Any signal and its Hilbert transform have same energy density spectrum.(a) True(b) FalseThis question was addressed to me in an interview.My doubt is from Modulation Using Non-Linear Devices (Balanced Modulator) in division Amplitude Modulation of Analog Communications

Any signal and its Hilbert transform have same energy density spectrum

1.	Any signal and its Hilbert transform have same energy density spectrum.(a) True(b) FalseThis question was addressed to me in an interview.My doubt is from Modulation Using Non-Linear Devices (Balanced Modulator) in division Amplitude Modulation of Analog Communications
Answer» The correct answer is (a) True The best I can explain: HILBERT transform of a signal results in a signal with same amplitude but a phase SHIFT of -90 degrees. Thus, a signal and it’s Hilbert transform have same amplitude SPECTRUM i.e. they have same energy density spectrum and also correlation spectrum.

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