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3. SOME COMMON Z-TRANSFORM PAIRS 2. IMPORTANT PROPERTIES OF THE Z-TRANSFORM Signal Transform 1. Linearity: 1. 6[n] 1 ROC All z Za1x1(n) + a2x2(n)] = a1X1(2)+ a2X2(2); ROC: ROC, ROC 2. u[n] (4.4) 3. -u-n-1] |z| > 1 |z| < 1 2. Sample shifting: 4. 5[n—m] 2x (n-no)] =20X(2); ROC: ROC (4.5) 3. Frequency shifting: 5. au[n] az All z except 0 (if m> 0) or x (if m < 0) |z| > |a| Za" (n)] = X(); ROC: ROC, scaled by |a| (4.6) 4. Folding: 6. —au[-n − 1] 7. nan u[n] 1 1-az Zx(-n)] X (1/2); ROC: Inverted ROC (4.7) 5. Complex conjugation: Za(n)] X(); ROC: ROC (4.8) 8. -nau[―n — 1] 9. [cos won]u[n] 10. [sin won]u[n] 11. [ cos won]u[n] 12. [ sin won]u[n] 92-1 (1-az-1)2 2-1 (1-02-132 1-[cos wo]-1 1-[2 cos wo]=-1+=-2 [sin wo]z-1 1-12 cos wo]z-1+2-2 1-[r cos wo]=-1 1-[2r cos wo]z=1+r²z-2 |z| < |a| |z| > |a| |z| < |a| |z|> 1 |z| > 1 |z| > r [rsin wolz-1 1-[2rcos wo]z=1+r²z=2 |=| > T P1) Determine the z-transform of the following sequences using the z-transform table and the z-transform properties. Express X(z) as a rational function in z¹. Verify your results using MATLAB. Indicate the region of convergence in each case, and provide a pole-zero plot. - - 1. x(n) = 28(n − 2) + 3u(n − 3). 2. x(n) = 3(0.75) cos(0.3лn)u(n) + 4(0.75)" sin(0.3πn)u(n) 3. x(n) = n sin()u(n) + (0.9)”u(n − 2). 4. x(n) = n²(2/3)n−²u(n − 1). - -

3. SOME COMMON Z-TRANSFORM PAIRS 2. IMPORTANT PROPERTIES OF THE Z-TRANSFORM Signal Transform 1. Linearity: 1. 6[n] 1 ROC All z Za1x1(n) + a2x2(n)] = a1X1(2)+ a2X2(2); ROC: ROC, ROC 2. u[n] (4.4) 3. -u-n-1] |z| > 1 |z| < 1 2. Sample shifting: 4. 5[n—m] 2x (n-no)] =20X(2); ROC: ROC (4.5) 3. Frequency shifting: 5. au[n] az All z except 0 (if m> 0) or x (if m < 0) |z| > |a| Za" (n)] = X(); ROC: ROC, scaled by |a| (4.6) 4. Folding: 6. —au[-n − 1] 7. nan u[n] 1 1-az Zx(-n)] X (1/2); ROC: Inverted ROC (4.7) 5. Complex conjugation: Za(n)] X(); ROC: ROC (4.8) 8. -nau[―n — 1] 9. [cos won]u[n] 10. [sin won]u[n] 11. [ cos won]u[n] 12. [ sin won]u[n] 92-1 (1-az-1)2 2-1 (1-02-132 1-[cos wo]-1 1-[2 cos wo]=-1+=-2 [sin wo]z-1 1-12 cos wo]z-1+2-2 1-[r cos wo]=-1 1-[2r cos wo]z=1+r²z-2 |z| < |a| |z| > |a| |z| < |a| |z|> 1 |z| > 1 |z| > r [rsin wolz-1 1-[2rcos wo]z=1+r²z=2 |=| > T P1) Determine the z-transform of the following sequences using the z-transform table and the z-transform properties. Express X(z) as a rational function in z¹. Verify your results using MATLAB. Indicate the region of convergence in each case, and provide a pole-zero plot. - - 1. x(n) = 28(n − 2) + 3u(n − 3). 2. x(n) = 3(0.75) cos(0.3лn)u(n) + 4(0.75)" sin(0.3πn)u(n) 3. x(n) = n sin()u(n) + (0.9)”u(n − 2). 4. x(n) = n²(2/3)n−²u(n − 1). - -

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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please solve q3 if you cant do the matlab code its okay but i will appreciate it  using the properties of z transform and common z transfrom pairs i have given in the images thank you

