A general bandpass signal can be expressed as x bp [n] = x c [n] cos(Ω c n) + x s [n] sin(Ω c n) = x[n] cos(Ω c n + θ[n]), (time-varying) phase of the bandpass signal. Generally, both xc[n] and xs[n]...

x_bp[n] = x_c[n] cos(Ω_cn) + x_s[n] sin(Ω_cn) = x[n] cos(Ω_cn + θ[n]),

(time-varying) phase of the bandpass signal. Generally, both xc[n] and xs[n] are lowpass signals with bandwidth well below Ωc. Hence, both x[n] and θ[n] are also lowpass signals. Show that when this signal is passed through a GLP system whose frequency response is shown in Fig. 6.13, the output is also a bandpass signal given by