Right ... I'm familiar with the source ... Thanks for the info ...
--- In [email protected], "Tomasz Janeczko" <[EMAIL PROTECTED]>
wrote:
>
> Hello,
>
> No, it is using FFT of any length without any padding.
> It is so called mixed-radix FFT algorithm.
> It was first published in 1969 by R.C. Singleton
>
> R. C. Singleton, "An Algorithm for Computing the Mixed Radix Fast
Fourier Transform", IEEE Trans. Audio Electroacoust., v. AU-17, p.
> 93, June 1969
>
> Best regards,
> Tomasz Janeczko
> amibroker.com
>
> ----- Original Message -----
> From: "Fred" <[EMAIL PROTECTED]>
> To: <[email protected]>
> Sent: Friday, October 06, 2006 6:41 PM
> Subject: [amibroker] Re: Polynomial Trendlines
>
>
> > Excellent ... One more question if I may ... You aren't using an
> > algorithm for FFT's that requires a power of two for length of
data
> > and then when used with a non power of two padding the array via
> > some method either with 0's or a repeat of some segment of the
data
> > etc ... right ?
> >
> > --- In [email protected], "Tomasz Janeczko" <groups@>
> > wrote:
> >>
> >> Fred,
> >>
> >> As for FFT function that is implemented in 4.86 - yes it works
> > with any
> >> length (not only power of 2) and it provides both real and
> > imaginary parts
> >>
> >> Here is an excerpt from the documentation I have already written
> > for it:
> >>
> >> FFT( array, len = 0 )
> >>
> >> performs FFT (Fast Fourier Transform) on last 'len' bars of the
> > array, if len is set to zero, then FFT is performed
> >>
> >> on entire array. len parameter must be even.
> >>
> >> Result:
> >>
> >> function returns array which holds FFT bins for first 'len'
bars.
> > There are len/2 FFT complex bins returned,
> >>
> >> where bin is a pair of numbers (complex number): first is real
> > part of the complex number and second number
> >>
> >> is the imaginary part of the complex number.
> >>
> >> result = FFT( array, 256 );
> >>
> >> where:
> >>
> >> 0th bin (result[0] and result[1]) represents DC component,
> >>
> >> 1st bin (result[1 ] and result[2]) represents real and imaginary
> > parts of lowest frequency range
> >>
> >> and so on upto result[ len - 2 ] and result[ len - 1 ]
> >>
> >> remaining elements of the array are set to zero.
> >>
> >> FFT bins are complex numbers and do not represent real amplitude
> > and phase. To obtain amplitude and
> >>
> >> phase from bins you need to convert inside the formula. The
> > following code snipplet does that:
> >>
> >>
> >>
> >> ffc = FFT(data,Len);
> >>
> >> for( i = 0; i < Len - 1; i = i + 2 )
> >>
> >> {
> >>
> >> amp[ i ] = amp[ i + 1 ] = sqrt(ffc[ i ]^ 2 + ffc[ i + 1 ]^2);
> >>
> >> phase[ i ] = phase[ i + 1 ] = atan2( ffc[ i + 1], ffc[ i ] );
> >>
> >> }
> >>
> >> IMPORTANT note: input array for FFT must NOT contain any Null
> > values. Use Nz() function to convert Nulls to zeros
> >>
> >> if you are not sure that input array is free from nulls.
> >>
> >>
> >> Best regards,
> >> Tomasz Janeczko
> >> amibroker.com
> >> ----- Original Message -----
> >> From: "Fred" <ftonetti@>
> >> To: <[email protected]>
> >> Sent: Friday, October 06, 2006 4:47 PM
> >> Subject: [amibroker] Re: Polynomial Trendlines
> >>
> >>
> >> > TJ,
> >> >
> >> > I have long since had FFT capability in AFL as the algorithms
> > are
> >> > very straight forward and relatively simple to do in AFL.
