![The pole -zero diagram in figure 1 corresponds to the Z-transform [X(z)] of a causal sequence (xIn]). Sketch the pole-zero diagram of Y(z), where y[n]-x-n5]. Also, determine the region of convergence for Y (z). 2. a. (15 Marks) rm z-plane Figure 1 b. Discuss any six applications of Multirate Digital Signal processing or explain the need of Multirate Signal Processing with suitable Example. (10 Marks)](http://img.homeworklib.com/questions/ee0f2490-30b5-11ec-8e89-a76af88d882e.png?x-oss-process=image/resize,w_560)
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The pole -zero diagram in figure 1 corresponds to the Z-transform [X(z)] of a causal sequence...
For x[n]-(0.3). 1. a. (2 pts) Find the z-transform, X(z b. (3 pts) Sketch the pole-zero...
For x[n]-(0.3). 1. a. (2 pts) Find the z-transform, X(z b. (3 pts) Sketch the pole-zero plot. c. (3 pts) Find the region of convergence of the transform. Sketch it in the z-plane. d. (3 pts) Use your answer in part a to write down the DTFT of x,[n]=(0.3)"u[n]. Why is it necessary to multiply by the unit step function to get the DTFT?
part c) Figure 1 5 ma Pag c) The zero-pole diagram of the Laplace transform of y(t), Y(s), is shown in fig. 2 jw Figure 2 [Please turn over] Page 2 of 9 Determine and justify the region of converg...
part c)
Figure 1 5 ma Pag c) The zero-pole diagram of the Laplace transform of y(t), Y(s), is shown in fig. 2 jw Figure 2 [Please turn over] Page 2 of 9 Determine and justify the region of convergence (ROC) ifit is known that Y(Go), that is the Fourier transform of y(t), exists. 5 marks/
Figure 1 5 ma Pag c) The zero-pole diagram of the Laplace transform of y(t), Y(s), is shown in fig. 2 jw Figure 2...
For each signal x(n) in Problems #(1)-(5), use Z Transform Tables to do the following: (a) Write ...
For each signal x(n) in Problems #(1)-(5), use Z Transform Tables to do the following: (a) Write the formulas for its Z Transform, X(e), and Region of Convergence, RoCr (b) List the values of all poles and all zeros. (c) Sketch the pole zero diagram. Label both axes. Give key values along both axes. sin ( (-n))u-n]. (Hints: cos(π/3) (5) x1n] , 1/2, sin(π/3)-V3/2) ,"
For each signal x(n) in Problems #(1)-(5), use Z Transform Tables to do the following:...
3. (Oppenheim Willsky) Determine the z-transform for each of the following sequences. Sketch the pole-zero plot...
3. (Oppenheim Willsky) Determine the z-transform for each of the following sequences. Sketch the pole-zero plot and indicate the region of convergence. Indicate whether or not the discrete-time Fourier transform of the sequence exists. (a) 8[n +5] (b) (-1)"u[n] (c) (-3)”u[-n – 2] (d) 27u[n] +(4)”u[n – 1]
2+z-1 1. The Z-transform of a signal x[n] is given as X(z) = }</21 < a)...
2+z-1 1. The Z-transform of a signal x[n] is given as X(z) = }</21 < a) Find the signal x[n] [7] b) Draw the pole – zero plot of the z-transform .[3] c) Is x[n] causal or not? Justify your answer [2]
a) List the relative attributes of using digital processing techniques compared to traditional analogue hardware for signal processing. [5 marks] b) Sketch a z-plane diagram including the unit ci...
a) List the relative attributes of using digital processing techniques compared to traditional analogue hardware for signal processing. [5 marks] b) Sketch a z-plane diagram including the unit circle. You have four Poles and two Zeros that you can place on the z-plane diagram. Place them in a position which would provide a digital band-stop filter characteristic with the 'notch' at a n/2 Justify your placement of the poles and zeros. 5 marks] c) The z-plane pole-zero plots of two...
digital control Task 1 Find the Z transform of the causal sequence {xx} where Xx =...
digital control Task 1 Find the Z transform of the causal sequence {xx} where Xx = (-1)". 2 Find the Z transform of the causal sequence {xx} where Xx = 4k - 2ak. 3 Find the Z transform of the causal sequences: (a) {k - 3} (b) {3k+2} 4 Find the inverse Z transformation of z? (2-3) F(z) = (22 - 22 + 1)(z - 2)
Laplace Transform 5. Given a causal LTI system with pole-zero cancellation such as H(s)= S+1 what...
