Classes
class	AnalyticSignal

class	Averager

class	BandlimitedSampledSignal

class	BlackmanHarrisWindow

class	BlackmanWindow

class	BoxFilter

class	ButterworthFilter

class	ChebyshevIFilter

class	CompositeSignal

class	CWT

class	DifferenceFilter

class	DigitalFilter

class	DigitalFilterSeries

class	FFTWindow

class	FFTWindowType

class	FIRFilter

class	GaussianFilter

class	GaussianWindow

class	HammingWindow

class	HannWindow

class	IIRFilter

class	InverseFilter

class	KaiserWindow

class	LanczosFilter

class	MinimumPhaseFilter

class	RCFilter

class	RectangularWindow

class	SavitzkyGolayFilter

class	SincFilter

class	SineFitter

class	SineFitterLimits

class	SineSubtract

class	SineSubtractResult

class	ThermalNoise

class	ThiranFilter

class	TransformedZPKFilter

class	TriangularWindow

class	TukeyWindow

Enumerations
enum	FilterTopology { LOWPASS, HIGHPASS, BANDPASS, NOTCH }

enum	DirectConvolveEdgeBehavior { ZEROES_OUTSIDE, REPEAT_OUTSIDE }

Functions
TGraph *	normalizeWaveform (TGraph *inGraph)

double *	getCorrelationFromFFT (int length, const FFTWComplex theFFT1, const FFTWComplex theFFT2)

TGraph *	getInterpolatedGraph (const TGraph *grIn, Double_t deltaT)
	Interpolation Routines that use ROOT::Math::Interpolator. More...

TGraph *	getInterpolatedGraphFreqDom (const TGraph *grIn, Double_t deltaT)
	Interpolation Routines that zeropads the FFT. More...

TGraph *	getConvolution (const TGraph grA, const TGraph grB)
	Convolution. More...

RFSignal *	getConvolution (RFSignal grA, RFSignal grB)
	Convolution. More...

double	getAbs (FFTWComplex &theNum)
	Returns the magnitude of a complex number. More...

double *	doInvFFT (int length, const FFTWComplex *theInput)
	Computes an inverse FFT. More...

FFTWComplex *	doFFT (int length, const double *theInput)
	Computes an FFT of an array of real numbers. More...

void	doFFT (int length, const double properly_aligned_input, FFTWComplex properly_aligned_output)

void	doInvFFTClobber (int length, FFTWComplex properly_aligned_input_that_will_likely_be_clobbered, double properly_aligned_output)

void	doInvFFTNoClobber (int length, const FFTWComplex properly_aligned_input, double properly_aligned_output)

TGraph *	convertMagnitudeToTimeDomain (const TGraph *inputMag)
	Converts inputMag (linear units) to time domain by means of hilbert transform assuming R_signal = 1/sqrt(2) (R_mag - i R^_mag);. More...

double *	getCorrelation (const TGraph gr1, const TGraph gr2, int firstIndex, int lastIndex)
	Computes the correlation of two subsets of TGraphs. More...

double *	getCorrelation (int length, const float oldY1, const float oldY2)
	Computes the correlation of two arrays. More...

double *	getCorrelation (int length, const double oldY1, const double oldY2)
	Computes the correlation of two arrays. More...

TGraph *	correlateAndAverage (Int_t numGraphs, TGraph **grPtrPtr)
	This is designed for when you want to average a number of graphs of the same thing together. It uses a correlation to find the deltaT between graphs and then shifts the graphs and coherently sums them. The return is the average of the input graphs. More...

TGraph *	correlateAndAveragePredeterminedZone (Int_t numGraphs, TGraph *grPtrPtr, Int_t correlationBinPtr, Int_t binWiggleRoom)

TGraph *	interpolateCorrelateAndAverage (Double_t deltaTInt, Int_t numGraphs, TGraph **grPtrPtr)
	This is designed for when you want to average a number of graphs of the same thing together. It uses a correlation to find the deltaT between graphs and then shifts the graphs and coherently sums them. The return is the average of the input graphs. More...

Double_t *	combineValuesUsingFFTs (Int_t numArrays, Double_t **thePtrPtr, Int_t eachLength)
	Returns the time domain result of a frequency domain sum of a number of arrays. As of writing this documentation, I'm not sure why this would be interesting. More...

TGraph *	makePowerSpectrum (const TGraph *grWave)
	Returns the power spectral density. Note the PSD is unormalised (or if you prefer is normalised to the sum squared amplitude of the time domain). See this short note for my terminology. More...

TGraph *	makePowerSpectrumPeriodogram (const TGraph *grWave)
	Returns the power spectral density. Note the PSD returned is the periodogram (or if you prefer is normalised to the mean squared amplitude of the time domain). See this short note for my terminology. More...

TGraph *	makePowerSpectrumVoltsSeconds (const TGraph *grWave)
	Returns the power spectral density. Note the PSD returned is normalised and divided by frequency bin width (or if you prefer it is normalised to the time-integral squared amplitude of the time domain and then divided by frequency bin width). See this short note for my terminology. As the name suggests this function expects the input waveform to be a volts-seconds one. More...

TGraph *	makePowerSpectrumVoltsSecondsBartlett (const TGraph *grWave)
	Returns the power spectral density of the input waveform convolved with a Bartlett Window. Note the PSD returned is normalised and divided by frequency bin width (or if you prefer it is normalised to the time-integral squared amplitude of the time domain and then divided by frequency bin width). See this short note for my terminology. As the name suggests this function expects the input waveform to be a volts-seconds one. More...

TGraph *	makePSVSBartlettPaddedOverlap (const TGraph *grWave, Int_t padFactor=4, Int_t numFreqs=64)
	Returns the power spectral density of the input waveform. In this one we first zero pad the waveform and then split it up into overlapping segments and convolve each segment with the Bartlett window before summing the resulting PSD's. As the name suggests this function expects the input waveform to be a volts-seconds one. No idea if this one actually works, or where I read oabout this crazy method which is supposed to reduce the variance of the PSD estimator. More...

TGraph *	makePowerSpectrumVoltsSecondsdB (const TGraph *grWave)
	Returns the power spectral density in dB units. Note the PSD returned is normalised and divided by frequency bin width (or if you prefer it is normalised to the time-integral squared amplitude of the time domain and then divided by frequency bin width). See this short note for my terminology. As the name suggests this function expects the input waveform to be a volts-seconds one. More...

TGraph *	makePowerSpectrumMilliVoltsNanoSeconds (const TGraph *grWave)
	Returns the power spectral density in dB units. Note the PSD returned is normalised and divided by frequency bin width (or if you prefer it is normalised to the time-integral squared amplitude of the time domain and then divided by frequency bin width). See this short note for my terminology. As the name suggests this function expects the input waveform to be a millivolts-nanoseconds one. More...

TGraph *	makePowerSpectrumMilliVoltsNanoSecondsdB (const TGraph *grWave)

TGraph *	makePowerSpectrumVoltsSecondsPadded (const TGraph *grWave, Int_t padFactor=4)
	Returns the power spectral density of the input waveform zero-padded by some factor. Note the PSD returned is normalised and divided by frequency bin width (or if you prefer it is normalised to the time-integral squared amplitude of the time domain and then divided by frequency bin width). See this short note for my terminology. As the name suggests this function expects the input waveform to be a volts-seconds one. More...

TGraph *	makePowerSpectrumVoltsSecondsPaddeddB (const TGraph *grWave, Int_t padFactor=4)
	Returns the power spectral density in dB units of the input waveform zero-padded by some factor. Note the PSD returned is normalised and divided by frequency bin width (or if you prefer it is normalised to the time-integral squared amplitude of the time domain and then divided by frequency bin width). See this short note for my terminology. As the name suggests this function expects the input waveform to be a volts-seconds one. More...

TGraph *	makeRawPowerSpectrum (const TGraph *grWave)
	Returns the power spectral density in completely unormalised unit (as in Parseval's theorem is not obeyed and there is an extra factor of N not removed form the PSD). See this short note for my terminology. More...

TGraph *	getCorrelationGraph (const TGraph gr1, const TGraph gr2, Int_t *zeroOffset=0)
	Returns the correlation of two TGraphs. More...

