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1-Verify the following: and find ak such that (n) = u(n) = u(n − 1) ∞ u(n) = a(n-k) == k=0 2-Verify that for the signal x = {1,2}, we have x(n) = 8(n) +28(n - 1) and then find the coefficients a; below, such that and v1 {0, 2, 1, 3, 1}, vi(n) = ag(n) + a₁d(n − 1) + a2d(n-2) + a3d(n − 3) + a4d(n − 4). 3- A signal xo, is odd if x。(n) = -xo(-n). Show that for such a signal, we have x,(0) = 0. Give an example of an odd signal. 4-Sketch the signals a(n) = cos(wn) for the values of w = 0,π/4, π/2,3π/4, π, 3π/2, and 27. 5-Take x(n) = 2 sin(n/6). what is the period of x? Find the amplitude and phase of y given by y(n) = x(n) - 2x(n - 1) + x(n-2). 6-Take wi(n) = 2 sin(πn/10), and w₂(n) = 1.5 cos(Tn/10). What is the period of w? Find the amplitude and phase of w given by w(n) = w(n) - 2 w₂(n).

1-Verify the following: and find ak such that (n) = u(n) = u(n − 1) ∞ u(n) = a(n-k) == k=0 2-Verify that for the signal x = {1,2}, we have x(n) = 8(n) +28(n - 1) and then find the coefficients a; below, such that and v1 {0, 2, 1, 3, 1}, vi(n) = ag(n) + a₁d(n − 1) + a2d(n-2) + a3d(n − 3) + a4d(n − 4). 3- A signal xo, is odd if x。(n) = -xo(-n). Show that for such a signal, we have x,(0) = 0. Give an example of an odd signal. 4-Sketch the signals a(n) = cos(wn) for the values of w = 0,π/4, π/2,3π/4, π, 3π/2, and 27. 5-Take x(n) = 2 sin(n/6). what is the period of x? Find the amplitude and phase of y given by y(n) = x(n) - 2x(n - 1) + x(n-2). 6-Take wi(n) = 2 sin(πn/10), and w₂(n) = 1.5 cos(Tn/10). What is the period of w? Find the amplitude and phase of w given by w(n) = w(n) - 2 w₂(n).

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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1-Verify the following: and find ak such that (n) = u(n) = u(n − 1) ∞ u(n) = a(n-k) == k=0 2-Verify that for the signal x = {1,2}, we have x(n) = 8(n) +28(n - 1) and then find the coefficients a; below, such that and v1 {0, 2, 1, 3, 1}, vi(n) = ag(n) + a₁d(n − 1) + a2d(n-2) + a3d(n − 3) + a4d(n − 4). 3- A signal xo, is odd if x。(n) = -xo(-n). Show that for such a signal, we have x,(0) = 0. Give an example of an odd signal. 4-Sketch the signals a(n) = cos(wn) for the values of w = 0,π/4, π/2,3π/4, π, 3π/2, and 27. 5-Take x(n) = 2 sin(n/6). what is the period of x? Find the amplitude and phase of y given by y(n) = x(n) - 2x(n - 1) + x(n-2). 6-Take wi(n) = 2 sin(πn/10), and w₂(n) = 1.5 cos(Tn/10). What is the period of w? Find the amplitude and phase of w given by w(n) = w(n) - 2 w₂(n).
Transcribed Image Text:1-Verify the following: and find ak such that (n) = u(n) = u(n − 1) ∞ u(n) = a(n-k) == k=0 2-Verify that for the signal x = {1,2}, we have x(n) = 8(n) +28(n - 1) and then find the coefficients a; below, such that and v1 {0, 2, 1, 3, 1}, vi(n) = ag(n) + a₁d(n − 1) + a2d(n-2) + a3d(n − 3) + a4d(n − 4). 3- A signal xo, is odd if x。(n) = -xo(-n). Show that for such a signal, we have x,(0) = 0. Give an example of an odd signal. 4-Sketch the signals a(n) = cos(wn) for the values of w = 0,π/4, π/2,3π/4, π, 3π/2, and 27. 5-Take x(n) = 2 sin(n/6). what is the period of x? Find the amplitude and phase of y given by y(n) = x(n) - 2x(n - 1) + x(n-2). 6-Take wi(n) = 2 sin(πn/10), and w₂(n) = 1.5 cos(Tn/10). What is the period of w? Find the amplitude and phase of w given by w(n) = w(n) - 2 w₂(n).
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