spectralKurtosis
Spectral kurtosis for signals and spectrograms.
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Syntax
Function call
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kurtosis,spread,centroid = spectralKurtosis(x,f,Name,Value)— sets additional parameters using one or more name-value arguments. For example, you can specify the window used for time domain input data, the amount of overlap between adjacent windows, and the type of spectrum used for frequency domain input data.
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spectralKurtosis(___;out=:plot)— plots the spectral kurtosis.-
If the input signal is in the time domain, the spectral kurtosis graph is plotted as a function of time.
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If the input signal is in the frequency domain, the spectral kurtosis graph is plotted depending on the frame number.
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Arguments
Input arguments
# f is the sampling frequency or frequency vector
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scalar | vector
Details
The sampling frequency or frequency vector in Hz, specified as a numeric scalar or vector. Interpretation x the function depends on the form f:
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If
f— numeric scalar, functionspectralKurtosisinterpretsxas a signal in the time domain, andf— as a sampling rate. In this casexmust be a real vector or a matrix. Ifx— the matrix,spectralKurtosisinterprets columns as separate channels. -
If
f— vector, functionspectralKurtosisinterpretsxas a signal in the frequency domain, andf— as a frequency vector in Hz corresponding to the linesx. In this casexmust be a real array of size , where — the number of spectral values at the specified frequenciesf, — the number of individual spectra, and — the number of channels.Number of rows in
xmust be equal to the number of elementsf.
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Name-value input arguments
Specify optional argument pairs as Name,Value, where Name — the name of the argument, and Value — the appropriate value. Name-value arguments should be placed after other arguments, but the order of the pairs does not matter.
Use commas to separate the name and value, and Name put it in quotation marks.
The following name-value arguments apply if x — a signal in the time domain.
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# Window — the window used in the time domain
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rectwin(round(f*0.03)) (by default) | vector
Details
The window used in the time domain, defined as a real vector. The number of vector elements must be in the range [1,size(x,1)]. The number of vector elements must also be greater. OverlapLength. If the argument is Window not specified, function spectralKurtosis uses the length of the window, which splits x into eight overlapping segments.
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# OverlapLength — the number of samples overlapping between adjacent windows
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round(f*0.02) (by default) | a non-negative integer scalar
Details
The number of samples overlapping between adjacent windows, set as an integer in the range [0,size(Window,1)). If the argument is OverlapLength not specified, function spectralKurtosis uses a value that provides 50% overlap between segments.
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# FFTLength — the number of elements in the DFT
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numel(Window) (default) | a positive integer scalar
Details
The number of elements used to calculate the DFT of window input samples, set as a positive integer scalar. If no argument is given, FFTLength by default, it is equal to the number of elements in Window.
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# SpectrumType — spectrum type
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"power" (default) | "magnitude"
Details
The type of spectrum specified as "power" or "magnitude":
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"power"— the spectral kurtosis is calculated for a one-sided power spectrum; -
"magnitude"— the spectral kurtosis is calculated for a one-sided amplitude spectrum.
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# out — type of output data
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:data (by default) | :plot
Details
Type of output data:
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:data— the function returns data; -
:plot— the function returns a graph.
Additional Info
Spectral kurtosis
Details
Spectral excess_ (SE) is a statistical tool that makes it possible to identify and accurately determine non—stationary or non-Gaussian behavior in the frequency domain, taking into account:
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small values at frequencies where only stationary Gaussian noise is present;
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high positive values at frequencies where transients occur.
This capability makes the SE a powerful tool for detecting and extracting signals related to malfunctions in rotating mechanical systems. By itself, the SE can identify features or conditional indicators for fault detection and classification. As preprocessing for other tools such as envelope analysis, the SE can provide key inputs such as the optimal band [1], [2].
Spectral kurtosis The signal it can be calculated based on the short-term Fourier transform (FFT) of the signal, :
where — the window function used in the CFTF.
Literature
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Antoni, J. «The Spectral Kurtosis: A Useful Tool for Characterising Non-Stationary Signals.» Mechanical Systems and Signal Processing. Vol. 20, Issue 2, 2006, pp. 282–307.
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Antoni, J., and R. B. Randall. «The Spectral Kurtosis: Application to the Vibratory Surveillance and Diagnostics of Rotating Machines.» Mechanical Systems and Signal Processing. Vol. 20, Issue 2, 2006, pp. 308–331.
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Peeters, G. «A Large Set of Audio Features for Sound Description (Similarity and ClassiDcation) in the CUIDADO Project.» Technical Report; IRCAM: Paris, France, 2004.