\text { Consider the continuous-time signal } x_{c}(t)=4 \cos (2 \pi 1000 t)+6 \cos (2 \pi 9000 t) \text {. } a) Assume that this signal is ideally sampled with

a sampling frequency F, and then ideally reconstructed by passing the sampled signal through an ideal low pass filter with cutoff frequency F. = F:/2 and gain G = T. Sketch both the sampled and reconstructed signals in the frequency domain and obtain a time-domain expression for the reconstructed signal. i) Fs = 10,000HZ ii) F, = 1000H z b) Repeat (a) if the cosines are replaced by sines in the equation for xe(t), i.e.,= 4sin(2 pi 1000t) + 6sin(2pi9000t).