> > However
> >> > FFT's typically require LOTS of data relative to the cycle
> > lengths
> >> > one is attempting to identify and do not provide particularly
> > good
> >> > resolution at the lower frequencies. From this perspective
> > tools
> >> > like MESA ( The algortihm, NOT the black box product ) provide
> > much
> >> > greater resolution with much less data.
> >> >
> >> > However, neither of these approaches is what I'm after at this
> >> > juncture ... What I'm after is the ability to do trigonometric
> > curve
> >> > fitting in a similar way to what the PolyFit AFL I posted
> > performs
> >> > linear curve fitting i.e. via the solution of simultaneous
> >> > equations. This involves some rather sophisticated ( at least
> > from
> >> > my perspective ) math which can be found for example in
Appendix
> > 6
> >> > of J.M. Hurst's book. Since the discussion there is only
about
> > 3
> >> > pages I'd be happy to post it or email it to anyone who has an
> >> > interest and is so inclined if they'd like to read it and
> > comment on
> >> > how to implement it.
> >> >
> >> > Fred
> >> >
> >> > PS ... Some final thoughts about FFT's and their
implementation
> > in
> >> > AB ... If you are going to provide this capability, please do
so
> > in
> >> > a manner that one can take advantage of ALL the information
that
> >> > would be the product of performing an FFT i.e. both the real &
> >> > imaginary arrays or a single array of complex numbers and the
> >> > ability to deal with complex numbers in AFL. This is needed
not
> >> > only to get amplitudes at particular frequencies but also
phase
> >> > shift and power.
> >> >
> >> > PPS ... IMHO a DFT type implementation that does not require
the
> >> > data being anaylized to be a power of 2 in length would be
> > superior
> >> > to a Cooley-Tukey implementation even if run time is a little
> >> > longer ...
> >> >
> >> > --- In [email protected], "Tomasz Janeczko" <groups@>
> >> > wrote:
> >> >>
> >> >> For that you need Fourier transform and FFT is coming as a
> > built
> >> > in function in 4.86
> >> >>
> >> >> Best regards,
> >> >> Tomasz Janeczko
> >> >> amibroker.com
> >> >> ----- Original Message -----
> >> >> From: "Fred" <ftonetti@>
> >> >> To: <[email protected]>
> >> >> Sent: Friday, October 06, 2006 3:48 AM
> >> >> Subject: [amibroker] Re: Polynomial Trendlines
> >> >>
> >> >>
> >> >> > Now if someone can take this method and/or AFL or at least
> >> > provide a
> >> >> > how to that takes us into Trigometric curve fitting and
> >> > extrapolation
> >> >> > i.e. the solution of simultaneous equations in the
> > generalized
> >> > format
> >> >> > of a spectral model i.e. ...
> >> >> >
> >> >> > S ~ (a1 cos w1t + b1 sin w1t) + ... + (Am cos wm + bm sin
wmt)
> >> >> >
> >> >> > Then we might have something fairly useful ...
> >> >> >
> >> >> > I suspect Gaussian Elimiation can be used for this as well,
> > but
> >> > I
> >> >> > don't have the skill level to calculate the necessary
matrix
> >> > entries
> >> >> > to get it down ...
> >> >> >
> >> >> > Any mathematicians out there ?
> >> >> >
> >> >> >
> >> >> > --- In [email protected], "Fred" <ftonetti@> wrote:
> >> >> >>
> >> >> >> When stretch over enough data almost any order will
become a
> >> > pseudo
> >> >> >> straight line ...
> >> >> >>
> >> >> >> By their nature a first order IS a straight line, 2nd U
> > shape,
> >> > 3rd
> >> >> >> order sine wave etc ...
> >> >> >>
> >> >> >> Try highlighting a SMALLER segment of data by using the
> >> > beginning
> >> >> > and
> >> >> >> ending range markers ...
> >> >> >>
> >> >> >>
> >> >> >> --- In [email protected], "d_hanegan" <dhanegan@>
> > wrote:
> >> >> >> >
> >> >> >> > Fred:
> >> >> >> >
> >> >> >> > Thanks for your posts and all of the information
> > concerning
> >> > the
> >> >> >> > Polynomial Trendlines. When I run the code, I pretty
much
> >> > just
> >> >> > get
> >> >> >> > a straight green line; it does not fit my data. I
thought
> > I
> >> > had
> >> >> >> > read all of the posts. Am I missing something?
