MultitaperSpectrum (FPScript)

21.09.2021

Computes the Slepian or DPSS Multitaper Fourier spectrum.

Syntax

MultitaperSpectrum(Signal, [ SpectrumType = SPECTRUM_DBNORM ], [ Adjustment = 4.0 ], [ WindowCount = WIN_NORMALIZEAMPLITUDE ], [ FFTLength = 0 ] [ , Peaks ])

 

The syntax of the MultitaperSpectrum function consists of the following parts:

Part

Description

Signal

The data to be analyzed. The data must have a constant sampling rate and must not contain void values.

Permitted data structures are data series, data matrix, signal und signal series. All real data types are permitted, except calendar time und time span.

Void values are not permitted in this argument.

For the X component additional restrictions do apply.The values must have a constant positive spacing. Void values are not permitted in this argument.

If the argument is a list, then the function is executed for each element of the list and the result is also a list.

SpectrumType

The spectral format to be computed.

The argument SpectrumType can have the following values:

Constant

Meaning

SPECTRUM_AMPLITUDE

Amplitude

SPECTRUM_RMSAMPLITUDE

RMS Amplitude

SPECTRUM_AMPLITUDE2

Amplitude2

SPECTRUM_DB O

Amplitude in dB (decibels)

O This constant requires the option Order Tracking or the option Spectral Analysis to be licensed.

SPECTRUM_DBNORM O

dB (decibels) peak normalized to zero

O This constant requires the option Order Tracking or the option Spectral Analysis to be licensed.

SPECTRUM_PSD O

PSD (Power Spectral Density)

O This constant requires the option Order Tracking or the option Spectral Analysis to be licensed.

SPECTRUM_TISA O

TISA (Time Integral Amplitude2)

O This constant requires the option Order Tracking or the option Spectral Analysis to be licensed.

SPECTRUM_MSA

MSA (Mean Amplitude2)

SPECTRUM_SSA O

SSA (Sum Amplitude2)

O This constant requires the option Order Tracking or the option Spectral Analysis to be licensed.

SPECTRUM_VARIANCE O

Power variance normalized

O This constant requires the option Order Tracking or the option Spectral Analysis to be licensed.

SPECTRUM_MAGNITUDE2 O

Magnitude2

O This constant requires the option Order Tracking or the option Spectral Analysis to be licensed.

SPECTRUM_MAGNITUDE O

Magnitude

O This constant requires the option Order Tracking or the option Spectral Analysis to be licensed.

+ SPECTRUM_PEAKS O

If this constant is added to one of the spectrum types above, then only peaks in the spectrum are output.

O This constant requires the option Spectral Analysis to be licensed.

+ SPECTRUM_SIGNIFICANCE50 O

If one of these constants is added to one of the spectrum types above, then the critical limit for the significance level 50 % is output as a curve across the frequency.

O This constant requires the option Spectral Analysis to be licensed.

+ SPECTRUM_SIGNIFICANCE90 O

If one of these constants is added to one of the spectrum types above, then the critical limit for the significance level 90 % is output as a curve across the frequency.

O This constant requires the option Spectral Analysis to be licensed.

+ SPECTRUM_SIGNIFICANCE95 O

If one of these constants is added to one of the spectrum types above, then the critical limit for the significance level 95 % is output as a curve across the frequency.

O This constant requires the option Spectral Analysis to be licensed.

+ SPECTRUM_SIGNIFICANCE99 O

If one of these constants is added to one of the spectrum types above, then the critical limit for the significance level 99 % is output as a curve across the frequency.

O This constant requires the option Spectral Analysis to be licensed.

+ SPECTRUM_SIGNIFICANCE99_9 O

If one of these constants is added to one of the spectrum types above, then the critical limit for the significance level 99.9 % is output as a curve across the frequency.

O This constant requires the option Spectral Analysis to be licensed.

