Fast Fourier Transform - Cycle Extraction - page 25
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Whaaattt!!!???
Angrysky,
I understand what you are trying to accomplish in principle, but I have no clue nor the technical prowess to even venture in programming what you are asking. Sorry mate, I wish i can help further.
Cheers,
PipI expect instant free coding for my insane, super implicate quantum spectrum frequency auto analyzer.
lol- j/k- thanks for even responding to my posts.
...
...those spectrum curves really know how to dance...
...those spectrum curves really know how to dance...
They sure do! Try running them in strategy tester under visual mode on highest settings...hypnotic!!
I expect instant free coding for my insane, super implicate quantum spectrum frequency auto analyzer. lol- j/k- thanks for even responding to my posts.
Perhaps if you break it down Barney style i may be able to help!
Careful- I hope no ones brain pops...
Sorry about all the cut and paste-another vague idea, but we need chaos cycles right?
If anyone has interest "Order Out OF Chaos" by Ilya Prigogine will give you some amazing thoughts and then I could just say what about this page- lol, so many ideas.
I seriously suggest checking out this PDF- but I am not a math head, I hope this is all as helpful as it looks.
A Random-Walk or Color-Chaos
on the Stock Market?
- Time-Frequency Analysis of S&P Indexes
Ping Chen
Ilya Prigogine Center for Studies in Statistical Mechanics & Complex Systems
The University of Texas, Austin, Texas 78712
http://pchen.ccer.edu.cn/homepage/Major%20papers%20by%20Chenping/SNDE96p.PDF
Chaos theory - Wikipedia, the free encyclopedia
In common usage, "chaos" means "a state of disorder".[23] However, in chaos theory, the term is defined more precisely. Although there is no universally accepted mathematical definition of chaos, a commonly used definition says that, for a dynamical system to be classified as chaotic, it must have the following properties:[24]
it must be sensitive to initial conditions;
it must be topologically mixing; and
its periodic orbits must be dense.
The requirement for sensitive dependence on initial conditions implies that there is a set of initial conditions of positive measure which do not converge to a cycle of any length.
...
It is interesting that the most practically significant condition, that of sensitivity to initial conditions, is actually redundant in the definition, being implied by two (or for intervals, one) purely topological conditions, which are therefore of greater interest to mathematicians.
Sensitivity to initial conditions is popularly known as the "butterfly effect", so called because of the title of a paper given by Edward Lorenz
...
A consequence of sensitivity to initial conditions is that if we start with only a finite amount of information about the system (as is usually the case in practice), then beyond a certain time the system will no longer be predictable. This is most familiar in the case of weather, which is generally predictable only about a week ahead.[29]
The Lyapunov exponent characterises the extent of the sensitivity to initial conditions. Quantitatively, two trajectories in phase space with initial separation diverge
where λ is the Lyapunov exponent. The rate of separation can be different for different orientations of the initial separation vector. Thus, there is a whole spectrum of Lyapunov exponents — the number of them is equal to the number of dimensions of the phase space. It is common to just refer to the largest one, i.e. to the Maximal Lyapunov exponent (MLE), because it determines the overall predictability of the system. A positive MLE is usually taken as an indication that the system is chaotic.
There are also measure-theoretic mathematical conditions (discussed in ergodic theory) such as mixing or being a K-system which relate to sensitivity of initial conditions and chaos.[4]
...
Distinguishing random from chaotic dataIt can be difficult to tell from data whether a physical or other observed process is random or chaotic, because in practice no time series consists of pure 'signal.' There will always be some form of corrupting noise, even if it is present as round-off or truncation error. Thus any real time series, even if mostly deterministic, will contain some randomness.[62][63]
All methods for distinguishing deterministic and stochastic processes rely on the fact that a deterministic system always evolves in the same way from a given starting point.[62][64] Thus, given a time series to test for determinism, one can:
pick a test state;
search the time series for a similar or 'nearby' state; and
compare their respective time evolutions.
Define the error as the difference between the time evolution of the 'test' state and the time evolution of the nearby state. A deterministic system will have an error that either remains small (stable, regular solution) or increases exponentially with time (chaos). A stochastic system will have a randomly distributed error.[65]
Essentially all measures of determinism taken from time series rely upon finding the closest states to a given 'test' state (e.g., correlation dimension, Lyapunov exponents, etc.). To define the state of a system one typically relies on phase space embedding methods.[66] Typically one chooses an embedding dimension, and investigates the propagation of the error between two nearby states. If the error looks random, one increases the dimension. If you can increase the dimension to obtain a deterministic looking error, then you are done. Though it may sound simple it is not really. One complication is that as the dimension increases the search for a nearby state requires a lot more computation time and a lot of data (the amount of data required increases exponentially with embedding dimension) to find a suitably close candidate. If the embedding dimension (number of measures per state) is chosen too small (less than the 'true' value) deterministic data can appear to be random but in theory there is no problem choosing the dimension too large – the method will work.