TGraph *	getNormalisedCorrelationGraph (const TGraph gr1, const TGraph gr2, Int_t *zeroOffset=0)
	Returns the normalised correlation of two TGraphs. More...

TGraph *	getNormalisedCorrelationGraphTimeDomain (const TGraph gr1, const TGraph gr2, Int_t *zeroOffset=0, Int_t useDtRange=0, Double_t dtMin=-1000, Double_t dtMax=1000)
	Returns the normalised correlation of two TGraphs. More...

TGraph *	getInterpolatedCorrelationGraph (const TGraph grIn1, const TGraph grIn2, Double_t deltaT)
	Returns the correlation of two interpolated TGraphs. More...

TGraph *	makeInverseInverseSpectrum (const TGraph *grWave)
	Returns the inverse FFT of the FFT of the input TGraph. Seems pointless. More...

TGraph *	combineGraphsUsingFFTs (Int_t numGraphs, TGraph *grPtr, const double theWeights=0)
	Returns the time domain result of a frequency domain sum of a number of TGraphs. In the sum each TGraph is weighted by a value. As of writing this documentation, I'm not sure why this would be interesting. More...

TGraph *	getBoxCar (const TGraph *grWave, Int_t halfWidth)
	Smooth graph using box car smoothing. More...

TGraph *	getHilbertTransform (const TGraph *grWave)
	The Hilbert transform of the input TGraph. More...

double *	getHilbertTransform (int N, const double *y)

TGraph *	getHilbertEnvelope (const TGraph *grWave)
	The Hilbert envelope of the input TGraph. This is defined as e_i=sqrt(v_i^2 + h_i^2), where e_i, v_i and h_i are the i-th sample of the envelope, input graph and hilbert transform of the input graph repsectively. More...

Double_t	sumPower (const TGraph *gr, Int_t firstBin=-1, Int_t lastBin=-1)
	The linear sum of the power in a TGraph (normally a PSD) More...

Double_t	integratePower (const TGraph *gr, Int_t firstBin=-1, Int_t lastBin=-1)
	The integral of the power in a TGraph (normally a PSD) (i.e the sum of bin content*bin width) More...

Double_t	sumVoltageSquared (const TGraph *gr, Int_t firstBin, Int_t lastBin)
	The sum of the voltage squared in a waveform. More...

Double_t	integrateVoltageSquared (const TGraph *gr, Int_t firstBin=-1, Int_t lastBin=-1)
	The integral of the v^2*dt in a waveform. Now works for unevenly sampled waeforms. More...

Int_t	getPeakBin (const TGraph *gr)
	Find the peak (maximum positive) bin in a TGraph. More...

Int_t	getPeakBin (const TGraph *gr, Int_t firstBin, Int_t lastBin)
	Find the peak (maximum positive) bin in a TGraph. More...

Double_t	getPeakXvalue (const TGraph *gr)
	Find the x value associated with the peak (maximum positive) in a TGraph. More...

Double_t	getPeakVal (const TGraph gr, int index=0)
	Find the peak (maximum positive) in a TGraph. More...

Double_t	getPeakVal (const TGraph gr, Int_t firstBin, Int_t lastBin, int index=0)
	Find the peak (maximum positive) in a TGraph. More...

Double_t	getPeakSqVal (const TGraph gr, int index=0)
	Find the peak (v^2) in a TGraph. More...

void	getPeakRmsSqVal (const TGraph gr, Double_t &peak, Double_t &rms, Int_t index=0)
	Find the peak (v^2) and RMS (of v^2) in a TGraph. More...

void	getPeakRmsRectified (const TGraph gr, Double_t &peak, Double_t &rms, Int_t index=0)
	Find the peak (v) and RMS (of v) of a rectified TGraph. More...

TGraph *	getSimplePowerEnvelopeGraph (const TGraph *gr)
	Returns the simple power envelope of a waveform. The waveform is first squared and then only local peaks are taken to form the power envelope. More...

TGraph *	smoothFFT (const TGraph *gr, Int_t factor)
	Returns a smoothed FFT where N-bins are averaged to reduce variance. More...

TGraph *	subtractGraphs (const TGraph grA, const TGraph grB)
	Returns the difference between two graphs (A-B). More...

TGraph *	divideGraphs (const TGraph grA, const TGraph grB)
	Returns the ratio between two graphs (A/B). More...

TGraph *	translateGraph (const TGraph *grWave, const Double_t deltaT)
	Returns a graph translated by deltaT. Such that t'=t+dt. More...

TGraph *	ratioSubtractOneGraphs (const TGraph grA, const TGraph grB)
	Returns the one minus the ratio between two graphs (A/B). More...

TGraph *	dbGraphs (const TGraph grA, const TGraph grB)
	Returns the ratio of two graphs as 10 *log(A/B) More...

TGraph *	padWave (const TGraph *grA, Int_t padFactor)
	Zero pad a wave making it a factor of N longer. More...

TGraph *	padWaveToLength (const TGraph *grA, Int_t newLength)
	Zero pad a wave making it up to newLength points. More...

TGraph *	rectifyWave (const TGraph *gr, Int_t makeNeg=0)
	Rectify a waveform, optionally returning an all negative waveform. More...

Double_t	bartlettWindow (Int_t j, Int_t n)
	The Bartlett window function (it's basically a triangle that peaks in the middle at 1 and goes to zero at the end points) More...

Double_t	welchWindow (Int_t j, Int_t n)
	The Welch window function similar to the Bartlett window except that it falls off from the middle as dx^2 (ie. less steeply). More...

void	takeDerivative (Int_t numPoints, const Double_t inputX, const Double_t inputY, Double_t outputX, Double_t outputY)
	This fucntions just calculates the simple bin by bin dv/dt derivative of the input data. More...

TGraph *	getDerviative (const TGraph *grIn)
	This returns a TGraph which is the derivative of the input graph. More...

TGraph *	getDerivative (const TGraph *grIn)
	This returns a TGraph which is the derivative of the input graph. More...

TGraph *	simplePassBandFilter (const TGraph *grWave, Double_t minFreq, Double_t maxFreq)
	This returns a TGraph which has had a simple pass band filter applied. More...

TGraph *	simpleNotchFilter (const TGraph *grWave, Double_t minFreq, Double_t maxFreq)
	This returns a TGraph which has had a simple notch band filter applied. More...

TGraph *	multipleSimpleNotchFilters (const TGraph *grWave, Int_t numNotches, const Double_t minFreq[], const Double_t maxFreq[])
	This returns a TGraph which has had N simple notch band filters applied. More...

TGraph *	cropWave (const TGraph *grWave, Double_t minTime, Double_t maxTime)
	This returns a TGraph which has been cropped in. More...

Double_t	getWaveformSNR (const TGraph *gr)
	This returns the SNR ratio of the input waveform. More...

Double_t	getWaveformSNR (const TGraph *gr, Double_t &peakToPeak, Double_t &rms)
	This returns the SNR ratio of the input waveform. More...

Double_t	getWaveformPeak (const TGraph *gr)
	This returns the largest (i.e most positive, or least negative) value. More...

Double_t	getEnvelopeSNR (const TGraph *gr)

Double_t	getEnvelopeSNR (const TGraph *gr, Double_t &peakToPeak, Double_t &rms, Double_t &timeOfPeak)

Double_t	simpleInterploate (Double_t x1, Double_t y1, Double_t x2, Double_t y2, Double_t x)
	Linear interpolate to find the value at some point near two known points. More...

double *	FFTCorrelation (int waveformlength, const FFTWComplex A, const FFTWComplex B, FFTWComplex *work=0, int min_i=0, int max_i=0, int order=1)

void	inPlaceShift (int N, double *x)

void	rotate (TGraph *g, int rot)

void	polySubtract (TGraph *g, int order=1)

double *	directConvolve (int N, const double x, int M, const double h, double *y=0, int delay=0, DirectConvolveEdgeBehavior edge_behavior=ZEROES_OUTSIDE)

void	wrap (size_t N, double *vals, double period=360)

void	wrap (size_t N, double *vals, double period, double center)

void	wrap (size_t N, float *vals, float period, float center)

void	wrap (size_t N, float *vals, float period=360)

int	fast_floor (double val)

double	wrap (double val, double period, double center)

double	wrap (double val, double period=360)

void	unwrap (size_t N, double *vals, double period=360)

void	unwrap (size_t N, float *vals, float period=360)

double	getDt (const TGraph *g, int realN=0)

double	evalEvenGraph (const TGraph *g, double x)

void	applyWindow (TGraph g, const FFTWindowType w)

double	randomRayleigh (double sigma=1, TRandom *rng=0)

double	sinc (double x, double eps=0)

int	loadWisdom (const char *file)

int	saveWisdom (const char *file)

