![[5 5 5 5 20 pts] A system is defined as shown on the right y[e]=[a1 -1 =3] .[e]=[31-13] 1=0 ן;ria Irrזן וחן](http://img.homeworklib.com/questions/44c75ba0-9680-11eb-b600-13b3aefd3dd5.png?x-oss-process=image/resize,w_560)
![a) Find Y[k] & X[k] b) Find H[k](Yes H[K]) c) Find h[n] d) Find y[n]=x[n]®, h[n]](http://img.homeworklib.com/questions/4529c2f0-9680-11eb-a21c-cf91b171a415.png?x-oss-process=image/resize,w_560)
Homework Answers
![hel yeni = [-2. 1,-1,- 3} 2011 = (3.1,-1,3] y (n=-28(n-u + 8 (0-2) – 8 (n-3) -38(0-4) X(n) = 2 sins + Slues) -sin-21 43 8(n-3](http://img.homeworklib.com/questions/45ac82a0-9680-11eb-9349-ef80f41b4d9e.png?x-oss-process=image/resize,w_560)
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[5 5 5 5 20 pts] A system is defined as shown on the right y[e]=[a1...
a = 3 signals and systems 1) [10 pts. Let a system be defined as ta...
a = 3
signals and systems
1) [10 pts. Let a system be defined as ta y(t) x(31 - 2a)dt 2a Is this system b) No b) No b) No vii) memoryless? a) Yes viii) Linear? a) Yes ix) Time invariant? a) Yes x) Causal? a) Yes xi) BIBO stable? a) Yes 2) [5 pts. What is the impulse response h(t)? 3) [10 pts.] Let a signal in s domain b) No b) No 2 Y(S) Sa What is the...
20. (5 pts.) X and Y have a joint distribution with pdf f(x,y) = e-(w+y) for...
20. (5 pts.) X and Y have a joint distribution with pdf f(x,y) = e-(w+y) for x > 0, y > 0. The random variable U is defined to be equal to U = e-(X+Y). Find the pdf of U.
III.(6 pts.) A system is defined the following pole zero plot, where H(0)-10. a) Find the step response of the system.< Note: step response, not impulse response. b) (+3) Find the output, y()....
III.(6 pts.) A system is defined the following pole zero plot, where H(0)-10. a) Find the step response of the system.< Note: step response, not impulse response. b) (+3) Find the output, y(). when the input is x()-8(0)-e) H(O) 10 -1 -2
III.(6 pts.) A system is defined the following pole zero plot, where H(0)-10. a) Find the step response of the system.
IV. (5 pts). Given the feedback system shown below, with H)--1 and Gs) 5+α where a...
IV. (5 pts). Given the feedback system shown below, with H)--1 and Gs) 5+α where a and K constants. Note that H(s) represents an unstable open-loop system. We are going to determine the value of the constants that make the overall closed-loop system stable. H(s) vu) x(t) wt) G(s) 0(s) a) Find the system function, Q(s), of the closed-loop system in terms ofa and K. A quick test that you probably got the right answer: ( ONMwm.→ b) Find the...
Question 4. (20 pts.) a) In the following system of linear equations, find k such that...
Question 4. (20 pts.) a) In the following system of linear equations, find k such that the system Has unique solution Has infinitely many solutions Has no solution x+z=0 x + 2y + 2z = 3 (x + kk + 1)y + z = k Question 5. (20 pts.) a)Find Eigenvalues and Eigenvectors of the following matrix 13 2 6 1 -2 3 16 4 12 b) Find the Fourier series representation of the function with period 21 given by...
1. (20 pts) An LTCI system is defined by the equation *0) + 1) + 4y0)...
1. (20 pts) An LTCI system is defined by the equation *0) + 1) + 4y0) = 10) (a) find the characteristic polynomial, characteristic function equation, characteristic root and characteristic modes of this system. (b) Find yo(t), the zero-input component of the responses y(t) for t > 0 with initial conditions yo(0) = 2 and y(0) = -1. 2. (20 pts) Repeat the previous problem if Vt) + 9y(t) = 351) + 2FE) and yo(0) = 0, Y%(0) = 6.
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...
(20 pts) Write down the definition of kernel which is defined on R. Prove that the...
(20 pts) Write down the definition of kernel which is defined on R. Prove that the function defined, for any x,y ER, K(x,y) e-\x-yl? is a PSD kernel. Can you also figure out the feature map Ø and the feature space H associated with this kernel. = e
Consider the DT LTI system defined by the mpulse response h[n] = ?[n] The input to...
Consider the DT LTI system defined by the mpulse response h[n] = ?[n] The input to this system is the signal rn: ?[n-1) (a) Sketch h[n] and r[n] (b) Determine the output of the systern, ylnj, using convolution. Sketch y[n] (c) Determine the DTFTs H(e) and X(e. Make fully-labeled sketches of the magni- tudes of these DTFTs (d) Recall that the discrete Fourier transform (DFT) is simply defined as samples of the discrete-time Fourier transform (DTFT). Compute the 4-point (N-4)...