3. SOME COMMON Z-TRANSFORM PAIRS 2. IMPORTANT PROPERTIES OF THE Z-TRANSFORM Signal Transform 1. Linearity: 1. 6[n] 1 ROC All z Za1x1(n) + a2x2(n)] = a1X1(2)+ a2X2(2); ROC: ROC, ROC 2. u[n] (4.4) 3. -u-n-1] |z| > 1 |z| < 1 2. Sample shifting: 4. 5[n—m] 2x (n-no)] =20X(2); ROC: ROC (4.5) 3. Frequency shifting: 5. au[n] az All z except 0 (if m> 0) or x (if m < 0) |z| > |a| Za" (n)] = X(); ROC: ROC, scaled by |a| (4.6) 4. Folding: 6. —au[-n − 1] 7. nan u[n] 1 1-az Zx(-n)] X (1/2); ROC: Inverted ROC (4.7) 5. Complex conjugation: Za(n)] X(); ROC: ROC (4.8) 8. -nau[―n — 1] 9. [cos won]u[n] 10. [sin won]u[n] 11. [ cos won]u[n] 12. [ sin won]u[n] 92-1 (1-az-1)2 2-1 (1-02-132 1-[cos wo]-1 1-[2 cos wo]=-1+=-2 [sin wo]z-1 1-12 cos wo]z-1+2-2 1-[r cos wo]=-1 1-[2r cos wo]z=1+r²z-2 |z| < |a| |z| > |a| |z| < |a| |z|> 1 |z| > 1 |z| > r [rsin wolz-1 1-[2rcos wo]z=1+r²z=2 |=| > T
Transcribed Image Text:3. SOME COMMON Z-TRANSFORM PAIRS 2. IMPORTANT PROPERTIES OF THE Z-TRANSFORM Signal Transform 1. Linearity: 1. 6[n] 1 ROC All z Za1x1(n) + a2x2(n)] = a1X1(2)+ a2X2(2); ROC: ROC, ROC 2. u[n] (4.4) 3. -u-n-1] |z| > 1 |z| < 1 2. Sample shifting: 4. 5[n—m] 2x (n-no)] =20X(2); ROC: ROC (4.5) 3. Frequency shifting: 5. au[n] az All z except 0 (if m> 0) or x (if m < 0) |z| > |a| Za" (n)] = X(); ROC: ROC, scaled by |a| (4.6) 4. Folding: 6. —au[-n − 1] 7. nan u[n] 1 1-az Zx(-n)] X (1/2); ROC: Inverted ROC (4.7) 5. Complex conjugation: Za(n)] X(); ROC: ROC (4.8) 8. -nau[―n — 1] 9. [cos won]u[n] 10. [sin won]u[n] 11. [ cos won]u[n] 12. [ sin won]u[n] 92-1 (1-az-1)2 2-1 (1-02-132 1-[cos wo]-1 1-[2 cos wo]=-1+=-2 [sin wo]z-1 1-12 cos wo]z-1+2-2 1-[r cos wo]=-1 1-[2r cos wo]z=1+r²z-2 |z| < |a| |z| > |a| |z| < |a| |z|> 1 |z| > 1 |z| > r [rsin wolz-1 1-[2rcos wo]z=1+r²z=2 |=| > T
P1) Determine the z-transform of the following sequences using the z-transform table and the z-transform properties. Express X(z) as a rational function in z¹. Verify your results using MATLAB. Indicate the region of convergence in each case, and provide a pole-zero plot. - - 1. x(n) = 28(n − 2) + 3u(n − 3). 2. x(n) = 3(0.75) cos(0.3лn)u(n) + 4(0.75)" sin(0.3πn)u(n) 3. x(n) = n sin()u(n) + (0.9)”u(n − 2). 4. x(n) = n²(2/3)n−²u(n − 1). - -
Transcribed Image Text:P1) Determine the z-transform of the following sequences using the z-transform table and the z-transform properties. Express X(z) as a rational function in z¹. Verify your results using MATLAB. Indicate the region of convergence in each case, and provide a pole-zero plot. - - 1. x(n) = 28(n − 2) + 3u(n − 3). 2. x(n) = 3(0.75) cos(0.3лn)u(n) + 4(0.75)" sin(0.3πn)u(n) 3. x(n) = n sin()u(n) + (0.9)”u(n − 2). 4. x(n) = n²(2/3)n−²u(n − 1). - -
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