TGraph *	welchPeriodogram (const TGraph gin, int segment_size, double overlap_fraction=0.5, const FFTWindowType window=&GAUSSIAN_WINDOW, bool truncate_extra=true, TGraph *gout=0)

double *	lombScarglePeriodogramSlow (int N, const double x, const double y, int nfreqs, const double freqs, double answer=0)

TGraph *	lombScarglePeriodogram (const TGraph g, double dt=0, double oversample_factor=4, double high_factor=2, TGraph replaceme=0, int extirpolation_factor=4)

TGraph *	lombScarglePeriodogram (int N, double dt, const double __restrict x, const double __restrict y, double oversample_factor=4, double high_factor=2, TGraph *replaceme=0, int extirpolation_factor=4)

void	stokesParameters (int N, const double hpol, const double hpol_hat, const double vpol, const double vpol_hat, double Iavg=0, double Qavg=0, double Uavg=0, double Vavg=0, double Iins=0, double Qins=0, double Uins=0, double Vins=0, bool only_max_instantaneous=true)

void	dftAtFreq (const TGraph g, double freq, double phase, double amp=0, double real=0, double *imag=0)

void	dftAtFreqAndMultiples (const TGraph g, double freq, int nmultiples, double phase, double amp=0, double real=0, double *imag=0)

FFTWComplex *	makeMinimumPhase (int N, const double *G, double mindb=-100)

TGraph *	makeMinimumPhase (const TGraph *g, double mindb=-100)

TGraph *	makeFixedDelay (const TGraph *g, double delay=1)

double	checkCausality (int N, const FFTWComplex *signal)

double *	rmsEnvelope (int N, double W, const double x, const double y, double *out=0)

double *	peakEnvelope (int N, double min_distance, const double x, const double y, double *out=0)

double *	getCrossCov (int length, const double oldY1, const double oldY2)

double *	getCrossCorr (int length, const double oldY1, const double oldY2)

TGraph *	getCovGraph (const TGraph gr1, const TGraph gr2, int *zeroOffset=0)

TGraph *	getCorrGraph (const TGraph gr1, const TGraph gr2, int *zeroOffset=0)

TGraph *	getInterpCovGraph (const TGraph gr1, const TGraph gr2, double deltaT)

TGraph *	getInterpCorrGraph (const TGraph gr1, const TGraph gr2, double deltaT)

TGraph *	getInterpolatedGraphInvert (const TGraph *g, double dt=0, int nout=0)

TGraph *	getInterpolatedGraphWeightedInvert (const TGraph *g, double dt=0, int nout=0)

TGraphErrors *	getInterpolatedGraphSparseInvert (const TGraph g, double dt=0, int nout=0, double max_dist=32, double eps=0, double weight_exp=0, double mu=1e-3, int regularization_order=0, double error_scale=1, TH2 A=0)

void	getInterpolatedGraphSparseInvert (const TGraph in, TGraph out, double max_dist=32, double eps=0, double weight_exp=0, double mu=1e-3, int regularization_order=0, double error_scale=1, TH2 *A=0)

TGraph *	getInterpolatedGraphInvertLapped (const TGraph *g, double dt=0, int lapsize=64, int nout=0)

TGraph *	getInterpolatedGraphInvertSplit (const TGraph *g, double dt=0, int splitsize=64, int overlap=8, int out=0)

TGraph *	getInterpolatedGraphDFT (const TGraph *g, double dt=0, int nout=0, double maxF=0)

FFTWComplex *	getUnevenDFT (const TGraph *g, double df, int npts)

TGraph *	supersample (const TGraph *g, int supersample_factor, int sinc_radius=16)

TGraph *	getInterpolatedGraphSincKernel (const TGraph *g, double dt=0, int nout=0)

TGraph *	getInterpolatedGraphLagrange (const TGraph *g, double dt=0, double supersample=1)

double	shannonWhitakerInterpolateValue (double t, const TGraph regular_graph, int max_lobe=0, const FFTWindowType win=0)

double	shannonWhitakerInterpolateValueAndError (double t, const TGraphErrors regular_graph, double err, int max_lobe=0, const FFTWindowType *win=0)

double	linearInterpolateValueAndError (double t, const TGraph regular_graph, double err=0)

double	shannonWhitakerInterpolateDerivative (double t, const TGraph *regular_graph)

Detailed Description

Stuff I use that should maybe be in FFTtools?

A set of basic filter operations that serve as examples and also should be quite useful SimplePassBandFilter just cuts everything outside the pass band in fourier space like a brick wall, with all the ensuing acausal goodness.

Digital Filter Implementation.

Cosmin Deaconu cozzy.nosp@m.d@ki.nosp@m.cp.uc.nosp@m.hica.nosp@m.go.ed.nosp@m.u

This is the namespace that holds all the various useful FFT related functions. All of the functions canbe called using something like FFTtools::doYourFunkyThing(arg1,arg2).

Enumeration Type Documentation

enum FFTtools::DirectConvolveEdgeBehavior

direct convolution for kernel can either assume zero's outside boundaries or repetition of first and last values

Definition at line 693 of file FFTtools.h.

Function Documentation

void FFTtools::applyWindow	(	TGraph *	g,
		const FFTWindowType *	w
	)

applies window to graph

Definition at line 2713 of file FFTtools.cxx.

Double_t FFTtools::bartlettWindow	(	Int_t	j,
		Int_t	n
	)

The Bartlett window function (it's basically a triangle that peaks in the middle at 1 and goes to zero at the end points)

Parameters

j	The index to evaluate the window at.
n	The length of sample.

Returns: The value of the window function at index j.

Definition at line 21 of file FFTtools.cxx.

double FFTtools::checkCausality	(	int	N,
		const FFTWComplex *	signal
	)

Checks if a signal is causal or not by comparing the imaginary part to the hilbert transform of the real part and returning the square difference (scaled by N). A perfectly causal system will return 0, but numerical inaccuracy may make that not true.

Definition at line 3372 of file FFTtools.cxx.

TGraph * FFTtools::combineGraphsUsingFFTs	(	Int_t	numGraphs,
		TGraph **	grPtr,
		const double *	theWeights = `0`
	)

Returns the time domain result of a frequency domain sum of a number of TGraphs. In the sum each TGraph is weighted by a value. As of writing this documentation, I'm not sure why this would be interesting.

Parameters

numGraphs	The number of TGraphs to sum.
grPtr	A pointer to an array of numGraphs TGraph pointers.
theWeights	An optional array of weights with which to sum the TGraphs.

Returns: A pointer to a TGraph containing the inverse FFT of the weighted summed FFT of the input graphs.

Definition at line 570 of file FFTtools.cxx.

Double_t * FFTtools::combineValuesUsingFFTs	(	Int_t	numArrays,
		Double_t **	thePtrPtr,
		Int_t	eachLength
	)

Returns the time domain result of a frequency domain sum of a number of arrays. As of writing this documentation, I'm not sure why this would be interesting.

Parameters

numArrays	The number of arrays to sum.
thePtrPtr	A pointer to a two-dimensional array of doubles [numArrays][eachLength].
eachLength	The length of each array.

Returns: The time domain result of the frequency domain summation.

Definition at line 538 of file FFTtools.cxx.

TGraph * FFTtools::convertMagnitudeToTimeDomain ( const TGraph * inputMag )

Converts inputMag (linear units) to time domain by means of hilbert transform assuming R_signal = 1/sqrt(2) (R_mag - i R^_mag);.

Parameters

inputMag TGraph containg the inputMagnitude

Returns: TGraph of the time domain signal

Definition at line 2256 of file FFTtools.cxx.

TGraph * FFTtools::correlateAndAverage	(	Int_t	numGraphs,
		TGraph **	grPtrPtr
	)

This is designed for when you want to average a number of graphs of the same thing together. It uses a correlation to find the deltaT between graphs and then shifts the graphs and coherently sums them. The return is the average of the input graphs.

