I have a small misunderstanding of cross power spectral density between two complex signals. I know that it is the Fourier transform of cross correlation between two signals. Let's say the complex signals are of the form (a+ib) and (c+id). Then the cross-correlation should result in something like
The real part result => ac - bd i.e. real1*rea12 - imag1*imag2;
complex part result => ad + bc i.e. real1*imag2 + real2 * imag1;
where real1, real2 represents the real part of both the signals and imag1, imag2 represents the imaginary part of both the signals.
But my professor said that the cross-correlation should result in
The real part result => ac + bd i.e. real1*rea12 + imag1*imag2;
complex part result => ad - bc i.e. real1*imag2 - real2 * imag1;
Where I am going wrong? Is my understanding of the equation form of cross-correlation correct? And also, I just want to know how to calculate cross PSD from this result. Can I just compute it like
Cross PSD result = |real_part result + imaginary_part result|.^2 ?
or Cross PSD result = |real_part result|.^2 + |imaginary_part result|.^2 ?