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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()....
1. Given the impulse response, h[n duration 50 samples. (-0.9)"u[n, find the step response for a step input of h-(0...
1. Given the impulse response, h[n duration 50 samples. (-0.9)"u[n, find the step response for a step input of h-(0.9)-10:491 -ones (1,50) s- conv(u,h) 2. Plot h and u using stem function for 50 samples only stem(10:491, s(1:50) 1. Given a system described by the following difference equation: yIn] 1143yn 1 0.4128y[n -2 0.0675x[n0.1349xn 0.675x[n-2] Determine the output y in response to zero input and the initial conditionsy-11 and yl-2] 2 for 50 samples using the following commands: a -,-1.143,...
Consider the LTI system described by the following impulse response: (a) h(n) = 2(0.5)n u(n). Determine:...
Consider the LTI system described by the following impulse response: (a) h(n) = 2(0.5)n u(n). Determine: (i) The system function representation; (ii) the difference-equation representation (Note: this is just terminology that refers to expressing the input and output time-domain signals in the form of an equation. E.g., what we did when we went over the equations for block diagrams); (iii) The pole-zero plot, sketched by hand; and (iv) the output y(n) if the input is x(n) = (0.25)n u(n) [10...
(20 pts.) Determine the output sequence of the system with impulse response h[n] 6. u[n] when the input signal is x[n]...
(20 pts.) Determine the output sequence of the system with impulse response h[n] 6. u[n] when the input signal is x[n] = 2e-n + sin(nn)- 2, -co <n< 0o. 7. (20 pts.) Determine the response of the system described by the difference equation 1 1 y(n)y(n1)n2)x(n 8 7 for input signal x(n) u(n) under the following initial conditions 1, y(-2) 0.5 y(-1)
(20 pts.) Determine the output sequence of the system with impulse response h[n] 6. u[n] when the input...
(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....
Question 1 (10 pts): Consider the continuous-time LTI system S whose unit impulse response h is given by Le., h consists of a unit impulse at time 0 followed by a unit impulse at time (a) (2pts)...
Question 1 (10 pts): Consider the continuous-time LTI system S whose unit impulse response h is given by Le., h consists of a unit impulse at time 0 followed by a unit impulse at time (a) (2pts) Obtain and plot the unit step response of S. (b) (2pts) Is S stable? Is it causal? Explain Two unrelated questions (c) (2pts) Is the ideal low-pass continuous-time filter (frequency response H(w) for H()0 otherwise) causal? Explain (d) (4 pts) Is the discrete-time...
The input-output relationship for a system is ¨y(t) + ˙y(t) = x(t). (a) Find the impulse...
The input-output relationship for a system is ¨y(t) + ˙y(t) = x(t). (a) Find the impulse response of the system. (b) Find the zero-state response when the input is a unit step. (c) Find the zero-state response when the input is x(t) = 1.6u(t) − 0.6u(t − 1).
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)
Problem 3.6 i) Compute the causal impulse response, h, and the anti-causal impulse response, h, for...
Problem 3.6 i) Compute the causal impulse response, h, and the anti-causal impulse response, h, for the system described by the input-output differential equation (D? + 9)y = (2D + 1)u. ii) Show that the anti-causal impulse response has a significant physical meaning: It is the autonomous output of a system that can be stopped (i.e. made equal to zero) by applying a Dirac-impulse 8(t) at the input. iii) How would an arbitrary solution in Sol (D2 +9), the set...
1. An LTI system has an impulse response h[n] for which thez transform is a. Plot...
1. An LTI system has an impulse response h[n] for which thez transform is a. Plot the pole-zero pattern for H(z). b. Using the fact that signals of the form z are eigenfunctions of LTI systems, determine the system output for all n if the input x [n] is given by 72 I3(2)
The impulse response h(t) of a linear time-invariant system is 2*pi[(t-2)/2]. Find and plot the output...
The impulse response h(t) of a linear time-invariant system is 2*pi[(t-2)/2]. Find and plot the output when the system is driven by an input signal that is identical to the impulse response.
1. Given the impulse response, h[n duration 50 samples. (-0.9)"u[n, find the step response for a step input of h-(0.9)-10:491 -ones (1,50) s- conv(u,h) 2. Plot h and u using stem function for 50 samples only stem(10:491, s(1:50) 1. Given a system described by the following difference equation: yIn] 1143yn 1 0.4128y[n -2 0.0675x[n0.1349xn 0.675x[n-2] Determine the output y in response to zero input and the initial conditionsy-11 and yl-2] 2 for 50 samples using the following commands: a -,-1.143,...
(20 pts.) Determine the output sequence of the system with impulse response h[n] 6. u[n] when the input signal is x[n] = 2e-n + sin(nn)- 2, -co <n< 0o. 7. (20 pts.) Determine the response of the system described by the difference equation 1 1 y(n)y(n1)n2)x(n 8 7 for input signal x(n) u(n) under the following initial conditions 1, y(-2) 0.5 y(-1)
(20 pts.) Determine the output sequence of the system with impulse response h[n] 6. u[n] when the input...
(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....
Question 1 (10 pts): Consider the continuous-time LTI system S whose unit impulse response h is given by Le., h consists of a unit impulse at time 0 followed by a unit impulse at time (a) (2pts) Obtain and plot the unit step response of S. (b) (2pts) Is S stable? Is it causal? Explain Two unrelated questions (c) (2pts) Is the ideal low-pass continuous-time filter (frequency response H(w) for H()0 otherwise) causal? Explain (d) (4 pts) Is the discrete-time...
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)
Problem 3.6 i) Compute the causal impulse response, h, and the anti-causal impulse response, h, for the system described by the input-output differential equation (D? + 9)y = (2D + 1)u. ii) Show that the anti-causal impulse response has a significant physical meaning: It is the autonomous output of a system that can be stopped (i.e. made equal to zero) by applying a Dirac-impulse 8(t) at the input. iii) How would an arbitrary solution in Sol (D2 +9), the set...
1. An LTI system has an impulse response h[n] for which thez transform is a. Plot the pole-zero pattern for H(z). b. Using the fact that signals of the form z are eigenfunctions of LTI systems, determine the system output for all n if the input x [n] is given by 72 I3(2)
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