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.

(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 y_2?(n) = T [x₂ (n)].?

(6) Compare the signals y_2?(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)

Transcribed Image Text:

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