In analogy with continuous-time singularity functions, we can define a set of discrete-t...

In analogy with continuous-time singularity functions, we can define a set of discrete-time signals. Specifically, let

and

And define

and

Note that

and

(a) What is

(b) Show that

(c) Sketch the signals u₂[n] and u₃[n]

(d) Sketch u_-2(n] and u_-3[n].

(e) Show that, in general, for k > 0,

(Hint: Use induction. From part (c), it is evident that u_k [n] satisfies eq. (P2.70-1) for k = 2 and 3. Then, assuming that eq. (P2.70.-1) satisfies

(f) Show that, in general, for k > 0,

(Hint: Again, use induction. Note that

Then, assuming that eq. (P2.70-2) is valid for as well.)