Predicting the future with Fourier transforms - page 51

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AlexeyFX:


Of course you can do better using F ourier, I don't understand anything about it.

Why all the pissing and moaning ... why are you taking offence. Integer probably went too far in accusing you of misunderstanding. I understand that it hurt.

(PS: integer, alexeyFX. invite you to channel your energy for the good of the thread, and mutual respect. amen)))

PS: AlexeyFX, what difference does it make whether it's better or worse, Integer didn't say that Fourier is the best at taking a preemptive action like yours, you may have better quality.

 
Trololo:

The question of the thread is different - is it even possible to get a preemptive action using Fourier.


I said it wasn't possible, and I explained why. This was followed by the reply that I don't understand anything without any explanation.

Trololo:

Why are you getting all pissed off? Interger may have overreacted to accusations of misunderstanding.


It's not an insult or even a peeve, just a desire to know what exactly I don't understand and what good I didn't see in Fourier. It's interesting...

 
AlexeyFX:


I said it was impossible and explained why. This was followed by a reply that I don't understand anything without any explanation.


This is not an insult or even a peeve, just a desire to know what exactly I don't understand and what good I didn't see in Fourier. I wonder...

I may be wrong, I'm happy to be corrected. In Fourier I see the possibility of getting infinitely (ideally) high frequency resolution using parametric methods, but this will have to be fiddled with. With wavelets I don't know how to achieve this yet.
 
Rorschach:
I may be wrong, glad to be corrected. In Fourier I see the possibility of getting infinitely (ideally) high frequency resolution using parametric methods, but this will have to be a lot of work. With wavelets I don't know how to achieve this yet.
So, it is infinite anyway - you take any frequency, integrate the series with sine and cosine, get the coefficient. There are no restrictions on the frequency value itself, except for maximum (Nyquist frequency) and minimum (within reasonable limits, but theoretically 0) values.
 
Rorschach:

The resolution depends on the sample length, so to get good resolution you need a large sample, and to get a short one you need to use a sampling model that can generate an arbitrarily long sequence.
No, only the minimum frequency that can be analysed depends on the sample length, and like I said, only for practical reasons (I usually don't analyse frequencies with a half-wave length shorter than the sample length).
 
Rorschach:

I was referring to the min frequency (step between spectral counts). Example, you want to separate harmonics with periods of 100 and 99.
Minimum frequency does not mean minimum distance between frequencies (i.e. resolution). It is always possible to get coefficients for harmonics with periods 100, 100.1, 100.000001 etc. by direct calculation.
 
Rorschach:


is that a typo?

Yeah, right. Right - "do not take harmonics with a half-wave length greater than the sampling length"

_____

We seem to be talking about different things. It is one thing if the task is to distinguish between two superimposed signals with frequencies w and w+dw, which indeed requires some minimum sample length. But at the same time nobody prevents us from calculating S(w) value at arbitrary w simply by definition of PF, because function S(w) turns out to be continuous. So I apologize for the misunderstanding.

 
By the way, the real infinite, in every sense, frequency resolution is the Hilbert transform
 
Rorschach:

Have you done any second generation wavelets (lifting scheme)? I read it in passing, there are no edge effects there.

I haven't... There probably cannot be any edge effects at all, it's still a consequence of the causality principle - the uncertainty at the edge of the signal can only be resolved by knowing the subsequent values. Such a filter can certainly be built theoretically, but in practice it would be unrealizable... Where did you read about edge effects, can you give me a link?
 
alsu:
I haven't... There can be no edge effects at all, probably, because it is, after all, a consequence of the causality principle - the uncertainty arising at the edge of the signal can only be resolved by knowing the subsequent values, such a filter can of course be built in theory, but in practice it would be unrealizable... Where did you read about edge effects, can you give me a link?

I came across them by accident, I don't remember where, I was looking for something. It's based on a decomposition of the model and the deviation from it.
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