Spatial Information Obtained with Sensing Arrays

2 Spatial Information Obtained with Sensing Arrays 

The practical relevance of this example becomes apparent when we realize that a physical object, for example, a cylinder with diameter d, is placed in a flowing stream of linear velocity V. It generates a Kalman vortice street of eddy currents. The shedding frequency / of the eddies is given by the empirical formula 

This tells us how much energy in the original signal remains after some arbitrary delay time t. Next we compute the cross-correlation function Rxy(t), which contains information about energy shared between channel X and channel Y. 

Fourier transformation of (10.13) and (10.14) to the frequency domain yields energy spectral densities, specifically 

We are interested in the energy that is common to the two signals and define coherence y2 as the ratio of cross-energy spectral density SXx(a ) to the product of autospectral energy densities. 

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