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

[Lux, Jim]

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 simulator. 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.