(b)To let r(t)=u(t), we must retain the frequency content between twm of Y (jw) and scale it properly. Therefore, Hw) is a low-pass filter with cutoff frequency at wm and gain =, as sketched belo HGO)(b) To let x(t) = v(t), we must retain the frequency content between ±wm of Y (jω) and scale it properly. Therefore, H(jω) is a low-pass filter with cutoff frequency at ωm and gain π 2 , as sketched below: H(jω) π 2 ω −ω m ω m 3