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For each signal x(n) in Problems #(1)-(5), use Z Transform Tables to do the following: (a) Write ...
The pole -zero diagram in figure 1 corresponds to the Z-transform [X(z)] of a causal sequence...
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)
Problem #1. Topics: Z Transform Find the Z transform of: x[n]=-(0.9 )n-2u-n+5] X(Z) Problem #2. T...
Problem #1. Topics: Z Transform Find the Z transform of: x[n]=-(0.9 )n-2u-n+5] X(Z) Problem #2. Topics: Filter Design, Effective Time Constant Design a causal 2nd order, normalized, stable Peak Filter centered at fo 1000Hz. Use only two conjugate poles and two zeros at the origin. The system is to be sampled at Fs- 8000Hz. The duration of the transient should be as close as possible to teft 7.5 ms. The transient is assumed to end when the largest pole elevated...
Given the following difference equation that describes the input output relationship, (a) Express Y(z), the z-transform...
Given the following difference equation that describes the input output relationship, (a) Express Y(z), the z-transform of the output, in terms of X(z), the z-transform of the input. (b) Find the system function H(z). (c) Identify the zeros and poles. Sketch the zero-pole plot. (d) For an input rn]- cos (n), find the output yn] (e) Use the zero-pole plot to explain what you obtain in d)
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]
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?
2-Use tables and properties to determine z-transform of the following signal x[n] = (+)*u[n] – (3)...
2-Use tables and properties to determine z-transform of the following signal x[n] = (+)*u[n] – (3) "u[n]
5. (22+2=4") Topic: The z-transform, z-transform properties Use the z-transform properties to determine the z-transform the...
5. (22+2=4") Topic: The z-transform, z-transform properties Use the z-transform properties to determine the z-transform the following signal and specify the region of convergence. x[n]=(1)"u[n]*2":[-n-1]+)?[n-2]
Problem 5. Determine the z-transform of the signal x[n] :=(-1)"nu[n]. You may use already known z-transforms,...
Problem 5. Determine the z-transform of the signal x[n] :=(-1)"nu[n]. You may use already known z-transforms, such as those listed in Table 5.1 (page 492) of the textbook, and properties of the z-transform. Moreover, notice that -1 = ejt. TABLE 5.1 Select (Unilateral) Z-Transform Pairs x[n] X[z] 8[n-k] ? 2-1 ոս[ո] (z - 1) z(z+1) (2-1)3 nºu[n] nu[n] z(z? + 4z +1) (2-1) Yºu[n] yn-u[n- 1] z-y 12 ny"u[n] (z-7) yz(z+y) (z-7)3 ny"u[n] n(n - 1)(n-2) (n-m+1) ym! lyl" cos...
Consider the signal x(n-õn-4] + 2õn-5] + õn_6]. (a) Find X(el the discrete-time Fourier transform of...
Consider the signal x(n-õn-4] + 2õn-5] + õn_6]. (a) Find X(el the discrete-time Fourier transform of xin]. Write expressions for the magnitude and phase of X(elu), and sketch these functions (b) Find all values of N for which the N-point DFT is a set of real numbers (c) Can you find a three-point causal signal x1n i.e., x1In] 0 for n <0 and n > 2) for which the three-point DFT of x (n] is: xn[nl (ie, xiin] O for...
3. For each of the following discrete-time sequences: (i) Find the Z-transform (ZT), if it exists,...
3. For each of the following discrete-time sequences: (i) Find the Z-transform (ZT), if it exists, and plot the region of convergence (ROC) in the Z-plane (ii) Find the poles and zeros and plot them in the 2-plane (iii) Determine whether the DTFT of the sequence exists (a) x[n] = 8[n – 1] + 28[n – 3] (b) [n] = (0.9e-j*)" u[n + 2] – 2-ul-n - 1] (c) x[n] = 2-" un + 1]
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)
Problem #1. Topics: Z Transform Find the Z transform of: x[n]=-(0.9 )n-2u-n+5] X(Z) Problem #2. Topics: Filter Design, Effective Time Constant Design a causal 2nd order, normalized, stable Peak Filter centered at fo 1000Hz. Use only two conjugate poles and two zeros at the origin. The system is to be sampled at Fs- 8000Hz. The duration of the transient should be as close as possible to teft 7.5 ms. The transient is assumed to end when the largest pole elevated...
Given the following difference equation that describes the input output relationship, (a) Express Y(z), the z-transform of the output, in terms of X(z), the z-transform of the input. (b) Find the system function H(z). (c) Identify the zeros and poles. Sketch the zero-pole plot. (d) For an input rn]- cos (n), find the output yn] (e) Use the zero-pole plot to explain what you obtain in d)
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]
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?
2-Use tables and properties to determine z-transform of the following signal x[n] = (+)*u[n] – (3) "u[n]
5. (22+2=4") Topic: The z-transform, z-transform properties Use the z-transform properties to determine the z-transform the following signal and specify the region of convergence. x[n]=(1)"u[n]*2":[-n-1]+)?[n-2]
Problem 5. Determine the z-transform of the signal x[n] :=(-1)"nu[n]. You may use already known z-transforms, such as those listed in Table 5.1 (page 492) of the textbook, and properties of the z-transform. Moreover, notice that -1 = ejt. TABLE 5.1 Select (Unilateral) Z-Transform Pairs x[n] X[z] 8[n-k] ? 2-1 ոս[ո] (z - 1) z(z+1) (2-1)3 nºu[n] nu[n] z(z? + 4z +1) (2-1) Yºu[n] yn-u[n- 1] z-y 12 ny"u[n] (z-7) yz(z+y) (z-7)3 ny"u[n] n(n - 1)(n-2) (n-m+1) ym! lyl" cos...
Consider the signal x(n-õn-4] + 2õn-5] + õn_6]. (a) Find X(el the discrete-time Fourier transform of xin]. Write expressions for the magnitude and phase of X(elu), and sketch these functions (b) Find all values of N for which the N-point DFT is a set of real numbers (c) Can you find a three-point causal signal x1n i.e., x1In] 0 for n <0 and n > 2) for which the three-point DFT of x (n] is: xn[nl (ie, xiin] O for...
3. For each of the following discrete-time sequences: (i) Find the Z-transform (ZT), if it exists, and plot the region of convergence (ROC) in the Z-plane (ii) Find the poles and zeros and plot them in the 2-plane (iii) Determine whether the DTFT of the sequence exists (a) x[n] = 8[n – 1] + 28[n – 3] (b) [n] = (0.9e-j*)" u[n + 2] – 2-ul-n - 1] (c) x[n] = 2-" un + 1]
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