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 previous problem. Use Parseval's Identity to compute the power P∞ of the output y(t). Use Parseval's Theorem to compute the energy E∞ of the impulse response h(t)
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LTI Systems. Consider two LTI subsystems that are connected in series
Using parsevals theorem and FT to find y(t) and its power (b) (4 pts) Fourier Series The input signal r(t) and impulse...
Using parsevals theorem and FT to find y(t) and its power
(b) (4 pts) Fourier Series The input signal r(t) and impulse response h(t) of an LTI system are as follows: z(t) = sin(2t)cos(t)-e131 + 2 and h(t) = sin(21) Use the Fourier Series method to find the output y(t) (c) (4 pts) Parseval's Identity and Theorem. Consider the system in the previous problem. Use Parseval's Identity to compute the power P of the output y(t). Use Parseval's Theorem to...
3. Consider an LTI system with the impulse response h(t)e Find the Fourier series representation for...
3. Consider an LTI system with the impulse response h(t)e Find the Fourier series representation for the output y(t) for each of the inputs below: b ra(t) in Figure 2. Figure 2: a2(t)
signals and systems Question 1 (30%): Consider a LTI systern which is comprised of four subsystems...
signals and systems
Question 1 (30%): Consider a LTI systern which is comprised of four subsystems whose impulse responses are hi(t), h2(t). ha(t), and ha(t). u(t) f(t) hi(t) h2(t) 13 ha(1) Where: hi (t) = δ(t + 1) h2(t) = 2(u(t)-u(t-1)] hs(t) = 201t-2) h1(t) = u(t + 2)-u(t) a) (8%) Compute the overall impulse response htotal(t) of the system comprised of hi(t), h2(t), hs(t), and h4(t). Sketch and write the expression for htotai(t) b) (4%) Is the total system...
This is a fourier series/ transform question Consider an LTI system whose response to the input...
This is a fourier series/ transform question
Consider an LTI system whose response to the input x)lee3ut) is y)12e-2e4Ju) (a) Find the frequency response of this system. (b) Determine the system's impulse response (c) Find the differential equation relating the input and the output of this system.
Consider a LTI system with impulse response h[n] = u[n]*a^n, where |a| < 1. a) Determine...
Consider a LTI system with impulse response h[n] = u[n]*a^n, where |a| < 1. a) Determine the frequency response of the system. b) Find the magnitude response and the phase response, given a = 1/2. No plots. c) Consider a LTI system whose impulse response h1[n] is a time-shifted version of h[n], i.e., h1[n] = h[n − n0]. Compute the frequency response H1(e^(jΩ)), and represent H1(e^(jΩ)) in terms of H(e^(jΩ)).
2. Consider the following interconnection of four LTI systems where each system is described by its...
2. Consider the following interconnection of four LTI systems where each system is described by its impulse response, denoted by h,(t) for i E (1,2,3,4): i (t) hi(t) r(t) z(t) (t)h) но hs(t) alt) h4(t) 2(t) It is not hard, but is tedious, to show that an interconnection of LTI systems is LTI. Assuming this result, consider the system a(t) b(t) where r(t) and b(t) are the same signals in the two block diagrams and h(t) is the impulse response...
(e) Consider an LTI system with impulse response h(t) = π8ǐnc(2(t-1). i. (5 pts) Find the frequency response H(jw). Hint: Use the FT properties and pairs tables. ii. (5 pts) Find the output y(t) when...
(e) Consider an LTI system with impulse response h(t) = π8ǐnc(2(t-1). i. (5 pts) Find the frequency response H(jw). Hint: Use the FT properties and pairs tables. ii. (5 pts) Find the output y(t) when the input is (tsin(t) by using the Fourier Transform method. 3. Fourier Transforms: LTI Systems Described by LCCDE (35 pts) (a) Consider a causal (meaning zero initial conditions) LTI system represented by its input-output relationship in the form of a differential equation:-p +3讐+ 2y(t)--r(t). i....
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)...
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...
LTI Systems and Discrete-Time Fourier Series-1 Problem Statement Consider a causal discrete-time LTI system whose input...
LTI Systems and Discrete-Time Fourier Series-1 Problem Statement Consider a causal discrete-time LTI system whose input r[n] and output yinl are related by the following equation: Find the Fourier series representation of the output y[n] for (b) ncos()
Using parsevals theorem and FT to find y(t) and its power
(b) (4 pts) Fourier Series The input signal r(t) and impulse response h(t) of an LTI system are as follows: z(t) = sin(2t)cos(t)-e131 + 2 and h(t) = sin(21) Use the Fourier Series method to find the output y(t) (c) (4 pts) Parseval's Identity and Theorem. Consider the system in the previous problem. Use Parseval's Identity to compute the power P of the output y(t). Use Parseval's Theorem to...
3. Consider an LTI system with the impulse response h(t)e Find the Fourier series representation for the output y(t) for each of the inputs below: b ra(t) in Figure 2. Figure 2: a2(t)
signals and systems
Question 1 (30%): Consider a LTI systern which is comprised of four subsystems whose impulse responses are hi(t), h2(t). ha(t), and ha(t). u(t) f(t) hi(t) h2(t) 13 ha(1) Where: hi (t) = δ(t + 1) h2(t) = 2(u(t)-u(t-1)] hs(t) = 201t-2) h1(t) = u(t + 2)-u(t) a) (8%) Compute the overall impulse response htotal(t) of the system comprised of hi(t), h2(t), hs(t), and h4(t). Sketch and write the expression for htotai(t) b) (4%) Is the total system...
This is a fourier series/ transform question
Consider an LTI system whose response to the input x)lee3ut) is y)12e-2e4Ju) (a) Find the frequency response of this system. (b) Determine the system's impulse response (c) Find the differential equation relating the input and the output of this system.
2. Consider the following interconnection of four LTI systems where each system is described by its impulse response, denoted by h,(t) for i E (1,2,3,4): i (t) hi(t) r(t) z(t) (t)h) но hs(t) alt) h4(t) 2(t) It is not hard, but is tedious, to show that an interconnection of LTI systems is LTI. Assuming this result, consider the system a(t) b(t) where r(t) and b(t) are the same signals in the two block diagrams and h(t) is the impulse response...
(e) Consider an LTI system with impulse response h(t) = π8ǐnc(2(t-1). i. (5 pts) Find the frequency response H(jw). Hint: Use the FT properties and pairs tables. ii. (5 pts) Find the output y(t) when the input is (tsin(t) by using the Fourier Transform method. 3. Fourier Transforms: LTI Systems Described by LCCDE (35 pts) (a) Consider a causal (meaning zero initial conditions) LTI system represented by its input-output relationship in the form of a differential equation:-p +3讐+ 2y(t)--r(t). i....
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)...
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...
LTI Systems and Discrete-Time Fourier Series-1 Problem Statement Consider a causal discrete-time LTI system whose input r[n] and output yinl are related by the following equation: Find the Fourier series representation of the output y[n] for (b) ncos()
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