but not 1.

In practice the bias is small, but care is taken never the less.

Cheers,
Magnus

On 2022-05-03 03:43, Lux, Jim wrote:
> On 5/2/22 6:09 PM, Magnus Danielson via time-nuts wrote:
>> Matthias,
>>
>> On 2022-05-02 17:12, Matthias Welwarsky wrote:
>>> Dear all,
>>>
>>> I'm trying to come up with a reasonably simple model for an OCXO 
>>> that I can
>>> parametrize to experiment with a GPSDO simlator. For now I have the 
>>> following
>>> matlab function that "somewhat" does what I think is reasonable, but 
>>> I would
>>> like a reality check.
>>>
>>> This is the matlab code:
>>>
>>> function [phase] = synth_osc(samples,da,wn,fn)
>>> # aging
>>> phase = (((1:samples)/86400).^2)*da;
>>> # white noise
>>> phase += (rand(1,samples)-0.5)*wn;
>>> # flicker noise
>>> phase += cumsum(rand(1,samples)-0.5)*fn;
>>> end
>>>
>>> There are three components in the model, aging, white noise and 
>>> flicker noise,
>>> with everything expressed in fractions of seconds.
>>>
>>> The first term basically creates a base vector that has a quadratic 
>>> aging
>>> function. It can be parametrized e.g. from an OCXO datasheet, daily 
>>> aging
>>> given in s/s per day.
>>>
>>> The second term models white noise. It's just a random number scaled 
>>> to the
>>> desired 1-second uncertainty.
>>>
>>> The third term is supposed to model flicker noise. It's basically a 
>>> random
>>> walk scaled to the desired magnitude.
>>
> <snip>
>>
>> Another thing. I think the rand function you use will give you a 
>> normal distribution rather than one being Gaussian or at least 
>> pseudo-Gaussian.
>
> rand() gives uniform distribution from [0,1). (Matlab's doc says 
> (0,1), but I've seen zero, but never seen 1.) What you want is 
> randn(), which gives a zero mean, unity variance Gaussian distribution.
>
> https://www.mathworks.com/help/matlab/ref/randn.html
>
>
>> A very quick-and-dirty trick to get pseudo-Gaussian noise is to take 
>> 12 normal distribution random numbers, subtract them pair-wise and 
>> then add the six pairs. 
>
> That would be for uniform distribution. A time-honored approach from 
> the IBM Scientific Subroutine Package.
>
>
>> The subtraction removes any bias. The 12 samples will create a 
>> normalized deviation of 1.0, but the peak-to-peak limit is limited to 
>> be within +/- 12, so it may not be relevant for all noise 
>> simultations. Another approach is that of Box-Jenkins that creates 
>> much better shape, but comes at some cost in basic processing. 
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