Let h[n] designate the impulse response of the quadrature system shown in Fig. P XXXXXXXXXXThe impulse response of the LTID subsystem H 0 (Ω) is h 0 [n]. (a) Show that the system h[n] is an LTID...

Let h[n] designate the impulse response of the quadrature system shown in Fig. P6.3-18. The impulse response of the LTID subsystem H₀(Ω) is h₀[n].

(a) Show that the system h[n] is an LTID system, and express h[n] in terms of the impulse response h₀[n].

(b) If H0(Ω) is an ideal lowpass filter of bandwidth B and is given by Π(Ω/2B), where Ωc + B ≤ π, then show that the quadrature system H(Ω) represents a bandpass filter of bandwidth 2B centered at Ω_c.