Parameters

numGraphs	Number of graphs to average
thePtrPtr	A pointer to a two-dimensional array of TGraphs *grPtrArray[numGraphs].

Returns: A pointer to a graph containing the averaged waveform.

Definition at line 2461 of file FFTtools.cxx.

TGraph * FFTtools::correlateAndAveragePredeterminedZone	(	Int_t	numGraphs,
		TGraph **	grPtrPtr,
		Int_t *	correlationBinPtr,
		Int_t	binWiggleRoom = `30`
	)

This is designed for when you want to average a number of graphs of the same thing together. It uses a correlation to find the deltaT between graphs and then shifts the graphs and coherently sums them. The return is the average of the input graphs This is intended to be used for a set of multiple waveforms where we have found some event-wide peak bin from previous correlation Using this method assures that the bin associated with the maximum correlation value is found within a limited range of the predetermined event wide peak bin

Parameters

numGraphs	Number of graphs to average
thePtrPtr	A pointer to a two-dimensional array of TGraphs *grPtrArray[numGraphs].
correlationBinPtr	A pointer to the pre-determined average correlation on an event-by-event basis
binWiggleRoom	How many bins either side of the bin associated with the peak value in the reduced range used to find the max correlation, with the default set to 20 bins

Returns: A pointer to a graph containing the averaged waveform.

Definition at line 2535 of file FFTtools.cxx.

TGraph * FFTtools::cropWave	(	const TGraph *	grWave,
		Double_t	minTime,
		Double_t	maxTime
	)

This returns a TGraph which has been cropped in.

Parameters

grWave	The input graph.
minTime	The lower edge of the time window.
maxTime	The upper edge of the time window.

Returns: The derviative of grWave.

Definition at line 2012 of file FFTtools.cxx.

TGraph * FFTtools::dbGraphs	(	const TGraph *	grA,
		const TGraph *	grB
	)

Returns the ratio of two graphs as 10 *log(A/B)

Parameters

grA	A pointer to the first graph.
grB	A pointer to the second graph.

Returns: A pointer to a TGraph containing 10 * log(A/B)

Definition at line 1682 of file FFTtools.cxx.

void FFTtools::dftAtFreq	(	const TGraph *	g,
		double	freq,
		double *	phase,
		double *	amp = `0`,
		double *	real = `0`,
		double *	imag = `0`
	)

Compute the DFT term at a given frequency. Probably not want you want to do for a series of frequencies where one can take advantage of trig relations, etc.

Parameters

g	What to look at
freq	the frequency
phase	pointer where phase will be stored or 0 to not store anything
amp	pointer where amplitude will be stored or 0 to not store anything
real	pointer where real will be stored or 0 to not store anything
imag	pointer where imag will be stored or 0 to not store anything

Definition at line 3206 of file FFTtools.cxx.

void FFTtools::dftAtFreqAndMultiples	(	const TGraph *	g,
		double	freq,
		int	nmultiples,
		double *	phase,
		double *	amp = `0`,
		double *	real = `0`,
		double *	imag = `0`
	)

Compute the DFT term at a given frequency and n multiples of it. Timebase does not have to be even. Phase and amp should be big enough to store nmultiples or 0 if you don't want to fill one.

Parameters

g	waveform to look at
freq	base frequency
nmultiples	number of multiples to consider
phase	pointer to array where phase will be stored, or 0 to not store anything.
amp	pointer to array where amp will be stored, or 0 to not store anything.
real	pointer where real will be stored or 0 to not store anything
imag	pointer where imag will be stored or 0 to not store anything

Definition at line 3034 of file FFTtools.cxx.

double * FFTtools::directConvolve	(	int	N,
		const double *	x,
		int	M,
		const double *	h,
		double *	y = `0`,
		int	delay = `0`,
		DirectConvolveEdgeBehavior	edge_behavior = `ZEROES_OUTSIDE`
	)

convolution without FFT of x with kernel h. y should have same size as x (it is cropped symmetrically) if delay = 0, h will be centered around its middle sample, if - M/2 , will be purely causal, etc.

Definition at line 2757 of file FFTtools.cxx.

TGraph * FFTtools::divideGraphs	(	const TGraph *	grA,
		const TGraph *	grB
	)

Returns the ratio between two graphs (A/B).

Parameters

grA	A pointer to the first graph.
grB	A pointer to the second graph.

Returns: A pointer to a TGraph containing the ratio (A/B) of the input graphs.

Definition at line 1632 of file FFTtools.cxx.

FFTWComplex * FFTtools::doFFT	(	int	length,
		const double *	theInput
	)

Computes an FFT of an array of real numbers.

Parameters

length	The length of the input array.
theInput	The input array of length real numbers.

Returns: An array of length/2 + 1 complex numbers

Definition at line 436 of file FFTtools.cxx.

void FFTtools::doFFT	(	int	length,
		const double *	properly_aligned_input,
		FFTWComplex *	properly_aligned_output
	)

Version of doFFT don't require copying of memory. If these are not aligned properly (i.e. allocated with fftw_malloc, memalign or equivalent), bad things might happen.

Definition at line 351 of file FFTtools.cxx.

double * FFTtools::doInvFFT	(	int	length,
		const FFTWComplex *	theInput
	)

Computes an inverse FFT.

Parameters

length	The length of the output array
theInput	The input array of complex numbers of (length/2 +1)

Returns: An array of length real numbers

Definition at line 482 of file FFTtools.cxx.

void FFTtools::doInvFFTClobber	(	int	length,
		FFTWComplex *	properly_aligned_input_that_will_likely_be_clobbered,
		double *	properly_aligned_output
	)

Version of doInvFFt don't require copying of memory. If these are not aligned properly (i.e. allocated with fftw_malloc, memalign or equivalent), bad things might happen. Note that the input may be clobbered in this case.

Definition at line 408 of file FFTtools.cxx.

void FFTtools::doInvFFTNoClobber	(	int	length,
		const FFTWComplex *	properly_aligned_input,
		double *	properly_aligned_output
	)

Version of doInvFFt that only requires copying of input. The input is copied to a properly-aligned temporary on the stack. If the output is not aligned properly (i.e. allocated with fftw_malloc, memalign or equivalent), bad things might happen. Things will probably be a bit faster if the input is aligned properly, as long as memcpy dispatches correctly.

Definition at line 372 of file FFTtools.cxx.

double FFTtools::evalEvenGraph	(	const TGraph *	g,
		double	x
	)

linearly interpolates value x in g . Similar to doing g->Eval() but much faster (since doesn't need to sort or binary search)

Definition at line 2881 of file FFTtools.cxx.

int FFTtools::fast_floor ( double val )

inline

Faster than the libm floor, which cares about errno and the floating point environment and all that crap

Definition at line 721 of file FFTtools.h.

double * FFTtools::FFTCorrelation	(	int	waveformlength,
		const FFTWComplex *	A,
		const FFTWComplex *	B,
		FFTWComplex *	work = `0`,
		int	min_i = `0`,
		int	max_i = `0`,
		int	order = `1`
	)

Correlation between two FFTs bandpasses between min_i and max_i using butterworth filter of order order work can be used for temporary to avoid allocation of new memory

Definition at line 2641 of file FFTtools.cxx.

double FFTtools::getAbs ( FFTWComplex & theNum )

Returns the magnitude of a complex number.

Parameters

theNum The complex number.

Returns: The magnitude of the complex number.

Definition at line 1388 of file FFTtools.cxx.

TGraph * FFTtools::getBoxCar	(	const TGraph *	grWave,
		Int_t	halfWidth
	)

Smooth graph using box car smoothing.

Parameters

grWave	A pointer to the input TGraph
halfWidth	The halfWidth in samples of the size of the box over which to smooth the input graph (eg. halfWidth=1 means that sample i is the average if i-1, i and i+1.

Returns: A pointer to a TGraph containing the smoothed graph.

Definition at line 984 of file FFTtools.cxx.

TGraph * FFTtools::getConvolution	(	const TGraph *	grA,
		const TGraph *	grB
	)

Convolution.

Parameters

grA	A pointer to the input TGraph A.
grB	A pointer to the input TGraph B

Returns: A pointer to the convolution of A and B stored in a TGraph, it is the users responsibility to delete this after use.

