Question

Any signal and its Hilbert transform are mutually orthogonal.

(a) True

(b) False

The question was posed to me by my college professor while I was bunking the class.

My doubt stems from Spectrum of Multitone Signal topic in division Amplitude Modulation of Analog Communications

Answer 1

Right choice is (a) True

To elaborate: Hilbert Transform of any signal produces a signal which has same amplitude as that of the original signal but suffers a phase-shift of -90 degree. Consider f(t) be any signal and fh(t) is it’s Hilbert transform.

If we integrate both of them under proper boundary conditions, we get 0 which shows that both are mutually perpendicular i.e.