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
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