6. ( ) The Direct form 2 realization of a filter is shown on the right....
6. ( ) The Direct form 2 realization of a filter is shown on the right. What is its filter equation? (An unlabeled link is 1.) (A) y{n}=(x[n]+x[n–1]-y[n–2]–y[n–3]), x[n] 1 1/4 y[n] 1 Tz (B) y[n]==(x[n–2]+x[n–3]+y[n-1]+y[n–2)), (©) y[n] = {(x[n]+x[n–1]+y[n–2]+y[n–3), (D) y[n]=} (-x[n–2]– x[n–3]+y[n–1]+y[n–2]), (E) none of the above. Q 7. ( The loop gain of a feedback control system is Gs 's-1)(52–2s+2) . What is its (s+1)(s?+2s+2) root locus for positive feedback (K< 0)? (A) ja (B) j x...
a = 3
signals and systems
1) [10 pts. Let a system be defined as ta y(t) x(31 - 2a)dt 2a Is this system b) No b) No b) No vii) memoryless? a) Yes viii) Linear? a) Yes ix) Time invariant? a) Yes x) Causal? a) Yes xi) BIBO stable? a) Yes 2) [5 pts. What is the impulse response h(t)? 3) [10 pts.] Let a signal in s domain b) No b) No 2 Y(S) Sa What is the...
20. (5 pts.) X and Y have a joint distribution with pdf f(x,y) = e-(w+y) for x > 0, y > 0. The random variable U is defined to be equal to U = e-(X+Y). Find the pdf of U.
III.(6 pts.) A system is defined the following pole zero plot, where H(0)-10. a) Find the step response of the system.< Note: step response, not impulse response. b) (+3) Find the output, y(). when the input is x()-8(0)-e) H(O) 10 -1 -2
III.(6 pts.) A system is defined the following pole zero plot, where H(0)-10. a) Find the step response of the system.
IV. (5 pts). Given the feedback system shown below, with H)--1 and Gs) 5+α where a and K constants. Note that H(s) represents an unstable open-loop system. We are going to determine the value of the constants that make the overall closed-loop system stable. H(s) vu) x(t) wt) G(s) 0(s) a) Find the system function, Q(s), of the closed-loop system in terms ofa and K. A quick test that you probably got the right answer: ( ONMwm.→ b) Find the...
Question 4. (20 pts.) a) In the following system of linear equations, find k such that the system Has unique solution Has infinitely many solutions Has no solution x+z=0 x + 2y + 2z = 3 (x + kk + 1)y + z = k Question 5. (20 pts.) a)Find Eigenvalues and Eigenvectors of the following matrix 13 2 6 1 -2 3 16 4 12 b) Find the Fourier series representation of the function with period 21 given by...
1. (20 pts) An LTCI system is defined by the equation *0) + 1) + 4y0) = 10) (a) find the characteristic polynomial, characteristic function equation, characteristic root and characteristic modes of this system. (b) Find yo(t), the zero-input component of the responses y(t) for t > 0 with initial conditions yo(0) = 2 and y(0) = -1. 2. (20 pts) Repeat the previous problem if Vt) + 9y(t) = 351) + 2FE) and yo(0) = 0, Y%(0) = 6.
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...
(20 pts) Write down the definition of kernel which is defined on R. Prove that the function defined, for any x,y ER, K(x,y) e-\x-yl? is a PSD kernel. Can you also figure out the feature map Ø and the feature space H associated with this kernel. = e
Consider the DT LTI system defined by the mpulse response h[n] = ?[n] The input to this system is the signal rn: ?[n-1) (a) Sketch h[n] and r[n] (b) Determine the output of the systern, ylnj, using convolution. Sketch y[n] (c) Determine the DTFTs H(e) and X(e. Make fully-labeled sketches of the magni- tudes of these DTFTs (d) Recall that the discrete Fourier transform (DFT) is simply defined as samples of the discrete-time Fourier transform (DTFT). Compute the 4-point (N-4)...
6. ( ) The Direct form 2 realization of a filter is shown on the right. What is its filter equation? (An unlabeled link is 1.) (A) y{n}=(x[n]+x[n–1]-y[n–2]–y[n–3]), x[n] 1 1/4 y[n] 1 Tz (B) y[n]==(x[n–2]+x[n–3]+y[n-1]+y[n–2)), (©) y[n] = {(x[n]+x[n–1]+y[n–2]+y[n–3), (D) y[n]=} (-x[n–2]– x[n–3]+y[n–1]+y[n–2]), (E) none of the above. Q 7. ( The loop gain of a feedback control system is Gs 's-1)(52–2s+2) . What is its (s+1)(s?+2s+2) root locus for positive feedback (K< 0)? (A) ja (B) j x...
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