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added a yet experimental feature of a phase 'optimized' real Fourier transform.

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suter_a
2015-09-24 15:33:47 +02:00
parent 1f95678764
commit f58cbf1874
9 changed files with 299 additions and 38 deletions
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119
src/classes/PFourier.cpp
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@ -8,7 +8,7 @@
***************************************************************************/
/***************************************************************************
* Copyright (C) 2007-2014 by Andreas Suter *
* Copyright (C) 2007-2015 by Andreas Suter *
* andreas.suter@psi.ch *
* *
* This program is free software; you can redistribute it and/or modify *
@ -163,7 +163,7 @@ PFourier::~PFourier()
}
//--------------------------------------------------------------------------
// Transform
// Transform (public)
//--------------------------------------------------------------------------
/**
* <p>Carries out the Fourier transform. It is assumed that fStartTime is the time zero
@ -201,7 +201,7 @@ void PFourier::Transform(UInt_t apodizationTag)
}
//--------------------------------------------------------------------------
// GetMaxFreq
// GetMaxFreq (public)
//--------------------------------------------------------------------------
/**
* <p>returns the maximal frequency in units choosen, i.e. Gauss, Tesla, MHz, Mc/s
@ -218,7 +218,7 @@ Double_t PFourier::GetMaxFreq()
}
//--------------------------------------------------------------------------
// GetRealFourier
// GetRealFourier (public)
//--------------------------------------------------------------------------
/**
* <p>returns the real part Fourier as a histogram.
@ -259,7 +259,108 @@ TH1F* PFourier::GetRealFourier(const Double_t scale)
}
//--------------------------------------------------------------------------
// GetImaginaryFourier
// GetPhaseOptRealFourier (public)
//--------------------------------------------------------------------------
/**
* <p>returns the phase corrected real Fourier transform. The correction angle is
* past back as well.
* <p>Currently it simply does the following thing: (i) rotate the complex Fourier
* transform through all angles in 1/2° steps, i.e.
* \f$ f_{\rm rot} = (f_{\rm real} + i f_{\rm imag}) \exp(- \alpha)\f$,
* hence \f$ f_{\rm rot} = f_{\rm real} \cos(\alpha) + f_{\rm imag} \sin(\alpha)\f$.
* (ii) search the maximum of \f$ sum_{\alpha} {\cal R}\{f_{\rm rot}\}\f$ for all
* \f$\alpha\f$. From this one gets \f$\alpha_{\rm opt}\f$. (iii) The 'optimal'
* real Fourier transform is \f$f_{\rm opt} = (f_{\rm real} + i f_{\rm imag})
* \exp(- \alpha_{\rm opt})\f$.
*
* \return the TH1F histo of the phase 'optimzed' real Fourier transform.
*
* \param phase return value of the optimal phase
* \param scale normalisation factor
* \param min minimal freq / field from which to optimise. Given in the choosen unit.
* \param max maximal freq / field up to which to optimise. Given in the choosen unit.
*/
TH1F* PFourier::GetPhaseOptRealFourier(Double_t &phase, const Double_t scale, const Double_t min, const Double_t max)
{
UInt_t noOfFourierBins = 0;
if (fNoOfBins % 2 == 0)
noOfFourierBins = fNoOfBins/2;
else
noOfFourierBins = (fNoOfBins+1)/2;
UInt_t minBin = 0;
UInt_t maxBin = noOfFourierBins;
// check if minimum frequency is given. If yes, get the proper minBin
if (min != -1.0) {
minBin = (UInt_t)(min/fResolution);
}
// check if maximum frequency is given. If yes, get the proper maxBin
if (max != -1.0) {
maxBin = (UInt_t)(max/fResolution);
}
// copy the real/imag Fourier from min to max
vector<Double_t> realF, imagF;
for (UInt_t i=minBin; i<=maxBin; i++) {
realF.push_back(fOut[i][0]);
imagF.push_back(fOut[i][1]);
}
// rotate trough real/imag Fourier through 360° with a 1/2° resolution and keep the integral
Double_t rotRealIntegral[720];
Double_t sum = 0.0;
Double_t da = 8.72664625997164774e-03; // pi / 360
for (UInt_t i=0; i<720; i++) {
sum = 0.0;
for (UInt_t j=0; j<realF.size(); j++) {
sum += realF[j]*cos(da*i) + imagF[j]*sin(da*i);
}
rotRealIntegral[i] = sum;
}
// find the maximum in rotRealIntegral
Double_t maxRot = 0.0;
UInt_t maxRotBin = 0;
for (UInt_t i=0; i<720; i++) {
if (maxRot < rotRealIntegral[i]) {
maxRot = rotRealIntegral[i];
maxRotBin = i;
}
}
// keep the optimal phase
phase = maxRotBin*da;
// clean up
realF.clear();
imagF.clear();
// invoke the real phase optimised histo to be filled. Caller is the owner!
Char_t name[256];
Char_t title[256];
snprintf(name, sizeof(name), "%s_Fourier_PhOptRe", fData->GetName());
snprintf(title, sizeof(title), "%s_Fourier_PhOptRe", fData->GetTitle());
TH1F *realPhaseOptFourier = new TH1F(name, title, noOfFourierBins, -fResolution/2.0, (Double_t)(noOfFourierBins-1)*fResolution+fResolution/2.0);
if (realPhaseOptFourier == 0) {
fValid = false;
cerr << endl << "**SEVERE ERROR** couldn't allocate memory for the real part of the Fourier transform." << endl;
return 0;
}
// fill realFourier vector
for (UInt_t i=0; i<noOfFourierBins; i++) {
realPhaseOptFourier->SetBinContent(i+1, scale*(fOut[i][0]*cos(phase) + fOut[i][1]*sin(phase)));
realPhaseOptFourier->SetBinError(i+1, 0.0);
}
return realPhaseOptFourier;
}
//--------------------------------------------------------------------------
// GetImaginaryFourier (public)
//--------------------------------------------------------------------------
/**
* <p>returns the imaginary part Fourier as a histogram.
@ -301,7 +402,7 @@ TH1F* PFourier::GetImaginaryFourier(const Double_t scale)
}
//--------------------------------------------------------------------------
// GetPowerFourier
// GetPowerFourier (public)
//--------------------------------------------------------------------------
/**
* <p>returns the Fourier power spectrum as a histogram.
@ -343,7 +444,7 @@ TH1F* PFourier::GetPowerFourier(const Double_t scale)
}
//--------------------------------------------------------------------------
// GetPhaseFourier
// GetPhaseFourier (public)
//--------------------------------------------------------------------------
/**
* <p>returns the Fourier phase spectrum as a histogram.
@ -402,7 +503,7 @@ TH1F* PFourier::GetPhaseFourier(const Double_t scale)
}
//--------------------------------------------------------------------------
// PrepareFFTwInputData
// PrepareFFTwInputData (private)
//--------------------------------------------------------------------------
/**
* <p>Feeds the Fourier data and apply the apodization.
@ -451,7 +552,7 @@ void PFourier::PrepareFFTwInputData(UInt_t apodizationTag)
}
//--------------------------------------------------------------------------
// ApodizeData
// ApodizeData (private)
//--------------------------------------------------------------------------
/**
* <p>Carries out the appodization of the data.