Question

# 3) Let x(t) be the continuous-time signal

x(t) = t2(0.94)t [u(t) − u(t − 100)]

where u(t) is the

unit step function. We sample x(t) with a sampling period of T = 0.4 over −∞ < t < ∞ to obtain x[n]. Assume that the sample for n = 0 is taken at t = 0. We then use sinc interpolation to generate xr(t) from x[n].

a) Plot x(t) using MATLAB over the smallest range that includes all nonzero values of x(t). b) Find x[n].

c) Find xr(t).

d) Plot x(t) − xr(t) using MATLAB over the same range that you used for part a.

e) What is the maximum value of |x(t) − xr(t)| over −∞ < t < ∞? f) Find the value of x(t) for t = 40

g) Find the value of xr(t) for t = 40

h) Find the value of x(t) for t = 40.25

i) Find the value of xr(t) for t = 40.25

j) Using only your answers to f,g,h,i can you determine whether T · ωmax ≤ π where ωmax corresponds to the frequency domain representation for x(t)? Explain your answer.