![Feedback Systems and Digital Filters The diagram shows a negative feedback configuration of two LTI systems. The feedforward system F(s) has an impulse response of f). The feedback system G(s) has an impulse response of g(0). The error function e() is given by: *0e() y(O) - F(s) G(s) The output is given by: y(t)-e(t) & f( We have yli)-[x(t)-g(t) ? y(t)] f(t). Taking LT: y(s)(1+F(s)o(s))=x(s)r(s). The overall transfer function is H(s) x(s) 1+F(s)G(s) 1](http://img.homeworklib.com/questions/9c08bc90-345d-11eb-bb8f-356b78a22c43.png?x-oss-process=image/resize,w_560)
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Feedback Systems and Digital Filters The diagram shows a negative feedback configuration of two LTI systems....
LTI Systems. Consider two LTI subsystems that are connected in series
(a) LTI Systems. Consider two LTI subsystems that are connected in series, where system Tl has step response s1(t)=u(t-1)-u(t-5) and system T2 has impulse response h2t = e-3tu(t). Find the overall impulse response h(t). Hint: you will need to find h1(t) first (b)Fourier Series. The input signal r(t) and impulse response h(t) of an LTI system are as follows:x(t) = sin(2t)cos(t)-ej3t +2 and h(t) = sin(2t)/t Use the Fourier Series method to find the output y(t) (c)Parseval's Identity and Theorem. Consider the system in the...
An unstable LTI system has the impulse response h(t)=sin (4t)u(t). Show that proportional feedback (G(s) =...
An unstable LTI system has the impulse response h(t)=sin (4t)u(t). Show that proportional feedback (G(s) = K) cannot BIBO-stabilize the system. Show that derivative control feedback (G(s) = Ks) can stabilize the system. Using derivative control, choose K so that the closed loop system is critically damped. 7. (a) (b) (c) %3D E(s) System но) X(s) (E +Y(s) Feedback G(s) Y(s) Y(s) system G(s) Feedback loop Figure 4. o of
4. LTI Systems and Erponential Response. (12 pts) (a) (2 pts) Suppose an LTI system has...
4. LTI Systems and Erponential Response. (12 pts) (a) (2 pts) Suppose an LTI system has input-output relationship y(t) 2r(t+3). What is the transfer function H(jw) of the given system. Show that H(jw)2. Hint: H(jw(tejdt (b) (5 pts) Suppose an LTI system has input-output relationship y(t)2r(t+3) as Problem 4-(a). Find the output y(t) using the complex exponential response method as discussed in lecture for the input r(t) = ej2t + 2 cos2(t). Hint: cos2(0) 1 (20 cos(26) an d 1-ejot...
5- Determine whether or not each of the following LTI systems with the given impulse response...
5- Determine whether or not each of the following LTI systems with the given impulse response are memoryless: a) h(t) = 56(t- 1) b) h(t) = eT u(t) e) h[n] sinEn) d) h[n] = 26[n] 6- Determine whether or not each of the following LTI systems with the given impulse response are stable: a) h(t) = 2 b) h(t) = e2tu(t - 1) c) h[n] = 3"u[n] d) h[n] = cos(Tm)u[n] 7- Determine whether or not each of the following...
LTI Systems-Stability Consider an LTI system with system function: s-1 H (s) = If the system...
LTI Systems-Stability Consider an LTI system with system function: s-1 H (s) = If the system is non-causal and un-stable, determine the time domain impulse response
Discrete-time convolution. Use of shift invariance for LTI systems. A discrete-time LTI system is described the...
Discrete-time convolution. Use of shift invariance for LTI systems. A discrete-time LTI system is described the its impulse response h[n]. h[n] = (5)"u[n]. n-3 1 An input x[n] = u[n – 4) is applied. The output of the system y[n] is given by: x[r] – 54 G)" ()") un 14 The correct answer is not provided gắn] = [16(5)” – 54(5) ] n] y[n] = [16()" – 54(+)"] uſn – 4
2.6.1 Consider a causal continuous-time LTI system described by the differential equation u"(t) +...
2.6.1-2.6.62.6.1 Consider a causal contimuous-time LTI system described by the differential equation$$ y^{\prime \prime}(t)+y(t)=x(t) $$(a) Find the transfer function \(H(s)\), its \(R O C\), and its poles.(b) Find the impulse response \(h(t)\).(c) Classify the system as stable/unstable.(d) Find the step response of the system.2.6.2 Given the impulse response of a continuous-time LTI system, find the transfer function \(H(s),\) the \(\mathrm{ROC}\) of \(H(s)\), and the poles of the system. Also find the differential equation describing each system.(a) \(h(t)=\sin (3 t) u(t)\)(b)...
