TJ, Thank you muchly although I didn't think there was a need to rush this on your part as I had already supplied a usable AFL for FFT. I'm sure however, that the one you built in will be faster and probably easier to use as well.
--- In [email protected], "Tomasz Janeczko" <[EMAIL PROTECTED]> wrote: > > Hello, > > Because of so much talk about FFT I decided to release 4.86.0 to "cool down" discussion > even considering the fact that account manager part > which is big thing is not yet complete and therefore has been hidden/disabled in this beta. > > The example formula that uses AB 4.86 FFT includes de-trending which is of course straightforward (calculate linear regression > and subtract regression line from the data - look at "de-trending" comment inside formula in the read-me). > > Best regards, > Tomasz Janeczko > amibroker.com > ----- Original Message ----- > From: Rakesh Sahgal > To: [email protected] > Sent: Wednesday, October 11, 2006 7:57 AM > Subject: Re: [amibroker] Re: Hurst Channels > > > Fred > > So in essence are you saying that to get a meaningful response from a FFT it is essential that the data series be de-trended? Also since TJ had in response to your query indicated that the FFT implementation he was going to include in AB was not going to be constrained by ^2 limitation requiring data padding/windowing(?), the problem of ascertaining cycles should be resolved if the data is detrended and then run through the FFT function in AB? > > Rakesh > > > On 10/11/06, Fred Tonetti <[EMAIL PROTECTED]> wrote: > Bill, > > > > As a follow up to my last > > > > Lets use the wave generator ( below in AFL ) to manufacture some synthetic data > > > > You can see that I purposely picked wave lengths that are powers of two The reason is that FFT's will of course resolve these quite well as long as you have the sample size set to be a power of 2 which is larger then the longest wavelength. The amplitudes and phase offsets are pretty much random. > > > > See the attachments > > > > #1 The individual and composite ( DATA ) waves we generated > > #2 The histogram or periodogram for the FFT Notice how it picked all wave lengths out with very little trouble. > > #3 The output cycles which are a result of the individual cycle lengths, amplitudes and phase offsets that the FFT detected. Notice how this is almost a perfect match of the input. The individual waves can of course be easily extrapolated and combined to present a picture of where the data should go in the future. > > > > #4 Another generated wave this time with trend added in Notice the effect on the white composite line. > > #5 The resulting histogram from the FFT WITHOUT detrending the data first. Notice how it has become "confused". > > #6 The resulting output waves now don't look much like the inputs. > > > > #7 Same histogram as in #5 but with detrending the data prior to invoking the FFT. Notice how now we are back to where we should be. > > #8 The resulting output waves as we would expect them to be > > > > #9 Another generated wave this time with a very high noise level ( the grey histogram ). You can see the effect it has had on the data we manufactured. > > #10 The histogram from FFT. Notice how even though the noise levels have gone up here, the FFT still had no real problems finding the cycles. > > #11 The resulting output waves which now look very much like the input WITHOUT the noise. > > > > #12 Here I have purposely changed the wave lengths from being powers of 2 to 7, 17, 27, 37 & 47 . Notice the effect it has had in the histogram I had to increase the data sample to 512 to get this resolution which is still somewhat "muddy" but all in all the FFT did a good job of finding the cycles. > > > > The other thing to keep in mind here with this particular wave generator is that I have not introduced any variation in wave length, amplitude or phase offset over the life of the data sample which in my opinion does happen For the purists that don't think this happens, then I would think that they would at least admit that non cyclic events can make it appear to DSP algorithms as if this were the case. > > > > rTrend = 0; > > rNoise = 0 ; > > dFactor = 1; > > > > rCyc1Amp = 3; > > rCyc2Amp = 5; > > rCyc3Amp = 7; > > rCyc4Amp = 9; > > rCyc5Amp = 11; > > > > rCyc1Len = 4; > > rCyc2Len = 8; > > rCyc3Len = 16; > > rCyc4Len = 32; > > rCyc5Len = 64; > > > > rCyc1Phase = 72; > > rCyc2Phase = 144; > > rCyc3Phase = 216; > > rCyc4Phase = 288; > > rCyc5Phase = 360; > > > > if (Source == "Generator" ) > > { > > pi = 4 * atan (1 ); > > > > StartX = 1000; > > > > Trend = (BI + 1) * rTrend * dFactor * (rCyc1Amp + rCyc2Amp + rCyc3Amp + rCyc4Amp + rCyc5Amp) / 5 ; > > > > Noise = (Random () - 0.5 ) * 2 * rNoise * dFactor * (rCyc1Amp + rCyc2Amp + rCyc3Amp + rCyc4Amp + rCyc5Amp) / 5 ; > > > > Cycle1 = cos ((BI / rCyc1Len + rCyc1Phase / 360 ) * 2 * pi) * (rCyc1Amp * dFactor) + Trend * 0.2 ; > > Cycle2 = cos((BI / rCyc2Len + rCyc2Phase / 360 ) * 2 * pi) * (rCyc2Amp * dFactor) + Trend * 0.2 ; > > Cycle3 = cos((BI / rCyc3Len + rCyc3Phase / 360 ) * 2 * pi) * (rCyc3Amp * dFactor) + Trend * 0.2 ; > > Cycle4 = cos((BI / rCyc4Len + rCyc4Phase / 360 ) * 2 * pi) * (rCyc4Amp * dFactor) + Trend * 0.2 ; > > Cycle5 = cos((BI / rCyc5Len + rCyc5Phase / 360 ) * 2 * pi) * (rCyc5Amp * dFactor) + Trend * 0.2 ; > > > > CycleX = Cycle1 + Cycle2 + Cycle3 + Cycle4 + Cycle5 + Noise; > > > > if (PlotIt == "IP Cycles") > > { > > Plot (Cycle1, "C1", colorRed); > > Plot (Cycle2, "C2", colorOrange); > > Plot (Cycle3, "C3", colorYellow); > > Plot (Cycle4, "C4", colorBrightGreen); > > Plot (Cycle5, "C5", colorBlue); > > Plot (CycleX, "Cx", colorWhite, styleThick ); > > Plot (Noise, "n", colorLightGrey, styleThick | styleHistogram); > > } > > > > Data = StartX + CycleX; > > } > > > > > > > > > > -------------------------------------------------------------------- -------- > I am using the free version of SPAMfighter for private users. > It has removed 8605 spam emails to date. > Paying users do not have this message in their emails. > Try SPAMfighter for free now! > Please note that this group is for discussion between users only. 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