> >> >> >> >
> >> >> >> > Thanks.
> >> >> >> >
> >> >> >> > Dan
> >> >> >> > --- In [email protected], "Fred" <ftonetti@>
wrote:
> >> >> >> > >
> >> >> >> > > Be AWARE ... that was a hand picked image ... if you
> > play
> >> > with
> >> >> >> > > PolyFit you will see that sometimes data fits the
> >> >> > extrapolations,
> >> >> >> > > sometimes it doesn't.
> >> >> >> > >
> >> >> >> > > The higher the order, the flakier the extrapolations
are
> >> > likely
> >> >> >> to
> >> >> >> > > become ...
> >> >> >> > >
> >> >> >> > > So ... Remember what it is ... a generator of an
> > equation
> >> > in
> >> >> > the
> >> >> >> > form
> >> >> >> > >
> >> >> >> > > Y = a + bx + cx^2 + ... + nx^(n-1)
> >> >> >> > >
> >> >> >> > > Where the coeeficients were pick to fit the data.
> >> >> >> > >
> >> >> >> > > IMHO what PolyFit is, epecially with very high orders
is
> > a
> >> > very
> >> >> >> > good
> >> >> >> > > detrender of IN SAMPLE data, nothing more, nothing
> > less ...
> >> >> > That
> >> >> >> > in
> >> >> >> > > and of itself is a useful tool ... Gaussian
Elimination
> > can
> >> >> > also
> >> >> >> > be
> >> >> >> > > the basis for some other things that are pretty decent
> > when
> >> > the
> >> >> >> > order
> >> >> >> > > is kept fairly low i.e. 3 or 4 ...
> >> >> >> > >
> >> >> >> > > --- In [email protected], "Ara Kaloustian"
> > <ara1@>
> >> >> > wrote:
> >> >> >> > > >
> >> >> >> > > > Polynomial TrendlinesFred,
> >> >> >> > > >
> >> >> >> > > > There have been a lot of posting on this subject.
> > Your
> >> > one
> >> >> >> > image
> >> >> >> > > however is a very powerful message of its potential.
> >> >> >> > > >
> >> >> >> > > > Now I have to go back and review all the post ...
> > hoping
> >> > to
> >> >> >> find
> >> >> >> > a
> >> >> >> > > good reference to study.
> >> >> >> > > >
> >> >> >> > > > Anyone using it succesfully now?
> >> >> >> > > >
> >> >> >> > > > Ara
> >> >> >> > > > ----- Original Message -----
> >> >> >> > > > From: Fred Tonetti
> >> >> >> > > > To: [email protected]
> >> >> >> > > > Sent: Tuesday, October 03, 2006 3:32 PM
> >> >> >> > > > Subject: [amibroker] RE: Polynomial Trendlines
> >> >> >> > > >
> >> >> >> > > >
> >> >> >> > > > Oops .
> >> >> >> > > >
> >> >> >> > > >
> >> >> >> > > >
> >> >> >> > > > Meant to include this visual .
> >> >> >> > > >
> >> >> >> > > >
> >> >> >> > > >
> >> >> >> > > > Green is calculated . White is extrapolated .
> >> >> >> > > >
> >> >> >> > > >
> >> >> >> > > >
> >> >> >> > > >
> >> >> >> > > >
> >> >> >> > > >
> >> >> >> > > >
> >> >> >> > > > ----------------------------------------------------
---
> > ---
> >> > ----
> >> >> > --
> >> >> >> -
> >> >> >> > ---
> >> >> >> > > ----------
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> >> >> >
> >> >> >
> >> >> >
> >> >> >
> >> >> > Please note that this group is for discussion between users
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> >> >> >
> >> >> > To get support from AmiBroker please send an e-mail
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> > to
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>
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