Multivariate power spectral density on a logarithmic scale can be performed by the LPSD algorithm, which is an application of Welch's averaged, modified periodogram method, spectral density estimates are not evaluated at freqencies which are linear multiples of the minimum frequency resolution 1/T where T is the window lenght, but on a logarithmic scale. The algorithm takes care of calculating the frequencies at which to evaluate the spectral estimate, aiming at minimizing the uncertainty in the estimate itself, and to recalculate a suitable window length for each frequency bin.
ao/lcohere estimates the coherence 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. Detrending is performed on each individual window.
Syntaxis
b = lcohere(a1,a2,a3,...,pl)
a1, a2, a3, ... are aos containing the input time series to be evaluated. They need to be in a number N >= 2. b includes the NXN output objects. The parameter list pl includes the following parameters:
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'.
If the user doesn't specify the value of a given parameter, the default value is used. |
The function makes coherence estimates between all input aos. Therefore, if the input argument list contains N analysis objects, the output a will contain NxN coherence estimates. The diagonal elements will be 1.
Example
Evaluation of the coherence 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; fs = 10; x = ao(plist('waveform','sine wave','f',0.1,'A',1,'nsecs',nsecs,'fs',fs)) + ... ao(plist('waveform','noise','type','normal','nsecs',nsecs,'fs',fs)); x.setYunits('m'); y = ao(plist('waveform','sine wave','f',0.1,'A',2,'nsecs',nsecs,'fs',fs,'phi',90)) + ... 4*ao(plist('waveform','noise','type','normal','nsecs',nsecs,'fs',fs)); y.setYunits('V'); z = lcohere(x,y,plist('win',specwin('Kaiser',1,200),'nfft',1000)); iplot(z(1,1)); iplot(z(1,2));