When a non-linear deterministic system is attended by external fluctuations, its trajectories present serious and permanent distortions. Furthermore, the noise is amplified due to the inherent non-linearity and reveals totally new dynamical properties. Statistical tests attempting to separate noise from the deterministic skeleton or inversely isolate the deterministic part risk failure. Things become worse when the deterministic component is a non-linear feedback system.[67] In presence of interactions between nonlinear deterministic components and noise, the resulting nonlinear series can display dynamics that traditional tests for nonlinearity are sometimes not able to capture.[68]
Now this is something i can understand!
Not sure that would help though
... wrong thread sorry
What about this?
I don't know if I get this at all or how to do anything, but I think there are many valuable clues for people smarter than me- I was trying not to scream, just some stuff I can tell is important
http://pchen.ccer.edu.cn/homepage/Major%20papers%20by%20Chenping/SNDE96p.PDF
In spectral representation, a plane wave has an infinite time-span but a zero-width in
frequency domain. In a correlation representation, a pulse has a zero-width time-span but a full
window in frequency space. To overcome their shortcomings, the wavelet representation with a
finite span both in time and frequency (or scale) can be constructed for an evolutionary time series.
The simplest time-frequency distribution is the short-time Fourier transform (STFT) by imposing a
shifting finite time-window in the conventional Fourier spectrum.
The concepts of instantaneous auto-correlation and instantaneous frequency are important in
developing generalized spectral analysis. A symmetric window in a localized time interval is
introduced in the instantaneous autocorrelation function in the bilinear Wigner distribution (WD),
the corresponding time-dependent frequency or simply time-frequency can be defined by the
Fourier spectrum of its autocorrelations [Wigner1932]:
WD t w S t t S t t)exp( iwt)dt
2
) * (
2
( , ) = ò ( + - - (4.1)
Continuous time-frequency representation can be approximated by a discretized twodimensional
time-frequency lattice. An important development in time-frequency analysis is the
linear Gabor transform which maps the time series into the discretized two-dimensional timefrequency
space [Gabor 1946]. According to the uncertainty principle in quantum mechanics and
information theory, the minimum uncertainty only occurs for the Gaussian function.
4p
1 Dt Df ³ (4.2)
where Dt measures the time uncertainty, Df the frequency uncertainty (angular frequency:
w= 2p f ).
Gabor introduced the Gaussian window in non-orthogonal base function h(t).
( ) ( ) ,
,
, S t C h t m n
m n
m n =å (4.3)
]*exp( )
(2 )
( )
( ) * exp[ 2
2
, - Dw
- D
= - i nt
L
t m t
h t a m n (4.4)
where Dt is the sample time-interval, Dw the sample frequency-interval, L the normalized Gaussian
window-size, m and n the time and frequency coordinate in discretized time-frequency space [Qian
and Chen 1994a].
edit: those eqations didn't copy right also-
- pg 23 starts getting very interesting- oops, shall we delete all our posts?
People may ask what will happen once the market knows about the limited predictability of
color chaos in the stock market? At this stage, we can only speculate the outcome under complex
dynamics and market uncertainty. We believe that the profit opportunities associated with color
chaos are limited and temporary, but the nonlinear pattern of persistent cycles will remain in
existence and perhaps evolve over time.
Hybrid Superheterodyne-FFT
https://en.wikipedia.org/wiki/Spectrum_analyzer
https://en.wikipedia.org/wiki/Frequency_domain
https://en.wikipedia.org/wiki/Spectral_theory
The wave vector gives us insight into physically meaningful properties of the electromagnetic wave such as its spatial extent and coupling requirements for wave vector matching...
Rough surfaces can be thought of as the superposition of many gratings of different periodicities. Kretschmann proposed[7] that a statistical correlation function be defined for a rough surface... equations follow
...
then the Fourier transform of the correlation function is...
https://en.wikipedia.org/wiki/Surface_plasmons
http://theresonanceproject.org/pdf/quaternions_spinors_twistors_paper.pdf
What Happened to Crodzilla
Hi Crodzilla,
Found this interesting thread, have read it all through but you seemed to have diappeared.
Did you suceed in finishing your research and turning it into a useful indicator.
I am monitoring an Indicator that gives similar results to Brian Milliards CCS program together with a Husrt cycle indicator, so far no conclusive resuts, but they both look good.
Allon
Crodzilla
Hi,
Has this thread died or is there someone out there still monitoring it or even more important in touch with Crodzilla about his research.
Would like to know how it panned out.
Allon