![53. For each of the systems with the pole-zero diagrams in Figure E.53 find the discrete-time radian frequencies, Ω max and Ωmin, in the range,-π Ω π for which the transfer function magnitude is a maximum and a minimum. If there is more than one value of S2max or S2,min, find all such values [zl 0.8 z] 0.5 0.5 -0.5 -0.5 0.8 -1 -1 0 Re(z) 0.5 0 08 Re() Figure E.53](http://img.homeworklib.com/questions/0d7044c0-a320-11eb-adf3-c9c3ba1b4dbd.png?x-oss-process=image/resize,w_560)
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53. For each of the systems with the pole-zero diagrams in Figure E.53 find the discrete-time...
The figure shows the pole diagrams and frequency responses of four continuous-time LTI systems. B...
signals and systems
The figure shows the pole diagrams and frequency responses of four continuous-time LTI systems. But they are out of order. Match each pole diagram with its frequency response POLE-ZERO DIAGRAM FREQUENCY RESPONSE POLE-ZERO DIAGRAM1 FREQUENCY RESPONSE1 0.4 0.35 0.3 0.25 0.15 0.1 0.05 3 2.5 -2 1.5.5 00.5 -6 42 POLE-ZERO DIAGRAM 2 FREQUENCY RESPONSE 2 0.6 0.5 0.4 0.3 10 -10 0.1 -3 -2.5 -2 1.5-0.5 0 0.5 -6 -42 POLE-ZERO DIAGRAM 3 FREQUENCY RESPONSE 3...
P5.6-3 displays the pole-zero plot of a system that has re 5.6-5 Figure second-order real, causal...
P5.6-3 displays the pole-zero plot of a system that has re 5.6-5 Figure second-order real, causal LTID s Figure P5.6-5 (a) Determine the five constants k, bi, b2, aj, and a2 that specify the transfer function (b) Using the techniques of Sec. 5.6, accurately hand-sketch the system magnitude response lH[eill over the range (-π π) (c) A signal x(t) = cos(2πft) is sampled at a rate Fs 1 kHz and then input into the above LTID system to produce DT...
1. Pole-zero placement. We wish to design a stable and causal second-order discrete-time (DT) fil...
1. Pole-zero placement. We wish to design a stable and causal second-order discrete-time (DT) filter (i.e., having two poles and two zeros, including those at 0 and oo) using pole-zero placement. (a) [5 pts] Where might you place the poles and zeros to achieve the following magnitude frequency response? Sketch the pole-zero plot in the complex z-plane. -Π -Tt/2 0 (b) [3 pts] Give an expression for the transfer function H(z). Justify your answer. (c) [2 pts] Write an expression...
Given a system with pole zero plot shown in Figure 4-37 and the fact that H(0)...
Given a system with pole zero plot shown in Figure 4-37 and the fact that H(0) = -5 Im{z} 2 1 -0.5 2 Re{z} 0 -1 -2 -2 -1 0 2 Figure 4-37 a) Find h[n] given that the system is causal b) Find h[n] given that the system is stable.
1. There are 8 pole-zero graphs of system transfer functions in Figure E-1. Answer the following...
1. There are 8 pole-zero graphs of system transfer functions in Figure E-1. Answer the following questions about their frequency responses, impulse responses and step responses. Frequency response: (a) Which have a phase approaching zero at very high frequencies? (b) Which have a phase that is discontinuous at zero frequency? (c) Which have a magnitude approaching zero at high frequencies? Step response: (a) Which have a step response that is non-zero in the limit to? (b) Which have a step...
A causal discrete-time LTI system is described by the equation
A causal discrete-time LTI system is described by the equationwhere z is the input signal, and y the output signal y(n) = 1/3x(n) + 1/3x(n -1) + 1/3x(n - 2) (a) Sketch the impulse response of the system. (b) What is the dc gain of the system? (Find Hf(0).) (c) Sketch the output of the system when the input x(n) is the constant unity signal, x(n) = 1. (d) Sketch the output of the system when the input x(n) is the unit step signal, x(n)...
1. A discrete-time system has seven poles at z 0 and seven zeros at Find the...
1. A discrete-time system has seven poles at z 0 and seven zeros at Find the transfer function H(z) and find the constant term bo such that the gain of the filter at zero angle (8-0) is 1, that is, a. Note that H (θ)-H(z)IFeje and H(θ)18-0-1 is equivalent to H(z)IF1-1 b. Plot the pole-zero diagram. c. Plot the magnitude response |H(6) d. Plot the phase response H(6) e. Find yin) as a function of x(n), x(n-1), x(n-2), x(n-3),x(n-4), x(n-5),x(n-6),x(n-7)
Can you solve this ? Case the confidence in the second-order approxima- tion during design, but...
Can you solve this ?
Case the confidence in the second-order approxima- tion during design, but then simulate the completed design. Let us look at an example that compares the responses of two different three- pole systems with that of a second-order system. Example 4.8 Comparing Responses of Three-Pole Systems PROBLEM: Find the step response of each of the transfer functions shown in Eqs. (4.62) through (4.64) and compare them. 24.542 T1 (s) 4s+24.542 (4.62) 245.42 T2(s) = (4.63) (s+10)(s24s+...
4. The continuous-time signal e(t) has the Fourier transform X(jw) shown below. Xe(ju) is zero ou...
4. The continuous-time signal e(t) has the Fourier transform X(jw) shown below. Xe(ju) is zero outside the region shown in the figure X.Gj) -2T (300) -2r(100) 0 2n(100) 2T (300) We need to filter re(t) to remove all frequencies higher than 200 Hz. (a) Plot the effective continuous-time filter we need to implement. Label your plot. b) Suppose we decide to implement the filtering in discrete-time using the overall process (sample, filter, reconstruct) shown in the figure in Problem 3....
