Problem 1 For any given sequence a[n], we call y[n] the sequence such that Y()= X(2²). Plot y[n] when a[n] is as follows. 3 a- -2-1 0 1 2 3 b- Consider now any sequence a[n]. Express y[n] in terms of x[n]. Hint: Consider separately y[2k] and y[2k+1]. C- Consider a[n]u[n] (unit step sequence). Derive y[n] in terms of n by taking the inverse z-transform of Y(z). Show that the relation between y[n] and [n] you found in the previous question is satisfied in the present case.

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Problem 1
For any given sequence x[n], we call y[n] the sequence such that Y(z) = X(2²).
4
Plot y[n] when r[n] is as follows. 3
2
a -
-2-1 0 1 2 3
b-
Consider now any sequence r[n]. Express y[n] in terms of r[n].
Hint: Consider separately y[2k] and y[2k+1].
C-
Consider a[n] =u[n] (unit step sequence). Derive y[n] in terms of n by taking the
inverse z-transform of Y(z). Show that the relation between y[n] and r[n] you found in the
previous question is satisfied in the present case.
Transcribed Image Text:Problem 1 For any given sequence x[n], we call y[n] the sequence such that Y(z) = X(2²). 4 Plot y[n] when r[n] is as follows. 3 2 a - -2-1 0 1 2 3 b- Consider now any sequence r[n]. Express y[n] in terms of r[n]. Hint: Consider separately y[2k] and y[2k+1]. C- Consider a[n] =u[n] (unit step sequence). Derive y[n] in terms of n by taking the inverse z-transform of Y(z). Show that the relation between y[n] and r[n] you found in the previous question is satisfied in the present case.
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