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.
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.
Introductory Circuit Analysis (13th Edition)
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Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f3fcee3-df4f-43f5-a70c-56c5ba155c30%2F16bbdda5-9b28-4094-8505-11e5383ab03b%2Fq54smdc_processed.png&w=3840&q=75)
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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