tojur
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Dear all:
I have to calculate the magnitude-squared coherence (MSC) between two signal. However, using a routine that uses only one taper (or no tapers at all) my result is always 1, despite the signals are clearly different. This doesn't happen if I use more than one taper. Searching a explication for this abnormal result, I come with a confusing characteristic of the MSC itself. The definition that I'm using is this
\[\gamma^2(\omega)=\frac{ |X(\omega)Y*(\omega)| ^2}{X(\omega)X*(\omega).Y(\omega)Y*(\omega) }\]
X and Y are the Fourier tranformed signals that depends on the frequency \[\omega\]. However, if you take any two complex numbers as the value of these functions in some fixed frequency, the result is always 1. Knowing that \[|z|^2=zz* \] then
\[\gamma^2=\frac{(XY*)(XY*)* }{XX*YY*}=\frac{(XY*)(X*Y) }{XX*YY*}=\frac{XX*YY* }{XX*YY*}=1\]
Certainly there must be something I must be misunderstanding but I can't see what it is. Can anyone explain to me what is the catch?
I have to calculate the magnitude-squared coherence (MSC) between two signal. However, using a routine that uses only one taper (or no tapers at all) my result is always 1, despite the signals are clearly different. This doesn't happen if I use more than one taper. Searching a explication for this abnormal result, I come with a confusing characteristic of the MSC itself. The definition that I'm using is this
\[\gamma^2(\omega)=\frac{ |X(\omega)Y*(\omega)| ^2}{X(\omega)X*(\omega).Y(\omega)Y*(\omega) }\]
X and Y are the Fourier tranformed signals that depends on the frequency \[\omega\]. However, if you take any two complex numbers as the value of these functions in some fixed frequency, the result is always 1. Knowing that \[|z|^2=zz* \] then
\[\gamma^2=\frac{(XY*)(XY*)* }{XX*YY*}=\frac{(XY*)(X*Y) }{XX*YY*}=\frac{XX*YY* }{XX*YY*}=1\]
Certainly there must be something I must be misunderstanding but I can't see what it is. Can anyone explain to me what is the catch?
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