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Consider a causal LTI S9Stem whch s Characterized by the differente euation a) Determine the transfer...
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...
For a causal LTI discrete-time system described by the difference equation:
For a causal LTI discrete-time system described by the difference equation: y[n] + y[n – 1] = x[n] a) Find the transfer function H(z).b) Find poles and zeros and then mark them on the z-plane (pole-zero plot). Is this system BIBO? c) Find its impulse response h[n]. d) Draw the z-domain block diagram (using the unit delay block z-1) of the discrete-time system. e) Find the output y[n] for input x[n] = 10 u[n] if all initial conditions are 0.
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. The transfer function of a CT LTI system is given by H(s) (s2 +6s +10) (s2 -4s +8) a) Draw the...
2. The transfer function of a CT LTI system is given by H(s) (s2 +6s +10) (s2 -4s +8) a) Draw the pole-zero plot of the transfer function. b) Show all possible ROC's associated with this transfer function. c) Obtain the impulse response h(t) associated with each ROC of the transfer function. d) Which one (if any) of the impulse responses of part c) is stable?
2. The transfer function of a CT LTI system is given by H(s) (s2...
7. A causal LTI system has a transfer function given by H (z) = -1 (1...
7. A causal LTI system has a transfer function given by H (z) = -1 (1 4 The input to the system is x[n] = (0.5)"u[n] + u[-n-1] ) Find the impulse response of the system b) Determine the difference equation that describes the system. c) Find the output y[n]. d) Is the system stable?
(2) (10 points) Consider a causal LTI system which its zero-pole plot of H(z) is shown...
(2) (10 points) Consider a causal LTI system which its zero-pole plot of H(z) is shown in Fig. 1 2. Suppose it is known that lim h[n]= 1) Determine the h[n] of the system. 2) Determine the difference equation of this system. jim (z) 3) Draw the the Block Diagram of this system. -1/3 Re (z) 2 Fig. 2
For the following transfer function of an LTI system: Q.3) For the following transfer function of an ITI system: 8-5 (a...
For the following transfer function of an LTI system:
Q.3) For the following transfer function of an ITI system: 8-5 (a) Sketch the pole-zero plot. (b) If the system is stable, determine the large Why. st pssible ROC. Is the systeu causal? Explairn (c) If the system is causal, determine the lar gest possible ROC. Is the system stable? Explain
Q.3) For the following transfer function of an ITI system: 8-5 (a) Sketch the pole-zero plot. (b) If the system...
Consider three (causal) LTI systems, corresponding to transfer functions described (except for gain K) by the...
Consider three (causal) LTI systems, corresponding to transfer functions described (except for gain K) by the following pole-zero plots. Im Im ++j10 X - -100 - 10 Re -10 : 5 * +-j10 Pole-Zero Plot for System A Pole-Zero Plot for System B Pole-Zero Plot for System C In each part below, determine which of the three systems can meet the given specifications, including any implications on what value(s) the transfer function's gain K must be. (a) (10 points) The...
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
Consider a causal LTI system described by e yin]-ανίn- μ) = xjn] A. What is the...
Consider a causal LTI system described by e yin]-ανίn- μ) = xjn] A. What is the condition of o over which the system is BIBO stable? B. For & = /½ and u 2, find this system transfer function. C. For the same conditions in part B, find the frequency response H() D. Determine the magnitude and phase of H(o). E. Use MATLAB to sketch the magnitude spectrum over 0< w s 2n
Consider a causal LTI system described by...
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...
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. The transfer function of a CT LTI system is given by H(s) (s2 +6s +10) (s2 -4s +8) a) Draw the pole-zero plot of the transfer function. b) Show all possible ROC's associated with this transfer function. c) Obtain the impulse response h(t) associated with each ROC of the transfer function. d) Which one (if any) of the impulse responses of part c) is stable?
2. The transfer function of a CT LTI system is given by H(s) (s2...
7. A causal LTI system has a transfer function given by H (z) = -1 (1 4 The input to the system is x[n] = (0.5)"u[n] + u[-n-1] ) Find the impulse response of the system b) Determine the difference equation that describes the system. c) Find the output y[n]. d) Is the system stable?
(2) (10 points) Consider a causal LTI system which its zero-pole plot of H(z) is shown in Fig. 1 2. Suppose it is known that lim h[n]= 1) Determine the h[n] of the system. 2) Determine the difference equation of this system. jim (z) 3) Draw the the Block Diagram of this system. -1/3 Re (z) 2 Fig. 2
For the following transfer function of an LTI system:
Q.3) For the following transfer function of an ITI system: 8-5 (a) Sketch the pole-zero plot. (b) If the system is stable, determine the large Why. st pssible ROC. Is the systeu causal? Explairn (c) If the system is causal, determine the lar gest possible ROC. Is the system stable? Explain
Q.3) For the following transfer function of an ITI system: 8-5 (a) Sketch the pole-zero plot. (b) If the system...
Consider three (causal) LTI systems, corresponding to transfer functions described (except for gain K) by the following pole-zero plots. Im Im ++j10 X - -100 - 10 Re -10 : 5 * +-j10 Pole-Zero Plot for System A Pole-Zero Plot for System B Pole-Zero Plot for System C In each part below, determine which of the three systems can meet the given specifications, including any implications on what value(s) the transfer function's gain K must be. (a) (10 points) The...
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
Consider a causal LTI system described by e yin]-ανίn- μ) = xjn] A. What is the condition of o over which the system is BIBO stable? B. For & = /½ and u 2, find this system transfer function. C. For the same conditions in part B, find the frequency response H() D. Determine the magnitude and phase of H(o). E. Use MATLAB to sketch the magnitude spectrum over 0< w s 2n
Consider a causal LTI system described by...
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