In Section 4.8.1, we considered the use of prefiltering to avoid aliasing. In practice,...

In Section 4.8.1, we considered the use of prefiltering to avoid aliasing. In practice, the antialiasing filter cannot be ideal. However, the nonideal characteristics can be at least partially compensated for with a discrete-time system applied to the sequence x[n] that is the output of the C/D converter.

Consider the two systems in Figure P4.62-1. The antialiasing filters H_ideal(jΩ) and H_aa(jΩ) are shown in Figure P4.62-2. H(e^jω) in Figure P4.62-1 is to be specified to compensate for the nonideal characteristics of H_aa(jΩ).

Sketch H(e^jω) so that the two sequences x[n] and w[n] are identical.