Package de.gsi.math.spectra

Class SpectrumTools

java.lang.Object

de.gsi.math.spectra.SpectrumTools

public class SpectrumTools
extends java.lang.Object

Class implements frequency interpolation of spectral peaks. The main idea behind these algorithm is: The resolution of frequency estimates that are solely based on the value of the highest bin of an FFT or DTFT spectrum is limited by the binning of the frequency spectrum, which assuming an FFT spectrum is determined by the number of samples N that have been used to compute the spectra (resolution = 1/N). The functions in this class provide algorithms that fit this frequency by taking the value not only of the highest but also adjacent bins into account. While the peak shape strongly depends on the underlying process, the gaussian interpolation gives typically the best results in most cases.

Author:

rstein

See Also:

reference: R.J. Steinhagen, "Tune and Chromaticity Diagnostics", in: Proceedings of the CERN Accelerator School, Dourdan, France, 2005

Constructor Summary

Constructors

Constructor	Description
SpectrumTools()

Method Summary

Modifier and Type	Method	Description
static double[]	computeFrequencyScale(int nMag)	compute equidistant frequency axis based on the length of the magnitude spectrum
static float[]	computeFrequencyScaleFloat(int nMag)	compute equidistant frequency axis based on the length of the magnitude spectrum
static double[]	computeMagnitudeSpectrum(double[] data)	compute magnitude power spectra
static double[]	computeMagnitudeSpectrum(double[] data, boolean truncateDCNyq)	compute magnitude power spectra
static void	computeMagnitudeSpectrum(double[] data, int fromPos, int length, double[] ret, int toPos, boolean truncateDCNyq)	compute magnitude power spectra
static float[]	computeMagnitudeSpectrum(float[] data)	compute magnitude power spectra
static float[]	computeMagnitudeSpectrum(float[] data, boolean truncateDCNyq)	compute magnitude power spectra
static void	computeMagnitudeSpectrum(float[] data, int fromPos, int length, float[] ret, int toPos, boolean truncateDCNyq)	compute magnitude power spectra
static double[]	computeMagnitudeSpectrum_dB(double[] data, boolean truncateDCNyq)	compute magnitude power spectra in decibel
static void	computeMagnitudeSpectrum_dB(double[] data, int fromPos, int length, double[] ret, int toPos, boolean truncateDCNyq)	compute magnitude power spectra in decibel
static float[]	computeMagnitudeSpectrum_dB(float[] data, boolean truncateDCNyq)	compute magnitude power spectra in decibel
static void	computeMagnitudeSpectrum_dB(float[] data, int fromPos, int length, float[] ret, int toPos, boolean truncateDCNyq)	compute magnitude power spectra in decibel
static double[][]	computeMaxima(double[] data)	compute maxima
static double[][]	computeMinima(double[] data)	compute minima
static double[]	computePhaseSpectrum(double[] data)	compute phase spectra ([-PI,+PI])
static float[]	computePhaseSpectrum(float[] data)	compute phase spectra ([-PI,+PI])
static double[][]	filterPeaksHarmonics(double[][] peaks, double[] magnitude, double estimate, boolean useRealAmplitudes)
static double[][]	filterPeaksSignalToNoise(double[][] peaks, double snRatio, boolean dBScale)
static double	interpolateBaryCentre(double[] data, int index)	interpolation using a bary-centre approach
static double	interpolateGaussian(double[] data, int index)	interpolation using a Gaussian interpolation
static double	interpolateNAFF(double[] data, int index)	interpolation using a NAFF/SUSSIX based approach
static double	interpolateParabolic(double[] data, int index)	interpolation using a parabolic interpolation
static double[]	interpolateSpectrum(double[] data, int noversampling)
static void	main(java.lang.String[] args)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

SpectrumTools

public SpectrumTools()

Method Detail

computeFrequencyScale

public static double[] computeFrequencyScale(int nMag)

compute equidistant frequency axis based on the length of the magnitude spectrum

Parameters:

nMag - requested length of output vector

Returns:

computed [0.0, 0.5] frequency scale

computeFrequencyScaleFloat

public static float[] computeFrequencyScaleFloat(int nMag)

compute equidistant frequency axis based on the length of the magnitude spectrum

Parameters:

nMag - requested length of output vector

Returns:

computed [0.0, 0.5] frequency scale

computeMagnitudeSpectrum

public static double[] computeMagnitudeSpectrum(double[] data)

compute magnitude power spectra

Parameters:

data - the input data Since due to intrinsic uncertainties the DC and Nyquist frequency components are less representative for the given spectrum, their values are set to their adjacent frequency bins.

Returns:

computed magnitude spectrum

See Also:

for the expected spectra layout

computeMagnitudeSpectrum

public static double[] computeMagnitudeSpectrum(double[] data,
                                                boolean truncateDCNyq)

compute magnitude power spectra

Parameters:

data - the input data

truncateDCNyq - true: whether to smooth spectra and to ZOH the DC and Nyquist frequencies

Returns:

computed magnitude spectrum

See Also:

for the expected spectra layout

computeMagnitudeSpectrum

public static void computeMagnitudeSpectrum(double[] data,
                                            int fromPos,
                                            int length,
                                            double[] ret,
                                            int toPos,
                                            boolean truncateDCNyq)

compute magnitude power spectra

Parameters:

data - the input data

fromPos - start of the data to read

length - length to read of the input data

ret - the output data

toPos - the position to start writing the result to

truncateDCNyq - true: whether to smooth spectra and to ZOH the DC and Nyquist frequencies

See Also:

for the expected spectra layout

computeMagnitudeSpectrum

public static float[] computeMagnitudeSpectrum(float[] data)

compute magnitude power spectra

Parameters:

data - the input data Since due to intrinsic uncertainties the DC and Nyquist frequency components are less representative for the given spectrum, their values are set to their adjacent frequency bins.