5 pts D Question 1 A system has the following impulse response: .2 Sample number, n From the choices below, select the frequency response of this system. H (eju)-e(1.5 ) (2 sin( 1.5ώ) +...
5 pts D Question 1 A system has the following impulse response: .2 Sample number, n From the choices below, select the frequency response of this system. H (eju)-e(1.5 ) (2 sin( 1.5ώ) + 4 sin(0.δώ)) H (ee) = e-j(1.5e-5) (cos( 1.5 ) +2 cos(0.54)) @ H (ee)-e-n1.si) (sin( 1.54) t. 2 sin(0.δώ)) (sin(l.50) +4sin(0.0) H (ee)-e-j(1.5i) (2 cos( 1.5ώ) + 4 cos(0.5a)) H (efo)-e-n1.5u) (cos( 1.50) + 2 cos(0.50)) https://rmitinstructure.comcoursesy 5 pts DQuestion 2 A system has the following...
signals and systems
The figure shows the pole diagrams and frequency responses of four continuous-time LTI systems. But they are out of order. Match each pole diagram with its frequency response POLE-ZERO DIAGRAM FREQUENCY RESPONSE POLE-ZERO DIAGRAM1 FREQUENCY RESPONSE1 0.4 0.35 0.3 0.25 0.15 0.1 0.05 3 2.5 -2 1.5.5 00.5 -6 42 POLE-ZERO DIAGRAM 2 FREQUENCY RESPONSE 2 0.6 0.5 0.4 0.3 10 -10 0.1 -3 -2.5 -2 1.5-0.5 0 0.5 -6 -42 POLE-ZERO DIAGRAM 3 FREQUENCY RESPONSE 3...
P5.6-3 displays the pole-zero plot of a system that has re 5.6-5 Figure second-order real, causal LTID s Figure P5.6-5 (a) Determine the five constants k, bi, b2, aj, and a2 that specify the transfer function (b) Using the techniques of Sec. 5.6, accurately hand-sketch the system magnitude response lH[eill over the range (-π π) (c) A signal x(t) = cos(2πft) is sampled at a rate Fs 1 kHz and then input into the above LTID system to produce DT...
1. Pole-zero placement. We wish to design a stable and causal second-order discrete-time (DT) filter (i.e., having two poles and two zeros, including those at 0 and oo) using pole-zero placement. (a) [5 pts] Where might you place the poles and zeros to achieve the following magnitude frequency response? Sketch the pole-zero plot in the complex z-plane. -Π -Tt/2 0 (b) [3 pts] Give an expression for the transfer function H(z). Justify your answer. (c) [2 pts] Write an expression...
Given a system with pole zero plot shown in Figure 4-37 and the fact that H(0) = -5 Im{z} 2 1 -0.5 2 Re{z} 0 -1 -2 -2 -1 0 2 Figure 4-37 a) Find h[n] given that the system is causal b) Find h[n] given that the system is stable.
1. There are 8 pole-zero graphs of system transfer functions in Figure E-1. Answer the following questions about their frequency responses, impulse responses and step responses. Frequency response: (a) Which have a phase approaching zero at very high frequencies? (b) Which have a phase that is discontinuous at zero frequency? (c) Which have a magnitude approaching zero at high frequencies? Step response: (a) Which have a step response that is non-zero in the limit to? (b) Which have a step...
1. A discrete-time system has seven poles at z 0 and seven zeros at Find the transfer function H(z) and find the constant term bo such that the gain of the filter at zero angle (8-0) is 1, that is, a. Note that H (θ)-H(z)IFeje and H(θ)18-0-1 is equivalent to H(z)IF1-1 b. Plot the pole-zero diagram. c. Plot the magnitude response |H(6) d. Plot the phase response H(6) e. Find yin) as a function of x(n), x(n-1), x(n-2), x(n-3),x(n-4), x(n-5),x(n-6),x(n-7)
Can you solve this ?
Case the confidence in the second-order approxima- tion during design, but then simulate the completed design. Let us look at an example that compares the responses of two different three- pole systems with that of a second-order system. Example 4.8 Comparing Responses of Three-Pole Systems PROBLEM: Find the step response of each of the transfer functions shown in Eqs. (4.62) through (4.64) and compare them. 24.542 T1 (s) 4s+24.542 (4.62) 245.42 T2(s) = (4.63) (s+10)(s24s+...
4. The continuous-time signal e(t) has the Fourier transform X(jw) shown below. Xe(ju) is zero outside the region shown in the figure X.Gj) -2T (300) -2r(100) 0 2n(100) 2T (300) We need to filter re(t) to remove all frequencies higher than 200 Hz. (a) Plot the effective continuous-time filter we need to implement. Label your plot. b) Suppose we decide to implement the filtering in discrete-time using the overall process (sample, filter, reconstruct) shown in the figure in Problem 3....
5 pts D Question 1 A system has the following impulse response: .2 Sample number, n From the choices below, select the frequency response of this system. H (eju)-e(1.5 ) (2 sin( 1.5ώ) + 4 sin(0.δώ)) H (ee) = e-j(1.5e-5) (cos( 1.5 ) +2 cos(0.54)) @ H (ee)-e-n1.si) (sin( 1.54) t. 2 sin(0.δώ)) (sin(l.50) +4sin(0.0) H (ee)-e-j(1.5i) (2 cos( 1.5ώ) + 4 cos(0.5a)) H (efo)-e-n1.5u) (cos( 1.50) + 2 cos(0.50)) https://rmitinstructure.comcoursesy 5 pts DQuestion 2 A system has the following...
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