Cross coherence estimates


The LTPDA method ao/cohere estimates the cross-coherence of time-series signals, included in the input aos following the Welch's averaged, modified periodogram method [1]. Data are windowed prior to the estimation of the spectra, by multiplying it with a spectral window object, and can be detrended by a 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.


b = cohere(a1,a2,pl)

a1 and a2 are the 2 aos containing the input time series to be evaluated, b is the output object and pl is an optional parameters list.


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 Kaiser windows, the PSLL.

As an alternative to setting the number of points 'Nfft' in each window, it's possible to ask for a given number of coherence 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 cross-coherence estimates between the 2 input aos. If passing two identical objects or linearly combined signals, the output will be 1 at all frequencies. The same will happen if analyzing only a single window.


The algorithm is based in standard MATLAB's tools, as the ones used by pwelch. The standard deviation of the mean is computed as [2]

is the coherence function.


Evaluation of the cross-coherence of two time-series represented by: a low frequency sinewave signal superimposed to white noise and a linear drift, and a low frequency sinewave signal at the same frequency, phase shifted and with different amplitude, superimposed to white noise.

% parameters nsecs = 5000; fs = 10; nfft = 1000; % build first signal components x1 = ao(plist('waveform','sine wave','f',0.1,'A',1,'nsecs',nsecs,'fs',fs,'yunits','m')) x2 = ao(plist('waveform','noise','type','normal','nsecs',nsecs,'fs',fs,'yunits','m')) x3 = ao(plist('tsfcn', 't','nsecs',nsecs,'fs',fs,'yunits','m')); % add components x = x1 + x2 + x3; % build second signal components y1 = ao(plist('waveform','sine wave','f',0.1,'A',2,'nsecs',nsecs,'fs',fs,'phi',90)); y2 = 4*ao(plist('waveform','noise','type','normal','nsecs',nsecs,'fs',fs)); % add components and set units y = y1 + y2; y.setYunits('V'); % compute coherence pl = plist('win','BH92','nfft',nfft, 'order',1); Cxy = cohere(x,y,pl); %plot iplot(Cxy);


  1. P.D. Welch, The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method Based on Time Averaging Over Short, Modified Periodograms, IEEE Trans. on Audio and Electroacoustics, Vol. 15, No. 2 (1967), pp. 70 - 73.
  2. G.C. Carter, C.H. Knapp, A.H. Nuttall, Estimation of the Magnitude-Squared Coherence Function Via Overlapped Fast Fourier Transform Processing , IEEE Trans. on Audio and Electroacoustics, Vol. 21, No. 4 (1973), pp. 337 - 344.

©LTP Team