In this computer-oriented problem, consisting of two parts, we demonstrate the effect of nonlinearity on eye patterns.

a. Consider a 4-ary PAM system, operating under idealized conditions: no channel noise and no ISI. the specifications are as follows: Nyquist bandwidth, W = 0.5 Hz Roll-off factor, = 0.5 Symbol duration, T = 2Tb for M = 4 and Tb is the bit duration. Compute the eye pattern for this noiseless PAM system.

b. Repeat the computation, this time assuming that the channel is nonlinear with the following input-output relationship:

where s(t) is the channel input and x(t) is the channel output (i.e., received signal); the a is a constant. Compute the eye pattern for the following three nonlinear conditions:
a = 0.05 0.1 0.2

Hence, discuss how varying the constant a affects the shape of the eye pattern for the 4-ary PAM system.