Consider the sampling signal

which we will use in the sampling of analog signals later on.

(a) Plot δ_T(t). Find

and carefully plot it for all t. What does the resulting signal ss(t) look like? In [18] the author calls it the €œstairway to the stars.€ Explain.

(b) Use MATLAB function stairsto plot ss_T(t) for T = 0.1. Determine what signal would be the limit as T †’ 0.

(c) A sampled signal is

Let x(t) =cos(2Ï€t)u(t) and T_s =0.1. Find the integral

and use MATLAB to plot it for 0 ‰¤ t ‰¤ 10. In a simple way this prob-lem illustrates the operation of a discrete to analog converter which converts a discrete-time into a continuous-time signal (its cousin is the digital to analog converter or DAC).

87 (t) = 8(t – kT) 5(t – k=0 SS7(t) ap(1)'g