Consider the multirate system shown in Figure P4.49-1 with input x[n] and output y[n]:...

Consider the multirate system shown in Figure P4.49-1 with input x[n] and output y[n]:

where Q₀(e^jω) and Q₁(e^jω) are the frequency responses of two LTI systems. H₀(e^jω) and H₁(e^jω) are ideal lowpass and highpass filters, respectively, with cutoff frequency at π/2 as shown in Figure P4.49-2:

The overall system is LTI if Q₀(e^jω) and Q₁(e^jω) are as shown in Figure P4.49-3:

For these choices of Q₀(e^jω) and Q₁(e^jω), sketch the frequency response

of the overall system.