pmtm (Multitaper) calculates PSD from Fourier coefficients as abs(Xx)^2; shouldn't that be Xx.conj(Xx)?

Nalani asked: 2021-03-04 matlab , signal , signal processing ,

Understand PMTM multitaper PSD calculation in MATLAB! Is abs(xx)^2 correct for power spectral density from Fourier coefficients? Explore the xx * conj(xx) a

Expert Answer

Kshitij Singh answered . 2025-07-30 12:40:21

There is no difference between

abs(Z).^2

And

Z.*conj(Z)

for a complex vector. They are equivalent. In fact, for a complex number the modulus (norm) is defined to be the square root of the product of Z and its conjugate.

Just convince yourself for a single complex number

Z = 1+1i;
abs(Z)^2  
Z*conj(Z)

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