Please answer the signals and systems question clearly :) Assume the following LTI system and the...
Please answer the signals and systems question clearly :)
Assume the following LTI system and the input signal whose spectrum depicted below 2. x(t) Y(o) H(a) X(a) 2π 2π 3TT 3π Find x(t), Y(ω), and y(t) for each of the following filters. 3 2 0 2 f)
Consider an LTI system with the impulse response h(t) = e- . Is the system casual?...
Consider an LTI system with the impulse response h(t) = e- . Is the system casual? Explain. Find and plot the output s(t) given that the system input is x(t) = u(t). Note that s(t) in this case is commonly known as the step response of the system. If the input is x(t) = u(t)-u(t-T). Express the output y(t) as a function of s(t). Also, explicitly write the output y(t) as a function of t. a) b) c)
Also, solve the following problem. Consider a system made by cascading two LTI systems. The first...
Also, solve the following problem. Consider a system made by cascading two LTI systems. The first system is described by y[n] = x [n] – ax (n – 3]. The second has impulse response h (n] = {po aP [n – 3p] with ( < a < 1. Find the impulse response of the overall system.
An unstable LTI system has the impulse response h(t)=sin (4t)u(t). Show that proportional feedback (G(s) = K) cannot BIBO-stabilize the system. Show that derivative control feedback (G(s) = Ks) can stabilize the system. Using derivative control, choose K so that the closed loop system is critically damped. 7. (a) (b) (c) %3D E(s) System но) X(s) (E +Y(s) Feedback G(s) Y(s) Y(s) system G(s) Feedback loop Figure 4. o of
4. LTI Systems and Erponential Response. (12 pts) (a) (2 pts) Suppose an LTI system has input-output relationship y(t) 2r(t+3). What is the transfer function H(jw) of the given system. Show that H(jw)2. Hint: H(jw(tejdt (b) (5 pts) Suppose an LTI system has input-output relationship y(t)2r(t+3) as Problem 4-(a). Find the output y(t) using the complex exponential response method as discussed in lecture for the input r(t) = ej2t + 2 cos2(t). Hint: cos2(0) 1 (20 cos(26) an d 1-ejot...
5- Determine whether or not each of the following LTI systems with the given impulse response are memoryless: a) h(t) = 56(t- 1) b) h(t) = eT u(t) e) h[n] sinEn) d) h[n] = 26[n] 6- Determine whether or not each of the following LTI systems with the given impulse response are stable: a) h(t) = 2 b) h(t) = e2tu(t - 1) c) h[n] = 3"u[n] d) h[n] = cos(Tm)u[n] 7- Determine whether or not each of the following...
LTI Systems-Stability Consider an LTI system with system function: s-1 H (s) = If the system is non-causal and un-stable, determine the time domain impulse response
Discrete-time convolution. Use of shift invariance for LTI systems. A discrete-time LTI system is described the its impulse response h[n]. h[n] = (5)"u[n]. n-3 1 An input x[n] = u[n – 4) is applied. The output of the system y[n] is given by: x[r] – 54 G)" ()") un 14 The correct answer is not provided gắn] = [16(5)” – 54(5) ] n] y[n] = [16()" – 54(+)"] uſn – 4
2.6.1-2.6.62.6.1 Consider a causal contimuous-time LTI system described by the differential equation$$ y^{\prime \prime}(t)+y(t)=x(t) $$(a) Find the transfer function \(H(s)\), its \(R O C\), and its poles.(b) Find the impulse response \(h(t)\).(c) Classify the system as stable/unstable.(d) Find the step response of the system.2.6.2 Given the impulse response of a continuous-time LTI system, find the transfer function \(H(s),\) the \(\mathrm{ROC}\) of \(H(s)\), and the poles of the system. Also find the differential equation describing each system.(a) \(h(t)=\sin (3 t) u(t)\)(b)...
Please answer the signals and systems question clearly :)
Assume the following LTI system and the input signal whose spectrum depicted below 2. x(t) Y(o) H(a) X(a) 2π 2π 3TT 3π Find x(t), Y(ω), and y(t) for each of the following filters. 3 2 0 2 f)
Consider an LTI system with the impulse response h(t) = e- . Is the system casual? Explain. Find and plot the output s(t) given that the system input is x(t) = u(t). Note that s(t) in this case is commonly known as the step response of the system. If the input is x(t) = u(t)-u(t-T). Express the output y(t) as a function of s(t). Also, explicitly write the output y(t) as a function of t. a) b) c)
Also, solve the following problem. Consider a system made by cascading two LTI systems. The first system is described by y[n] = x [n] – ax (n – 3]. The second has impulse response h (n] = {po aP [n – 3p] with ( < a < 1. Find the impulse response of the overall system.
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