2.1 A power-type signal x(t) is passed through a filter with impulse response h(t). Assume the Fourier transform of h(t)is H (ƒ). Define the time-average autocorrelation function of x(t) as R¸

(7) = lim ſ™½¸ x(t)x* (t−7) dt . The power spectral density of the signal x(t) is defined as T→∞0-T/2 the Fourier transform of the time-average autocorrelation functionS (ƒ) = F[R₂ (7)] x(t). LTI -y(t) h(t) Prove that the power spectrum density of the output y(t)is S₁ (ƒ)=S₂(ƒ)|H (ƒ)³².