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

[Carsten Andrich]

On 10.05.22 10:37, Neville Michie wrote:
> The use of forward then reverse Fourier transforms is one of the most important
> achievements of the Fourier transform. When one data set is convolved with
> another data set, it appears impossible to undo the tangle.
> But if the data is transformed into the Fourier domain, serial division can separate
> the data, and transformation back will yield the original data.

Absolutely, but in this case I was wondering why to do the costly O(n 
log n) forward transform at all, if its output can be directly computed 
in O(n).


On 10.05.22 12:58, Attila Kinali wrote:
>> If you happen to find the paper, please share a reference. I'm curious
>> about implementation details and side-effects, e.g., whether
>> implementing the filter via circular convolution (straightforward
>> multiplication in frequency-domain) carries any penalties regarding
>> stochastic properties due to periodicity of the generated noise.
> Yes, for one, noise is not periodic, neither is the filter you need.
> You can't build a filter with a 1/sqrt(f) slope over all the
> frequency range. That would require a fractional integrator, which
> is a non-trivial task. Unless you actually do fractional integration,
> all time domain filters will be approximations of the required filter.

Any chance the Paper was "FFT-BASED METHODS FOR SIMULATING FLICKER FM" 
by Greenhall [1]?

I've had a look at the source code of the bruiteur tool, which you 
previously recommended, and it appears to opt for the circular 
convolution approach. Would you consider that the state-of-the-art for 
1/sqrt(f)? The same is used here [3]. Kasdin gives an extensive overview 
over the subject [2], but I haven't read the 20+ pages paper yet.


> I had the same question when I first saw this. Unfortunately I don't have a good
> answer, besides that forward + inverse ensures that the noise looks like it is
> supposed to do, while I'm not 100% whether there is an easy way to generate
> time-domain Gauss i.i.d. noise in the frequency domain.
>
> If you know how, please let me know.
Got an idea on that, will report back.


> But be aware, while the Gauss bell curve is an eigenfunction of the Fourier
> transform, the noise we feed into it is not the Gauss bell curve.
Thanks for pointing that out. It appears I went for the first reasonable 
sounding explanation to support my gut feeling without thinking it 
through :D

Best regards,
Carsten


[1] https://apps.dtic.mil/sti/pdfs/ADA485683.pdf
[2] https://ieeexplore.ieee.org/document/381848
[3] https://rjav.sra.ro/index.php/rjav/article/view/40