SpectrumTools (math 8.1.4 API)

java.lang.Object
- de.gsi.math.spectra.SpectrumTools

```
public class SpectrumTools
extends 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 and Description

SpectrumTools()

Constructors
Constructor and Description
`SpectrumTools()`

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and 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_dB(double[] data, boolean truncateDCNyq)` compute magnitude power spectra in decibel
`static float[]`	`computeMagnitudeSpectrum_dB(float[] data, boolean truncateDCNyq)` compute magnitude power spectra in decibel
`static double[]`	`computeMagnitudeSpectrum(double[] data)` compute magnitude power spectra
`static double[]`	`computeMagnitudeSpectrum(double[] data, 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 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(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 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_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 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
  - 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(String[] args)
```

Class SpectrumTools

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

SpectrumTools

Method Detail

computeFrequencyScale

computeFrequencyScaleFloat

computeMagnitudeSpectrum

computeMagnitudeSpectrum

computeMagnitudeSpectrum

computeMagnitudeSpectrum

computeMagnitudeSpectrum_dB

computeMagnitudeSpectrum_dB

computeMaxima

computeMinima

computePhaseSpectrum

computePhaseSpectrum

filterPeaksHarmonics

filterPeaksSignalToNoise

interpolateBaryCentre

interpolateGaussian

interpolateNAFF

interpolateParabolic

interpolateSpectrum

main