SPECTRUM_HARMONICS O

Outputs the spectral information about the peaks in the spectrum as a data matrix. These are for the Fourier spectrum: Frequency, Amplitude, Phase, PSD, % Power and Relative Power %. % Power is normalized to the sum of 100 and Relative Power % is normalized to a maximum of 100 %. For the Uneven Data Fourier Spectrum: Frequency, Amplitude, PSD, % Power and Relative Power %. For the periodogram: Frequency, Amplitude, Amplitude SD, PSD, % Power and Relative Power %. For the Multitaper Spectrum: Frequency, Amplitude, Phase, PSD, % Power, Relative Power % and F value. If the argumentPeaks is not specified, then a peak count of 10 is taken as a default. This type is permitted for one-dimensional data sets only.

O This constant requires the option Spectral Analysis to be licensed.

Permitted data structures are scalar value. All integral data types are permitted.

If the argument is a list, then the first element in the list is taken. If this is also a list, then the process is repeated.

If this argument is omitted, it will be set to the default value SPECTRUM_DBNORM.

Adjustment

The one-sided Fourier width as a multiple of the frequency interval.

Permitted data structures are scalar value. All real data types are permitted.

The value must be greater or equal to 2.0 and less or equal to 5.0.

If the argument is a list, then the first element in the list is taken. If this is also a list, then the process is repeated.

If this argument is omitted, it will be set to the default value 4.0.

WindowCount

The number of windows to be applied and averaged in the DPSS sequence. The valid range is between 1 and 2 * Adjustment -1. As an option, a constant can be added to select amplitude or power normalization. The default value 0 + WIN_NORMALIZEAMPLITUDE chooses the maximum number of windows and amplitude normalization.

The argument WindowCount can have the following values:

Constant

Meaning

+ WIN_NORMALIZEAMPLITUDE

If this constant is added to one of the window constants above, an amplitude normalization is performed after applying the window. In this case the gain of the used window function is used for normalization which is the sum of all values of the window divided by their number. This compensates the damping of the amplitudes caused by the window. Therefore it is especially useful for measuring peaks within the spectrum.

+ WIN_NORMALIZEPOWER O

Adding this constant does not affect in this case because the spectrum is always power normalized as long as amplitude normalization is not selected.

O This constant requires the option Order Tracking or the option Spectral Analysis to be licensed.

Permitted data structures are scalar value. All integral data types are permitted.

If the argument is a list, then the first element in the list is taken. If this is also a list, then the process is repeated.

If this argument is omitted, it will be set to the default value WIN_NORMALIZEAMPLITUDE.

FFTLength

The length of the Fourier transform. Zero padding applies if the FFT length is greater than the data length. The valid range is from the data length to the maximum limit of FFT. The default value is -1, which sets the FFT length equal to the next highest power of two. The default value is 0, which sets FFT length equal to the data length.

Permitted data structures are scalar value. All integral data types are permitted.

The value must be greater or equal to -1 and less or equal to 2147483648.

If the argument is a list, then the first element in the list is taken. If this is also a list, then the process is repeated.

If this argument is omitted, it will be set to the default value 0.

Peaks

If specified, only bin-interpolated peaks in the spectrum are output. The peaks can be specified as a number of peaks, a positive number from 1 to 100, or as an F value, a negative number from -1000 to -0.5. This argument is permitted for one-dimensional data sets only.

Permitted data structures are scalar value. All real data types are permitted.

If the argument is a list, then the first element in the list is taken. If this is also a list, then the process is repeated.

Remarks

The data structure of the result is a signal or signal series. If the argument Signal is a data series or data matrix, then the X component of the result contains Nyquist-normalized frequencies.

Available in

Option Spectral Analysis

Examples

MultitaperSpectrum(Signal, SPECTRUM_DBNORM, 3, 0 + WIN_NORMALIZEPOWER, 4096)

Calculates the multitaper Fourier spectrum for the signal 'Signal'. This method is used when a spectral estimation with low variance is required, such as for measuring power. dB is normalized as the spectrum type and 3 is selected as the window adjustment. The number of DPSS windows is set to the maximum value. The FFT length is 4096. This is an example from the Fourier Spectral Analysis Tutorial.

See Also

FourierSpectrum Function

Periodogram Function

Spectral Analysis Option

Fourier Spectral Analysis Object

Data Tapering Window

Fourier Spectral Analysis

Fourier Spectral Analysis Tutorial

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