Definition at line 2309 of file FFTtools.cxx.

RFSignal * FFTtools::getConvolution	(	RFSignal *	grA,
		RFSignal *	grB
	)

Convolution.

Parameters

grA	A pointer to the input RFSignal A.
grB	A pointer to the input RFSignal B

Returns: A pointer to the convolution of A and B stored in a TGraph, it is the users responsibility to delete this after use.

Definition at line 2399 of file FFTtools.cxx.

double * FFTtools::getCorrelation	(	const TGraph *	gr1,
		const TGraph *	gr2,
		int	firstIndex,
		int	lastIndex
	)

Computes the correlation of two subsets of TGraphs.

Parameters

gr1	The first TGraph in the correlation.
gr2	The second TGraph in the correlation.
firstIndex	The index of the first sample in the sub traces.
lastIndex	The index of the last sample in the sub traces.

Returns: The correlation as an array of lastIndex-firstIndex real numbers.

Definition at line 902 of file FFTtools.cxx.

double * FFTtools::getCorrelation	(	int	length,
		const float *	oldY1,
		const float *	oldY2
	)

Computes the correlation of two arrays.

Parameters

length	The length of the arrays
oldY1	The first array in the correlation.
oldY2	The second array in the correlation.

Returns: The correlation as an array of length real numbers.

Definition at line 852 of file FFTtools.cxx.

double * FFTtools::getCorrelation	(	int	length,
		const double *	oldY1,
		const double *	oldY2
	)

Computes the correlation of two arrays.

Parameters

length	The length of the arrays
oldY1	The first array in the correlation.
oldY2	The second array in the correlation.

Returns: The correlation as an array of length real numbers.

Definition at line 868 of file FFTtools.cxx.

TGraph * FFTtools::getCorrelationGraph	(	const TGraph *	gr1,
		const TGraph *	gr2,
		Int_t *	zeroOffset = `0`
	)

Returns the correlation of two TGraphs.

Parameters

gr1	The first input TGraph
gr2	The second input TGraph

Returns: A pointer to a TGraph containing the correlation of gr1 and gr2.

Definition at line 754 of file FFTtools.cxx.

TGraph * FFTtools::getDerivative ( const TGraph * grIn )

This returns a TGraph which is the derivative of the input graph.

Parameters

grIn	The input graph.

Returns: The derviative of grIn.

Definition at line 1922 of file FFTtools.cxx.

TGraph * FFTtools::getDerviative ( const TGraph * grIn )

This returns a TGraph which is the derivative of the input graph.

Parameters

grIn	The input graph.

Returns: The derviative of grIn.

Definition at line 1917 of file FFTtools.cxx.

double FFTtools::getDt	(	const TGraph *	g,
		int	realN = `0`
	)

computes reasonable dt from unevenly sampled graph

Definition at line 2734 of file FFTtools.cxx.

TGraph * FFTtools::getHilbertEnvelope ( const TGraph * grWave )

The Hilbert envelope of the input TGraph. This is defined as e_i=sqrt(v_i^2 + h_i^2), where e_i, v_i and h_i are the i-th sample of the envelope, input graph and hilbert transform of the input graph repsectively.

Parameters

grWave A pointer to the input TGraph

Returns: A pointer to a TGraph containing the Hilbert envelope function.

Definition at line 964 of file FFTtools.cxx.

TGraph * FFTtools::getHilbertTransform ( const TGraph * grWave )

The Hilbert transform of the input TGraph.

Parameters

grWave A pointer to the input TGraph

Returns: A pointer to a TGraph containing the Hilbert transform

Definition at line 951 of file FFTtools.cxx.

double * FFTtools::getHilbertTransform	(	int	N,
		const double *	y
	)

Hilbert transform on an array y is input,N is length

Definition at line 936 of file FFTtools.cxx.

TGraph * FFTtools::getInterpolatedCorrelationGraph	(	const TGraph *	grIn1,
		const TGraph *	grIn2,
		Double_t	deltaT
	)

Returns the correlation of two interpolated TGraphs.

Parameters

grIn1	The first input TGraph
grIn2	The second input TGraph
deltaT	The desired time step for the interpolated graphs

Returns: A pointer to a TGraph containing the correlation of gr1 and gr2, after each is interpolated to have a timestep of deltaT.

std::cout << grCor->GetN() << "\n";

Definition at line 838 of file FFTtools.cxx.

TGraph * FFTtools::getInterpolatedGraph	(	const TGraph *	grIn,
		Double_t	deltaT
	)

Interpolation Routines that use ROOT::Math::Interpolator.

Parameters

grIn	A pointer to the input TGraph.
deltaT	The desired period (1/rate) of the interpolated waveform.

Returns: A pointer to ther interpolated TGraph, it is the users responsibility to delete this after use.

Definition at line 32 of file FFTtools.cxx.

TGraph * FFTtools::getInterpolatedGraphFreqDom	(	const TGraph *	grIn,
		Double_t	deltaT
	)

Interpolation Routines that zeropads the FFT.

Parameters

grIn	A pointer to the input TGraph.
deltaT	The desired period (1/rate) of the interpolated waveform.

Returns: A pointer to ther interpolated TGraph, it is the users responsibility to delete this after use.

Definition at line 84 of file FFTtools.cxx.

TGraph * FFTtools::getNormalisedCorrelationGraph	(	const TGraph *	gr1,
		const TGraph *	gr2,
		Int_t *	zeroOffset = `0`
	)

Returns the normalised correlation of two TGraphs.

Parameters

gr1	The first input TGraph (must be zero meaned)
gr2	The second input TGraph (must be zero meaned)

Returns: A pointer to a TGraph containing the correlation of gr1 and gr2 where each point is normalised by the number of valid samples in the correlation and by the product of the RMS of the input graphs.

Definition at line 709 of file FFTtools.cxx.

TGraph * FFTtools::getNormalisedCorrelationGraphTimeDomain	(	const TGraph *	gr1,
		const TGraph *	gr2,
		Int_t *	zeroOffset = `0`,
		Int_t	useDtRange = `0`,
		Double_t	dtMin = `-1000`,
		Double_t	dtMax = `1000`
	)

Returns the normalised correlation of two TGraphs.

Parameters

gr1	The first input TGraph (must be zero meaned)
gr2	The second input TGraph (must be zero meaned)
zeroOffset	A pointer to an integer where the sample corresponding to zero offset will be stored
useDtRange	A flag to enable the setting of a limited range of deltat's to try
dtMin	The minimum delta-t to include in the correlation, the maximum delta-t to include in the correlation

Returns: A pointer to a TGraph containing the correlation of gr1 and gr2 where each point is normalised by the number of valid samples in the correlation and by the product of the RMS of the input graphs.

Definition at line 627 of file FFTtools.cxx.

Int_t FFTtools::getPeakBin ( const TGraph * gr )

Find the peak (maximum positive) bin in a TGraph.

Parameters

gr	A pointer to the input TGraph

Returns: The index of the bin with peak value.

Definition at line 1456 of file FFTtools.cxx.

Int_t FFTtools::getPeakBin	(	const TGraph *	gr,
		Int_t	firstBin,
		Int_t	lastBin
	)

Find the peak (maximum positive) bin in a TGraph.

Parameters

gr	A pointer to the input TGraph
firstBin	The first bin to include.
lastBin	The last bin to include.

Returns: The index of the bin with peak value.

Definition at line 1490 of file FFTtools.cxx.

void FFTtools::getPeakRmsRectified	(	const TGraph *	gr,
		Double_t &	peak,
		Double_t &	rms,
		Int_t *	index = `0`
	)

Find the peak (v) and RMS (of v) of a rectified TGraph.

Parameters

gr	A pointer to the input TGraph.
peak	A reference to a Double_t where the peak value will be stored.
rms	A reference to a Double_t where the rms value will be stored.
index	An optional pointer in which the peak bin can be stored.

Definition at line 1586 of file FFTtools.cxx.

void FFTtools::getPeakRmsSqVal	(	const TGraph *	gr,
		Double_t &	peak,
		Double_t &	rms,
		Int_t *	index = `0`
	)

Find the peak (v^2) and RMS (of v^2) in a TGraph.

