In many audio applications, it is necessary to sample a continuous-time signal xc(t) at...

In many audio applications, it is necessary to sample a continuous-time signal x_c(t) at a sampling rate 1/T = 44 kHz. Figure P4.66-1 shows a straightforward system, including a continuous-time antialias filter H_a0(j Ω), to acquire the desired samples. In many applications, the “4x oversampling” system shown in Figure P4.66-2 is used instead of the conventional system shown in Figure P4.66-1. In the system in Figure P4.66-2,

Assuming that H(e^jω) is ideal, find the minimal set of specifications on the antialias filter H_a1(j Ω), i.e., the smallest Ω_p and the largest Ω_s , such that the overall system of Figure P4.66-2 is equivalent to the system in Figure P4.66-1.