\text { Consider the passband signal } u_{p}(t)=\operatorname{sinc}(20 t)^{2} \cos (2000 \pi t)+\operatorname{sinc}(20 t) \sin (2000 \pi t) \text {. } (a) Find uc and us, the I and Q

components of the signal, using the reference frequency fe = 1000. (b) Find Uc and Us, the spectra of the I and Q components. (c) Find u(t), the complex envelope, and e(t), the envelope. (d) Find the bandwidth of u, and the bandwidth of u. (For the definition of bandwidth of a passband signal, use the convention of equation (2.67) and the lecture notes, not of Figure 2.25.) (e) Draw a circuit using multipliers and low pass filters that extracts uc and us from the passband signal up- (f) Assume that each of the filters in the previous part have ideal low pass frequency responses.Specify the interval of possible choices for the upper end of the frequency band passed by each filter.