Orthogonal Cross Correlation

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roxy1001

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I want to use cross correlation technique to obtain relative phase difference between Current & Voltage waveform of the same frequency.
I was reading following technique where U1(k) which is the discrete voltage across the piezo-transducer and I(k) is the discrete current. U2(k) is obtained by shifting U1(k) to the right by No samples to obtain a delay equivalent to a quadrature phase shift

where M is the sampling rate



This algorithm uses orthogonal signal U1 and U2 ..whats the significance of using U2 when we can obtain phase difference directly by using cross-correlation function of U1(k) & I(k) only ?
 

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