Consider a harmonic pulse of T samples: with fixed amplitude A and frequency f, and random phase 𝜙, uniformly distributed on the interval from 0 to 2𝜋. a) Show that the variance of X( f ) is b)...

Consider a harmonic pulse of T samples:

with fixed amplitude A and frequency f, and random phase 𝜙, uniformly distributed on the interval from 0 to 2𝜋.

a) Show that the variance of X( f ) is

b) Assume that x(t) is corrupted with additive white Gaussian noise v(t) ∼ N ( 0, 𝜎²
_v
) , that is uncorrelated with x(t). Using Parseval’s identity, show that the broadband input SNR is