Figure P4.23-1 shows a continuous-time filter that is implemented using anLTI discrete-t...

Figure P4.23-1 shows a continuous-time filter that is implemented using anLTI discrete-time filter ideal lowpass filter with frequency response over −π ≤ ω ≤ π as

(a) If the continuous-time Fourier transform of x_c(t), namely , is as shown in Figure P4.23-2 and ωc = , sketch and label X(e^jω), Y(e^jω) and for each of the following cases:

(b) For 1/T₁ = 1/T₂ = 6 × 10³, and for input signals x_c(t) whose spectra are bandlimited to (but otherwise unconstrained), what is the maximum choice of the cutoff frequency ω_c of the filter H(ejω) for which the overall system is LTI? For this maximum choice of ω_c, specify