Returns:

computed magnitude spectrum

See Also:

for the expected spectra layout

computeMagnitudeSpectrum

public static float[] computeMagnitudeSpectrum(float[] data,
                                               boolean truncateDCNyq)

compute magnitude power spectra

Parameters:

data - the input data

truncateDCNyq - true: whether to smooth spectra and to ZOH the DC and Nyquist frequencies

Returns:

computed magnitude spectrum

See Also:

for the expected spectra layout

computeMagnitudeSpectrum

public static void computeMagnitudeSpectrum(float[] data,
                                            int fromPos,
                                            int length,
                                            float[] ret,
                                            int toPos,
                                            boolean truncateDCNyq)

compute magnitude power spectra

Parameters:

data - the input data

fromPos - starting position of the data

length - length of the data

ret - the output data, should be an array of data.length/2

toPos - position to write to in the output array

truncateDCNyq - true: whether to smooth spectra and to ZOH the DC and Nyquist frequencies

See Also:

for the expected spectra layout

computeMagnitudeSpectrum_dB

public static double[] computeMagnitudeSpectrum_dB(double[] data,
                                                   boolean truncateDCNyq)

compute magnitude power spectra in decibel

Parameters:

data - the input data

truncateDCNyq - true: whether to smooth spectra and to ZOH the DC and Nyquist frequencies

Returns:

computed magnitude spectrum in [dB]

See Also:

for the expected spectra layout

computeMagnitudeSpectrum_dB

public static void computeMagnitudeSpectrum_dB(double[] data,
                                               int fromPos,
                                               int length,
                                               double[] ret,
                                               int toPos,
                                               boolean truncateDCNyq)

compute magnitude power spectra in decibel

Parameters:

data - the input data

fromPos - starting position of the data

length - length of the data

ret - the output data, should be an array of data.length/2

toPos - position to write to in the output array

truncateDCNyq - true: whether to smooth spectra and to ZOH the DC and Nyquist frequencies

See Also:

for the expected spectra layout

computeMagnitudeSpectrum_dB

public static float[] computeMagnitudeSpectrum_dB(float[] data,
                                                  boolean truncateDCNyq)

compute magnitude power spectra in decibel

Parameters:

data - the input data

truncateDCNyq - true: whether to smooth spectra and to ZOH the DC and Nyquist frequencies

Returns:

computed magnitude spectrum in [dB]

See Also:

for the expected spectra layout

computeMagnitudeSpectrum_dB

public static void computeMagnitudeSpectrum_dB(float[] data,
                                               int fromPos,
                                               int length,
                                               float[] ret,
                                               int toPos,
                                               boolean truncateDCNyq)

compute magnitude power spectra in decibel

Parameters:

data - the input data

fromPos - starting position of the data

length - length of the data

ret - the output data, should be an array of data.length/2

toPos - position to write to in the output array

truncateDCNyq - true: whether to smooth spectra and to ZOH the DC and Nyquist frequencies

See Also:

for the expected spectra layout

computeMaxima

public static double[][] computeMaxima(double[] data)

compute maxima

Parameters:

data - input data

Returns:

maxima locations

computeMinima

public static double[][] computeMinima(double[] data)

compute minima

Parameters:

data - input data

Returns:

computed minima

computePhaseSpectrum

public static double[] computePhaseSpectrum(double[] data)

compute phase spectra ([-PI,+PI])

Parameters:

data - the input data

Returns:

computed phase spectrum

See Also:

for the expected spectra layout

computePhaseSpectrum

public static float[] computePhaseSpectrum(float[] data)

compute phase spectra ([-PI,+PI])

Parameters:

data - the input data

Returns:

phase spectrum

See Also:

for the expected spectra layout

filterPeaksHarmonics

public static double[][] filterPeaksHarmonics(double[][] peaks,
                                              double[] magnitude,
                                              double estimate,
                                              boolean useRealAmplitudes)

filterPeaksSignalToNoise

public static double[][] filterPeaksSignalToNoise(double[][] peaks,
                                                  double snRatio,
                                                  boolean dBScale)

interpolateBaryCentre

public static double interpolateBaryCentre(double[] data,
                                           int index)

interpolation using a bary-centre approach

Parameters:

data - data array

index - 0< index < data.length, location of the to be interpolated peak

Returns:

interpolated bary centre

interpolateGaussian

public static double interpolateGaussian(double[] data,
                                         int index)

interpolation using a Gaussian interpolation

Parameters:

data - data array

index - 0< index < data.length, location of the to be interpolated peak

Returns:

interpolated gauss index

interpolateNAFF

public static double interpolateNAFF(double[] data,
                                     int index)

interpolation using a NAFF/SUSSIX based approach

Parameters:

data - data array

index - 0< index < data.length, location of the to be interpolated peak

Returns:

NAFF-interpolated peak position

interpolateParabolic

public static double interpolateParabolic(double[] data,
                                          int index)

interpolation using a parabolic interpolation

Parameters:

data - data array

index - 0< index < data.length, location of the to be interpolated peak

Returns:

parabolic-interpolated peak position

interpolateSpectrum

public static double[] interpolateSpectrum(double[] data,
                                           int noversampling)

main

public static void main(java.lang.String[] args)