Parameters

gr	A pointer to the input TGraph.
peak	A reference to a Double_t where the peak value will be stored.
rms	A reference to a Double_t where the rms value will be stored.
index	An optional pointer in which the peak bin can be stored.

Definition at line 1570 of file FFTtools.cxx.

Double_t FFTtools::getPeakSqVal	(	const TGraph *	gr,
		int *	index = `0`
	)

Find the peak (v^2) in a TGraph.

Parameters

gr	A pointer to the input TGraph.
index	An optional pointer in which the peak bin can be stored.

Returns: The peak (v^2)value.

Definition at line 1550 of file FFTtools.cxx.

Double_t FFTtools::getPeakVal	(	const TGraph *	gr,
		int *	index = `0`
	)

Find the peak (maximum positive) in a TGraph.

Parameters

gr	A pointer to the input TGraph.
index	An optional pointer in which the peak bin can be stored.

Returns: The peak value.

Definition at line 1510 of file FFTtools.cxx.

Double_t FFTtools::getPeakVal	(	const TGraph *	gr,
		Int_t	firstBin,
		Int_t	lastBin,
		int *	index = `0`
	)

Find the peak (maximum positive) in a TGraph.

Parameters

gr	A pointer to the input TGraph.
firstBin	The first bin to include.
lastBin	The last bin to include.
index	An optional pointer in which the peak bin can be stored.

Returns: The peak value.

Definition at line 1529 of file FFTtools.cxx.

Double_t FFTtools::getPeakXvalue ( const TGraph * gr )

Find the x value associated with the peak (maximum positive) in a TGraph.

Parameters

gr	A pointer to the input TGraph

Returns: The x value of the bin with peak value.

Definition at line 1473 of file FFTtools.cxx.

TGraph * FFTtools::getSimplePowerEnvelopeGraph ( const TGraph * gr )

Returns the simple power envelope of a waveform. The waveform is first squared and then only local peaks are taken to form the power envelope.

Parameters

gr	A pointer to the input TGraph.

Returns: A pointer to a TGraph containing the power envelope

Definition at line 1817 of file FFTtools.cxx.

Double_t FFTtools::getWaveformPeak ( const TGraph * gr )

This returns the largest (i.e most positive, or least negative) value.

Parameters

gr	The input graph.

Returns: The peak

Definition at line 2176 of file FFTtools.cxx.

Double_t FFTtools::getWaveformSNR ( const TGraph * gr )

This returns the SNR ratio of the input waveform.

Parameters

gr	The input graph.

Returns: The SNR of the input waveform, where S is half of the peak-to-peak and N is the RMS of the first 25 ns.

Definition at line 2081 of file FFTtools.cxx.

Double_t FFTtools::getWaveformSNR	(	const TGraph *	gr,
		Double_t &	peakToPeak,
		Double_t &	rms
	)

This returns the SNR ratio of the input waveform.

Parameters

gr	The input graph.
peakToPeak	A reference to a double which will be set to half of the peak-to-peak
rms	A reference to a double which will be set to the RMS of teh first 25 samples

Returns: The SNR of the input waveform, where S is half of the peak-to-peak and N is the RMS of the first 25 samples.

Definition at line 2092 of file FFTtools.cxx.

void FFTtools::inPlaceShift	(	int	N,
		double *	x
	)

in place array rotation

Definition at line 2721 of file FFTtools.cxx.

Double_t FFTtools::integratePower	(	const TGraph *	gr,
		Int_t	firstBin = `-1`,
		Int_t	lastBin = `-1`
	)

The integral of the power in a TGraph (normally a PSD) (i.e the sum of bin content*bin width)

Parameters

gr	A pointer to the input TGraph (normally a PSD)
firstBin	The first bin to include in the integral.
lastBin	The last bin to include in the integral.

Returns: The integral value.

Definition at line 1406 of file FFTtools.cxx.

Double_t FFTtools::integrateVoltageSquared	(	const TGraph *	gr,
		Int_t	firstBin = `-1`,
		Int_t	lastBin = `-1`
	)

The integral of the v^2*dt in a waveform. Now works for unevenly sampled waeforms.

Parameters

gr	A pointer to the input TGraph
firstBin	The first bin to include in the integral.
lastBin	The last bin to include in the integral.

Returns: The value of the integral.

Definition at line 1436 of file FFTtools.cxx.

TGraph * FFTtools::interpolateCorrelateAndAverage	(	Double_t	deltaTInt,
		Int_t	numGraphs,
		TGraph **	grPtrPtr
	)

This is designed for when you want to average a number of graphs of the same thing together. It uses a correlation to find the deltaT between graphs and then shifts the graphs and coherently sums them. The return is the average of the input graphs.

Parameters

deltaTInt	The time-step to interpolate to before doing the correlation and averaging
numGraphs	Number of graphs to average
thePtrPtr	A pointer to a two-dimensional array of TGraphs *grPtrArray[numGraphs].

Returns: A pointer to a graph containing the averaged waveform.

Definition at line 2447 of file FFTtools.cxx.

TGraph * FFTtools::lombScarglePeriodogram	(	const TGraph *	g,
		double	dt = `0`,
		double	oversample_factor = `4`,
		double	high_factor = `2`,
		TGraph *	replaceme = `0`,
		int	extirpolation_factor = `4`
	)

fast periodogoram (as in Press & Rybicki) . Implementation in Periodogram.cxx

Definition at line 250 of file Periodogram.cxx.

double * FFTtools::lombScarglePeriodogramSlow	(	int	N,
		const double *	x,
		const double *	y,
		int	nfreqs,
		const double *	freqs,
		double *	answer = `0`
	)

"normal" lomb-scargle periodogram, not using the N log N algorithm in Press & Rybicki)

Definition at line 327 of file Periodogram.cxx.

TGraph * FFTtools::makeFixedDelay	(	const TGraph *	g,
		double	delay = `1`
	)

Compute a fixed group delay version of a time-domain signal.

Parameters

g	the time-domain signal, probably needs to be zero-padded
phase	the phase (in radians) of the output

Returns: fixed phase version of g

Definition at line 3341 of file FFTtools.cxx.

TGraph * FFTtools::makeInverseInverseSpectrum ( const TGraph * grWave )

Returns the inverse FFT of the FFT of the input TGraph. Seems pointless.

Parameters

grWave A pointer to the input TGraph

Returns: A pointer to a TGraph containing the inverse FFT of the FFT of grWave.

Definition at line 919 of file FFTtools.cxx.

FFTWComplex * FFTtools::makeMinimumPhase	(	int	N,
		const double *	G,
		double	mindb = `-100`
	)

Given a desired amplitude response G, makes a minimum phase version of the waveform. This takes advantage of the fact that for a minimum phase signal, the phase response equals the hilbert transform of the log magnitude.

Parameters

N,the	length of the amplitude response (typically the time domain length/ 2 + 1),
F,the	amplitude response G(w) with w in normalized units (first component is dc, last is nyquist). This is in linear units.
mindb,an	absolute zero in the frequency response cannot be represented with a minimum phase filter. Anything with a (power) magnitude smaller than mindb will be made equal to mindb

Returns: A minimum phase version of the waveform.

Definition at line 3278 of file FFTtools.cxx.

TGraph * FFTtools::makeMinimumPhase	(	const TGraph *	g,
		double	mindb = `-100`
	)

Compute a minimum phase version of a time-domain signal.

Parameters

g	the time-domain signal, probably needs to be zero-padded
mindb,an	absolute zero in the frequency response cannot be represented with a minimum phase filter. Anything with a (power) magnitude smaller than mindb will be made equal to mindb

Returns: minimum phase version of g

Definition at line 3317 of file FFTtools.cxx.

TGraph * FFTtools::makePowerSpectrum ( const TGraph * grWave )

Returns the power spectral density. Note the PSD is unormalised (or if you prefer is normalised to the sum squared amplitude of the time domain). See this short note for my terminology.

Parameters

grWave The input time domain waveform

Returns: A pointer to a TGraph containing the power spectrum.

Definition at line 1031 of file FFTtools.cxx.

TGraph * FFTtools::makePowerSpectrumMilliVoltsNanoSeconds ( const TGraph * grWave )

Returns the power spectral density in dB units. Note the PSD returned is normalised and divided by frequency bin width (or if you prefer it is normalised to the time-integral squared amplitude of the time domain and then divided by frequency bin width). See this short note for my terminology. As the name suggests this function expects the input waveform to be a millivolts-nanoseconds one.

