LTPDA Toolbox | contents | ![]() ![]() |
Multivariate power spectral density is performed by the Welch's averaged, modified periodogram method.
ao/cpsd estimates the cross-spectral density of time-series
signals, included in the input aos. Data are windowed prior to the estimation of the spectra, by multiplying
it with a spectral window object, and can be detrended by polinomial of time in order to reduce the impact
of the border discontinuities. The window length is adjustable to shorter lenghts to reduce the spectral
density uncertainties, and the percentage of subsequent window overlap can be adjusted as well.
Syntaxis
b = cpsd(a1,a2,pl)
a1 and a2 are the 2 aos containing the input time series to be evaluated; b is the output object. The parameter list pl includes the following parameters:
The length of the window is set by the value of the parameter 'Nfft', so that the window is actually rebuilt using only the key features of the window, i.e. the name and, for Keiser windows, the PSLL.
As an alternative, the user can input, as a value for the 'Win' key, a string corresponding to the name of the window. In the case of Kaiser window, it's necessary to specify the additional parameter 'psll'.
As an alternative to setting the number of points 'Nfft' in each window, it's possible to ask for a given number of CPSD estimates by setting the 'Navs' parameter, and the algorithm takes care of calculating the correct window length, according to the amount of overlap between subsequent segments.
If the user doesn't specify the value of a given parameter, the default value is used. |
The function makes CPSD estimates between the 2 input aos. The input argument list must contain 2 analysis objects, and the output will contain the CPSD estimate. If passing two identical objects ai, the output will be equivalent to the output of psd(ai).
Example
Evaluation of the CPSD of two time-series represented by: a low frequency sinewave signal superimposed to white noise, and a low frequency sinewave signal at the same frequency, phase shifted and with different amplitude, superimposed to white noise.
nsecs = 1000; x = ao(plist('waveform','sine wave','f',0.1,'A',1,'nsecs',nsecs,'fs',10)) + ... ao(plist('waveform','noise','type','normal','nsecs',nsecs,'fs',10)); x.setYunits('m'); y = ao(plist('waveform','sine wave','f',0.1,'A',2,'nsecs',nsecs,'fs',10,'phi',90)) + ... 4*ao(plist('waveform','noise','type','normal','nsecs',nsecs,'fs',10)); y.setYunits('V'); z = cpsd(x,y,plist('nfft',1000)); iplot(z);
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Power spectral density estimates | Cross coherence estimates | ![]() |
©LTP Team