Laplace Transform
5. Given a causal LTI system with pole-zero cancellation such as H(s)= S+1 what is the region of convergence and why. (5+1)(3+2) i. ROC = undefined ii. ROC = Re(s) > 0 iii. ROC = Re(s) >-2 iv. ROC = Re(s) >-1
5 . A) A causal Continuous-time system has the following pole-zero diagram: jw S-plane Re -1...
5 . A) A causal Continuous-time system has the following pole-zero diagram: jw S-plane Re -1 - Let y(t) = s(t) represent the response of this system to a unit-step signal 0; otherwise. Assume that the Unit-Step response s(t) of this system is known to approach 1 as t o. Determine y(t) = s(t), justify your answers mathematically.
Let x(n) be the sequence with the pole-zero plot . Sketch the pole –zero plot for...
Let x(n) be the sequence with the pole-zero plot . Sketch the pole –zero plot for y(n)= (1/2)n x(n)
For x[n]-(0.3). 1. a. (2 pts) Find the z-transform, X(z b. (3 pts) Sketch the pole-zero plot. c. (3 pts) Find the region of convergence of the transform. Sketch it in the z-plane. d. (3 pts) Use your answer in part a to write down the DTFT of x,[n]=(0.3)"u[n]. Why is it necessary to multiply by the unit step function to get the DTFT?
part c)
Figure 1 5 ma Pag c) The zero-pole diagram of the Laplace transform of y(t), Y(s), is shown in fig. 2 jw Figure 2 [Please turn over] Page 2 of 9 Determine and justify the region of convergence (ROC) ifit is known that Y(Go), that is the Fourier transform of y(t), exists. 5 marks/
Figure 1 5 ma Pag c) The zero-pole diagram of the Laplace transform of y(t), Y(s), is shown in fig. 2 jw Figure 2...
For each signal x(n) in Problems #(1)-(5), use Z Transform Tables to do the following: (a) Write the formulas for its Z Transform, X(e), and Region of Convergence, RoCr (b) List the values of all poles and all zeros. (c) Sketch the pole zero diagram. Label both axes. Give key values along both axes. sin ( (-n))u-n]. (Hints: cos(π/3) (5) x1n] , 1/2, sin(π/3)-V3/2) ,"
For each signal x(n) in Problems #(1)-(5), use Z Transform Tables to do the following:...
3. (Oppenheim Willsky) Determine the z-transform for each of the following sequences. Sketch the pole-zero plot and indicate the region of convergence. Indicate whether or not the discrete-time Fourier transform of the sequence exists. (a) 8[n +5] (b) (-1)"u[n] (c) (-3)”u[-n – 2] (d) 27u[n] +(4)”u[n – 1]
2+z-1 1. The Z-transform of a signal x[n] is given as X(z) = }</21 < a) Find the signal x[n] [7] b) Draw the pole – zero plot of the z-transform .[3] c) Is x[n] causal or not? Justify your answer [2]
a) List the relative attributes of using digital processing techniques compared to traditional analogue hardware for signal processing. [5 marks] b) Sketch a z-plane diagram including the unit circle. You have four Poles and two Zeros that you can place on the z-plane diagram. Place them in a position which would provide a digital band-stop filter characteristic with the 'notch' at a n/2 Justify your placement of the poles and zeros. 5 marks] c) The z-plane pole-zero plots of two...
digital control Task 1 Find the Z transform of the causal sequence {xx} where Xx = (-1)". 2 Find the Z transform of the causal sequence {xx} where Xx = 4k - 2ak. 3 Find the Z transform of the causal sequences: (a) {k - 3} (b) {3k+2} 4 Find the inverse Z transformation of z? (2-3) F(z) = (22 - 22 + 1)(z - 2)
Laplace Transform
5. Given a causal LTI system with pole-zero cancellation such as H(s)= S+1 what is the region of convergence and why. (5+1)(3+2) i. ROC = undefined ii. ROC = Re(s) > 0 iii. ROC = Re(s) >-2 iv. ROC = Re(s) >-1
5 . A) A causal Continuous-time system has the following pole-zero diagram: jw S-plane Re -1 - Let y(t) = s(t) represent the response of this system to a unit-step signal 0; otherwise. Assume that the Unit-Step response s(t) of this system is known to approach 1 as t o. Determine y(t) = s(t), justify your answers mathematically.
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