2.2.6.4 Bivariate Spectral Density with Lag Window


Tutorial

  1. Open the sample project file in Origin, go to Folder Spectral Analysis using the Project Explorer. Activate the workbook Bivariate spectral data.
    Bi dan pe data.png
  2. Highlight column A and B in worksheet. Click the Time Series Analysis App icon Time Series Analysis icon.png in the Apps Gallery window.
  3. Choose Spectral Analysis tab. Click Bivariate Spectral Density with Lag Window icon to open the dialog.
    Bi lag toolbar.png
  4. In the Setting branch, choose No correction. Enter 0.2 in Tapering Proportion. Choose Tukey window type. Enter 50 and 0 in Cut-off of Lag Window and Aligment Shift between Two Time Series.
    Bi lag dialog.png
  5. Click Preview button to display smoothed spectrum.
  6. Click OK button to output the report.
    Bi lag report.png

Algorithm

The smoothed sample cross spectrum is a complex valued function of frequency \omega, f_{xy}(\omega)=cf(\omega)+iqf(\omega), defined by its real part or co-spectrum

cf(\omega)=\frac{1}{2\pi}\sum_{k=-M+1}^{M-1}\omega_kC_{xy}(k+S)cos(\omega k)

and imaginary part or quadrature spectrum:

qf(\omega)=\frac{1}{2\pi}\sum_{k=-M+1}^{M-1}\omega_kC_{xy}(k+S)sin(\omega k)

where \omega_k =\omega_{-k}, for k=0,1,...,M-1, is the smoothing lag window as described in Univariate Spectral Density with Lag Window.

The results are calculated for frequency values

\omega_j = \frac{2\pi j}{L},j=0,1...,[L/2]

where [ ] denotes the integer part.

Reference

  1. nag_tsa_spectrum_bivar_cov (g13ccc)
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