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The input x(t) and output y(t) of a causal LTI system are related through the block-diagram...
2. Consider the causal LTI system in which the input x(t) and output y(t) are related...
2. Consider the causal LTI system in which the input x(t) and output y(t) are related through the following block diagram respresentation: x(t) y(t) + 1/s # 7 -5 1/s 10 6 a. Find the system function. (2.5 points). b. Determine the differential equation relating y(t) and x(t). (2.5 points). c. Show that this system can be realized as a cascade interconnection of four first order subsystems. Give the system function for each subsystem, and sketch the block diagram of...
5. 10pt] The input and output of a stable and causal LTI system are related by...
5. 10pt] The input and output of a stable and causal LTI system are related by the differential dt2 dt Find the impulse response of this system
discrete time signals and systems causal LTI system has the block diagram: (a) find a difference...
discrete time signals and systems
causal LTI system has the block diagram:
(a) find a difference equation relating y[n] and x[n]
(b) determine if the system is stable
// هبه ۸[u] [u]x
Problem 3. The input and the output of a stable and causal LTI system are related...
Problem 3. The input and the output of a stable and causal LTI system are related by the differential equation dy ) + 64x2 + 8y(t) = 2x(t) dt2 dt i) Find the frequency response of the system H(jw) [2 marks] ii) Using your result in (i) find the impulse response of the system h(t). [3 marks] iii) Find the transfer function of the system H(s), i.e. the Laplace transform of the impulse response [2 marks] iv) Sketch the pole-zero...
Consider a causal LTI system whose input xn] and output y[n] are related by the differenoe equati...
Consider a causal LTI system whose input xn] and output y[n] are related by the differenoe equation yn In--n] a. Find the impulse response of the system (without using any transform). (5 marks) b. Using convolution determine yin, 1f XIn = 1 un.(6 marks
Consider a causal LTI system whose input xn] and output y[n] are related by the differenoe equation yn In--n] a. Find the impulse response of the system (without using any transform). (5 marks) b. Using convolution...
Consider an LTI system whose input x[n] and output y[n] are related by the difference equation...
Consider an LTI system whose input x[n] and output y[n] are related by the difference equation y[n – 1] + 3 y[n] + $y[n + 1] = x[n]. Determine the three possible choices for the impulse response that makes this system 1) causal, 2) two-sided and 3) anti-causal. Then for each case, determine if the system is stable or not. Causality Impulse Response Stability Causal Unstable v two-sided Unstable anti-Causal Unstable y In your answers, enter z(n) for a discrete-time...
(2) Consider the causal discrete-time LTI system with an input r (n) and an output y(n)...
(2) Consider the causal discrete-time LTI system with an input r (n) and an output y(n) as shown in Figure 1, where K 6 (constant), system #1 is described by its impulse response: h(n) = -36(n) + 0.48(n- 1)+8.26(n-2), and system # 2 has the difference equation given by: y(n)+0.1y(n-1)+0.3y(n-2)- 2a(n). (a) Determine the corresponding difference equation of the system #1. Hence, write its fre- quency response. (b) Find the frequency response of system #2. 1 system #1 system #2...
dy(D), 5) Consider a causal LTI system S described by the following differential equation: 2 +...
dy(D), 5) Consider a causal LTI system S described by the following differential equation: 2 + 3y(t) = x(t). Draw a block digram representation for S. Then, convert this differential equation into an integral equation, and draw a corresponding block diagram representation. dt
A causal LTI system yields the following input output relationship. Find h(t), the impulse response of...
A causal LTI system yields the following input output relationship. Find h(t), the impulse response of the system. (Hint: Try first to determine the output when the input is u(t)) a(t) y(t) LTT →t 2 2 Figure 1: An input-output pair
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)...
2. Consider the causal LTI system in which the input x(t) and output y(t) are related through the following block diagram respresentation: x(t) y(t) + 1/s # 7 -5 1/s 10 6 a. Find the system function. (2.5 points). b. Determine the differential equation relating y(t) and x(t). (2.5 points). c. Show that this system can be realized as a cascade interconnection of four first order subsystems. Give the system function for each subsystem, and sketch the block diagram of...
5. 10pt] The input and output of a stable and causal LTI system are related by the differential dt2 dt Find the impulse response of this system
discrete time signals and systems
causal LTI system has the block diagram:
(a) find a difference equation relating y[n] and x[n]
(b) determine if the system is stable
// هبه ۸[u] [u]x
Problem 3. The input and the output of a stable and causal LTI system are related by the differential equation dy ) + 64x2 + 8y(t) = 2x(t) dt2 dt i) Find the frequency response of the system H(jw) [2 marks] ii) Using your result in (i) find the impulse response of the system h(t). [3 marks] iii) Find the transfer function of the system H(s), i.e. the Laplace transform of the impulse response [2 marks] iv) Sketch the pole-zero...
Consider a causal LTI system whose input xn] and output y[n] are related by the differenoe equation yn In--n] a. Find the impulse response of the system (without using any transform). (5 marks) b. Using convolution determine yin, 1f XIn = 1 un.(6 marks
Consider a causal LTI system whose input xn] and output y[n] are related by the differenoe equation yn In--n] a. Find the impulse response of the system (without using any transform). (5 marks) b. Using convolution...
Consider an LTI system whose input x[n] and output y[n] are related by the difference equation y[n – 1] + 3 y[n] + $y[n + 1] = x[n]. Determine the three possible choices for the impulse response that makes this system 1) causal, 2) two-sided and 3) anti-causal. Then for each case, determine if the system is stable or not. Causality Impulse Response Stability Causal Unstable v two-sided Unstable anti-Causal Unstable y In your answers, enter z(n) for a discrete-time...
(2) Consider the causal discrete-time LTI system with an input r (n) and an output y(n) as shown in Figure 1, where K 6 (constant), system #1 is described by its impulse response: h(n) = -36(n) + 0.48(n- 1)+8.26(n-2), and system # 2 has the difference equation given by: y(n)+0.1y(n-1)+0.3y(n-2)- 2a(n). (a) Determine the corresponding difference equation of the system #1. Hence, write its fre- quency response. (b) Find the frequency response of system #2. 1 system #1 system #2...
dy(D), 5) Consider a causal LTI system S described by the following differential equation: 2 + 3y(t) = x(t). Draw a block digram representation for S. Then, convert this differential equation into an integral equation, and draw a corresponding block diagram representation. dt
A causal LTI system yields the following input output relationship. Find h(t), the impulse response of the system. (Hint: Try first to determine the output when the input is u(t)) a(t) y(t) LTT →t 2 2 Figure 1: An input-output pair
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)...
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