Cross-spectral Analysis

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Cross-spectral Analysis. Investigates the dependence or relationship between two time series. Begin by reviewing cross-correlation function – how similar two time series x , y are. L = lag N = # of elements in time series. Covariance or cross-covariance. Cross-correlation. - PowerPoint PPT Presentation

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Cross-spectral AnalysisInvestigates the dependence or relationship between two time series.

Begin by reviewing cross-correlation function how similar two time series x , y areL = lagN = # of elements in time seriesCovariance or cross-covariance

Cross-correlation-1 < xy < 1

Ensenada de la Paz

Year DayCurrent velocity in Ensenada de La Paz

Current velocity and water level (red) in Ensenada de La PazYear Day

Current velocity and water level (red) in Ensenada de La PazYear Day

Cross-correlation between current velocity and water level in Ensenada de La Paz

Cross-correlation between current velocity and water level in Ensenada de La Paz

A generalization of:

* is the complex conjugateComplex Cross-correlation

L w1w2Complex Cross-correlation between vectors at 2 depths in Ensenada de La Paz

Complex Cross-correlation between vectors at 2 depths in Ensenada de La Paz

Complex Cross-correlation between vectors at 2 depths in Ensenada de La PazCoherence spectrum (coherency)

= 0.1, 0.05, 0.01X is the Fourier Transform< > = running mean12

Current velocity and water level (red) in Ensenada de La PazYear Day

cpd

= 0.1, 0.05, 0.01Coherence squaredwindow size= 2

= 0.1, 0.05, 0.01

JAMES RIVER DATA

Coherence 2Phase (deg)95%99%Window size= 10

Coherence 2Phase (deg)95%99%Window size= 24

Coherence 2Phase (deg)95%99%Window size= 10

Coherence 2Phase (deg)95%99%Window size= 10

Coherence 2Phase (deg)95%99%Window size= 24

Coherence 2Phase (deg)95%99%Window size= 24