Parameters

grWave The input time domain waveform with units of millivolts-nanoseconds.

Returns: A pointer to a TGraph containing the power spectrum in dB units, the frequency units are MHz.

Definition at line 1147 of file FFTtools.cxx.

TGraph * FFTtools::makePowerSpectrumPeriodogram ( const TGraph * grWave )

Returns the power spectral density. Note the PSD returned is the periodogram (or if you prefer is normalised to the mean squared amplitude of the time domain). See this short note for my terminology.

Parameters

grWave The input time domain waveform

Returns: A pointer to a TGraph containing the power spectrum.

Definition at line 1070 of file FFTtools.cxx.

TGraph * FFTtools::makePowerSpectrumVoltsSeconds ( const TGraph * grWave )

Returns the power spectral density. Note the PSD returned is normalised and divided by frequency bin width (or if you prefer it is normalised to the time-integral squared amplitude of the time domain and then divided by frequency bin width). See this short note for my terminology. As the name suggests this function expects the input waveform to be a volts-seconds one.

Parameters

grWave The input time domain waveform with units of volts-seconds.

Returns: A pointer to a TGraph containing the power spectrum.

Definition at line 1106 of file FFTtools.cxx.

TGraph * FFTtools::makePowerSpectrumVoltsSecondsBartlett ( const TGraph * grWave )

Returns the power spectral density of the input waveform convolved with a Bartlett Window. Note the PSD returned is normalised and divided by frequency bin width (or if you prefer it is normalised to the time-integral squared amplitude of the time domain and then divided by frequency bin width). See this short note for my terminology. As the name suggests this function expects the input waveform to be a volts-seconds one.

Parameters

grWave The input time domain waveform with units of volts-seconds.

Returns: A pointer to a TGraph containing the power spectrum.

Definition at line 1017 of file FFTtools.cxx.

TGraph * FFTtools::makePowerSpectrumVoltsSecondsdB ( const TGraph * grWave )

Returns the power spectral density in dB units. Note the PSD returned is normalised and divided by frequency bin width (or if you prefer it is normalised to the time-integral squared amplitude of the time domain and then divided by frequency bin width). See this short note for my terminology. As the name suggests this function expects the input waveform to be a volts-seconds one.

Parameters

grWave The input time domain waveform with units of volts-seconds.

Returns: A pointer to a TGraph containing the power spectrum in dB units, the frequency units are MHz.

Definition at line 1286 of file FFTtools.cxx.

TGraph * FFTtools::makePowerSpectrumVoltsSecondsPadded	(	const TGraph *	grWave,
		Int_t	padFactor = `4`
	)

Returns the power spectral density of the input waveform zero-padded by some factor. Note the PSD returned is normalised and divided by frequency bin width (or if you prefer it is normalised to the time-integral squared amplitude of the time domain and then divided by frequency bin width). See this short note for my terminology. As the name suggests this function expects the input waveform to be a volts-seconds one.

Parameters

grWave	The input time domain waveform with units of volts-seconds.
padFactor	The factor by which to zero pad the wave.

Returns: A pointer to a TGraph containing the power spectrum.

Definition at line 1336 of file FFTtools.cxx.

TGraph * FFTtools::makePowerSpectrumVoltsSecondsPaddeddB	(	const TGraph *	grWave,
		Int_t	padFactor = `4`
	)

Returns the power spectral density in dB units of the input waveform zero-padded by some factor. Note the PSD returned is normalised and divided by frequency bin width (or if you prefer it is normalised to the time-integral squared amplitude of the time domain and then divided by frequency bin width). See this short note for my terminology. As the name suggests this function expects the input waveform to be a volts-seconds one.

Parameters

grWave	The input time domain waveform with units of volts-seconds.
padFactor	The factor by which to zero pad the wave.

Returns: A pointer to a TGraph containing the power spectrum in dB units with MHz as the frequency unit.

Definition at line 1346 of file FFTtools.cxx.

TGraph * FFTtools::makePSVSBartlettPaddedOverlap	(	const TGraph *	grWave,
		Int_t	padFactor = `4`,
		Int_t	numFreqs = `64`
	)

Returns the power spectral density of the input waveform. In this one we first zero pad the waveform and then split it up into overlapping segments and convolve each segment with the Bartlett window before summing the resulting PSD's. As the name suggests this function expects the input waveform to be a volts-seconds one. No idea if this one actually works, or where I read oabout this crazy method which is supposed to reduce the variance of the PSD estimator.

Parameters

grWave	The input time domain waveform with units of volts-seconds.
padFactor	The factor by which to zero pad the wave see padWave
numFreqs	The number of frequency bins required in the output, which is related to the length of overlapping segments.

Returns: A pointer to a TGraph containing the power spectrum.

Definition at line 1856 of file FFTtools.cxx.

TGraph * FFTtools::makeRawPowerSpectrum ( const TGraph * grWave )

Returns the power spectral density in completely unormalised unit (as in Parseval's theorem is not obeyed and there is an extra factor of N not removed form the PSD). See this short note for my terminology.

Parameters

grWave The input time domain waveform.

Returns: A pointer to a TGraph containing the power spectrum.

Definition at line 1354 of file FFTtools.cxx.

TGraph * FFTtools::multipleSimpleNotchFilters	(	const TGraph *	grWave,
		Int_t	numNotches,
		const Double_t	minFreq[],
		const Double_t	maxFreq[]
	)

This returns a TGraph which has had N simple notch band filters applied.

Parameters

grWave	The input graph.
numNotches	The number of notch regiosn
minFreq	An array of lower frequency of the notches.
maxFreq	An array upper frequency of the notch.

Returns: The derviative of grWave.

Definition at line 2038 of file FFTtools.cxx.

TGraph * FFTtools::normalizeWaveform ( TGraph * inGraph )

stuff I want to add to FFTtools

Definition at line 752 of file AnitaTemplates.cc.

TGraph * FFTtools::padWave	(	const TGraph *	grA,
		Int_t	padFactor
	)

Zero pad a wave making it a factor of N longer.

Parameters

grA	A pointer to the input graph.
padFactor	The factor by whcih to increas the length (eg. new length = factor * old length)

Returns: A pointer to the zero padded TGraph.

Definition at line 1745 of file FFTtools.cxx.

TGraph * FFTtools::padWaveToLength	(	const TGraph *	grA,
		Int_t	newLength
	)

Zero pad a wave making it up to newLength points.

Parameters

grA	A pointer to the input graph.
newLength	The new length the graph should be (it gets zero padded on either side)

Returns: A pointer to the zero padded TGraph.

Definition at line 1769 of file FFTtools.cxx.

double* FFTtools::peakEnvelope	(	int	N,
		double	min_distance,
		const double *	x,
		const double *	y,
		double *	out = `0`
	)

Peak envelope Approximates envelope by connecting peaks of |y|.

Parameters

N	the number of points in input / output arrays
min_distance	the minimum distance between peaks. This should be close to the half-period of the carrier wave you expect.
x	input x values (times)
y	input y values (voltages)
out	output y values (voltages) , or 0 to allocate new

Returns: output values

void FFTtools::polySubtract	(	TGraph *	g,
		int	order = `1`
	)

does fit to polynomial of order order then subtracts it

Definition at line 2745 of file FFTtools.cxx.

double FFTtools::randomRayleigh	(	double	sigma = `1`,
		TRandom *	rng = `0`
	)

random variable from rayleigh distribution

Definition at line 2792 of file FFTtools.cxx.

TGraph * FFTtools::ratioSubtractOneGraphs	(	const TGraph *	grA,
		const TGraph *	grB
	)

Returns the one minus the ratio between two graphs (A/B).

Parameters

grA	A pointer to the first graph.
grB	A pointer to the second graph.

Returns: A pointer to a TGraph containing the one minus the ratio (1 - A/B) of the input graphs.

Definition at line 1652 of file FFTtools.cxx.

TGraph * FFTtools::rectifyWave	(	const TGraph *	gr,
		Int_t	makeNeg = `0`
	)

Rectify a waveform, optionally returning an all negative waveform.

