Question: Consider the system y(n) = T [x(n) = x(n 2 )] (a)?Determine if the system is time invariant. (b) Clarify the result in part (a)

Consider the system y(n) = T [x(n) = x(n2)]

(a)?Determine if the system is time invariant.

(b) Clarify the result in part (a) assume that the signal is applied into the system.

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(1) Sketch the signal x(n).

(2) Determine and sketch the signal y (n) = T [x (n)].

(3) Sketch the signal y?2(n) = y (n - 2).

(4) Determine and sketch the signal x2(n) = x (n - 2)

(5) Determine and sketch the signal y2?(n) = T [x2 (n)].?

(6) Compare the signals y2?(n) and y (n-2). What is your conclusion??

(c) Repeat part (b) for the system y (n) = x(n) ? x(n-1)

Can you use this result to make any statement about the time invariance of this system? Why?

(d) Repeat parts (b) and (c) for the system y(n) = T[x (n)] = nx (n)

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