Parameters

gr	A pointer to the input graph.
makeNeg	An optional parameter which if true will return a negative waveform.

Returns: A pointer to the rectified TGraph

Definition at line 1799 of file FFTtools.cxx.

double* FFTtools::rmsEnvelope	(	int	N,
		double	W,
		const double *	x,
		const double *	y,
		double *	out = `0`
	)

Avg RMS envelope Approximates envelope by computing rms in each window

Parameters

N	length of input (and output) arrays
W	window length, in units of the x values (not all windows may contain the same length)
x	input x values
y	input y values
out	output y values, if 0 output will be allocated

Returns: output

void FFTtools::rotate	(	TGraph *	g,
		int	rot
	)

inplace graph rotation

Definition at line 2627 of file FFTtools.cxx.

double FFTtools::shannonWhitakerInterpolateDerivative	(	double	t,
		const TGraph *	regular_graph
	)

Derivative of Shannon-Whitaker interpolation of a regular graph

Definition at line 733 of file RFInterpolate.cxx.

double FFTtools::shannonWhitakerInterpolateValue	(	double	t,
		const TGraph *	regular_graph,
		int	max_lobe = `0`,
		const FFTWindowType *	win = `0`
	)

Shannon-Whitaker interpolation of a regular graph

Definition at line 575 of file RFInterpolate.cxx.

Double_t FFTtools::simpleInterploate	(	Double_t	x1,
		Double_t	y1,
		Double_t	x2,
		Double_t	y2,
		Double_t	x
	)

Linear interpolate to find the value at some point near two known points.

Parameters

x1	x value of point 1
y1	y value of point 1
x2	x value of point 2
y2	y value of point 2
x	is the point of interest

Returns: y

Definition at line 2304 of file FFTtools.cxx.

TGraph * FFTtools::simpleNotchFilter	(	const TGraph *	grWave,
		Double_t	minFreq,
		Double_t	maxFreq
	)

This returns a TGraph which has had a simple notch band filter applied.

Parameters

grWave	The input graph.
minFreq	The lower frequency of the notch.
maxFreq	The upper frequency of the notch.

Returns: The derviative of grWave.

Definition at line 1975 of file FFTtools.cxx.

TGraph * FFTtools::simplePassBandFilter	(	const TGraph *	grWave,
		Double_t	minFreq,
		Double_t	maxFreq
	)

This returns a TGraph which has had a simple pass band filter applied.

Parameters

grWave	The input graph.
minFreq	The lowest frequency to pass.
maxFreq	The highest frequency to pass.

Returns: The derviative of grWave.

Definition at line 1938 of file FFTtools.cxx.

double FFTtools::sinc	(	double	x,
		double	eps = `0`
	)

sinc function, if |x| < eps, sinc(x) = 1

Definition at line 2609 of file FFTtools.cxx.

TGraph * FFTtools::smoothFFT	(	const TGraph *	gr,
		Int_t	factor
	)

Returns a smoothed FFT where N-bins are averaged to reduce variance.

Parameters

gr	A pointer to the input TGraph.
factor	The factor by which to smooth (eg. 2 returns a PSD with half as many frequency bins).

Returns: A pointer to a TGraph containing the smoothed PSD.

Definition at line 1715 of file FFTtools.cxx.

TGraph * FFTtools::subtractGraphs	(	const TGraph *	grA,
		const TGraph *	grB
	)

Returns the difference between two graphs (A-B).

Parameters

grA	A pointer to the first graph.
grB	A pointer to the second graph.

Returns: A pointer to a TGraph containing the difference (A-B) between the input graphs.

Definition at line 1599 of file FFTtools.cxx.

Double_t FFTtools::sumPower	(	const TGraph *	gr,
		Int_t	firstBin = `-1`,
		Int_t	lastBin = `-1`
	)

The linear sum of the power in a TGraph (normally a PSD)

Parameters

gr	A pointer to the input TGraph (normally a PSD)
firstBin	The first bin to include in the sum.
lastBin	The last bin to include in the sum.

Returns: The summed power

Definition at line 1393 of file FFTtools.cxx.

Double_t FFTtools::sumVoltageSquared	(	const TGraph *	gr,
		Int_t	firstBin,
		Int_t	lastBin
	)

The sum of the voltage squared in a waveform.

Parameters

gr	A pointer to the input TGraph
firstBin	The first bin to include in the sum.
lastBin	The last bin to include in the sum.

Returns: The value of the sum.

Definition at line 1423 of file FFTtools.cxx.

void FFTtools::takeDerivative	(	Int_t	numPoints,
		const Double_t *	inputX,
		const Double_t *	inputY,
		Double_t *	outputX,
		Double_t *	outputY
	)

This fucntions just calculates the simple bin by bin dv/dt derivative of the input data.

Parameters

numPoints	The number of points in the input data (the output will be numPoints-1 in length).
inputX	The input time values.
inputY	The input voltage values.
outputX	The output time values.
outputY	The output voltage values.

Definition at line 1905 of file FFTtools.cxx.

TGraph * FFTtools::translateGraph	(	const TGraph *	grWave,
		const Double_t	deltaT
	)

Returns a graph translated by deltaT. Such that t'=t+dt.

Parameters

grWave	A pointer to the input graph.
deltaT	The amount to move time axis by

Returns: A pointer to a TGraph containing the translated graph

Definition at line 1619 of file FFTtools.cxx.

void FFTtools::unwrap	(	size_t	N,
		double *	vals,
		double	period = `360`
	)

unwraps periodic array of doubles.

Definition at line 2857 of file FFTtools.cxx.

void FFTtools::unwrap	(	size_t	N,
		float *	vals,
		float	period = `360`
	)

unwraps periodic array of floats.

Definition at line 2845 of file FFTtools.cxx.

TGraph * FFTtools::welchPeriodogram	(	const TGraph *	gin,
		int	segment_size,
		double	overlap_fraction = `0.5`,
		const FFTWindowType *	window = `&GAUSSIAN_WINDOW`,
		bool	truncate_extra = `true`,
		TGraph *	gout = `0`
	)

Make a welch periodogram of evenly sampled input. A Bartlett periodogram can be emulated using overlap_fraction = 0 and window = &RECTANGULAR_WINDOW

Parameters

gin	evenly sampled graph to estimate power spectrum of
segment_siz	ethe number of samples in each segment
overlap_fraction	the fraction of overlap for each segment. 0 is no overlap. 1 is non-sensical full overlap which will probably cause some calamity.
window	the window to use for each segment
truncate_extra	If true, any partial segment is discarded. Otherwise, it will be zero-padded
gout	if non-zero, this TGraph will be used for output

Returns: the Welch Periodogram

Definition at line 258 of file Periodogram.cxx.

Double_t FFTtools::welchWindow	(	Int_t	j,
		Int_t	n
	)

The Welch window function similar to the Bartlett window except that it falls off from the middle as dx^2 (ie. less steeply).

Parameters

j	The index to evaluate the window at
n	The length of sample.

Returns: The value of the window function at index j.

Definition at line 27 of file FFTtools.cxx.

void FFTtools::wrap	(	size_t	N,
		double *	vals,
		double	period = `360`
	)

wraps periodic array of doubles. center assumed to be period/2

Definition at line 2851 of file FFTtools.cxx.

void FFTtools::wrap	(	size_t	N,
		double *	vals,
		double	period,
		double	center
	)

wraps periodic array of doubles.

Definition at line 2872 of file FFTtools.cxx.

void FFTtools::wrap	(	size_t	N,
		float *	vals,
		float	period,
		float	center
	)

wraps periodic array of floats

Definition at line 2864 of file FFTtools.cxx.

void FFTtools::wrap	(	size_t	N,
		float *	vals,
		float	period = `360`
	)

wraps periodic array of floats. center assumed to be period/2

Definition at line 2839 of file FFTtools.cxx.

double FFTtools::wrap	(	double	val,
		double	period,
		double	center
	)

inline

Wraps a value to be within period centered at center. This could be implemented in terms of the other wraps, but in practice it's better to inline since the period and center are usually known at compile them.

Definition at line 728 of file FFTtools.h.

double FFTtools::wrap	(	double	val,
		double	period = `360`
	)

inline

Wraps a value to be within period. Center assumed to be period/2

Definition at line 732 of file FFTtools.h.

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