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3. The a-transform of the unit-step response (the output when the input is ure) of a...
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...
A continuous-time LTI system has unit impulse response h(t). The Laplace transform of h(t), also called...
A continuous-time LTI system has unit impulse response h(t). The
Laplace transform of h(t), also called the “transfer function” of
the LTI system, is
.
For each of the following cases, determine the region of
convergence (ROC) for H(s) and the corresponding h(t), and
determine whether the Fourier transform of h(t) exists.
(a) The LTI system is causal but not stable.
(b) The LTI system is stable but not causal.
(c) The LTI system is neither stable nor causal
8...
Consider the LTI system with input ??(??) = ?? ?????(??) and the impulse response ?(??) =...
Consider the LTI system with input ??(??) = ?? ?????(??) and the
impulse response ?(??) = ?? ?2????(??). A. (3 points) Determine
??(??) and ??(??) and the ROCs B. (3 points) Using the
convolutional property of the Laplace transform, determine ??(??),
the Laplace transform of the output, ??(??) C. (3 points) From the
answer of part B, find ??(??)
9 points) Consider the LTI system with input x(t)eu(t) and the impulse response h(t)-e-2u(t) A. 3 points) Determine X(s) and H(s)...
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...
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
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...
Consider an LTI system with input sequence x[n] and output sequence y[n] that satisfy the difference equation
Consider an LTI system with input sequence x[n] and output sequence y[n] that satisfy the difference equation 3y[n] – 7y[n – 1] + 2y[n – 2] = 3x[n] – 3x[n – 1] (2.1) The fact that sequences x[ ] and y[ ] are in input-output relation and satisfy (2.1) does not yet determine which LTI system. a) We assume each possible input sequence to this system has its Z-transform and that the impulse response of this system also has its Z-transform. Express the...
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.
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...
Term brua 2019 Instructor: Ahnet A 1. Determine the Laplace transform and the associated region of...
Term brua 2019 Instructor: Ahnet A 1. Determine the Laplace transform and the associated region of convergence and pole-zero plot for each of the following functions of time (b) r(t)te-24 elsewhere (d) a(t) (t)+u(t) 2. Determine the function of time, a(t), for each of the following Laplace transforms and their associated regions of convergenice: )부부, Rds) > 1 d)승부 R1(s) >-1 3. Consider an LTI systern with input r(t)-ε-lu(t) and impulse response h(t)-e-2u(t). (a) Determine the Laplace transforms of ar(t)...
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...
A continuous-time LTI system has unit impulse response h(t). The
Laplace transform of h(t), also called the “transfer function” of
the LTI system, is
.
For each of the following cases, determine the region of
convergence (ROC) for H(s) and the corresponding h(t), and
determine whether the Fourier transform of h(t) exists.
(a) The LTI system is causal but not stable.
(b) The LTI system is stable but not causal.
(c) The LTI system is neither stable nor causal
8...
Consider the LTI system with input ??(??) = ?? ?????(??) and the
impulse response ?(??) = ?? ?2????(??). A. (3 points) Determine
??(??) and ??(??) and the ROCs B. (3 points) Using the
convolutional property of the Laplace transform, determine ??(??),
the Laplace transform of the output, ??(??) C. (3 points) From the
answer of part B, find ??(??)
9 points) Consider the LTI system with input x(t)eu(t) and the impulse response h(t)-e-2u(t) A. 3 points) Determine X(s) and H(s)...
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...
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
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...
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.
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...
Term brua 2019 Instructor: Ahnet A 1. Determine the Laplace transform and the associated region of convergence and pole-zero plot for each of the following functions of time (b) r(t)te-24 elsewhere (d) a(t) (t)+u(t) 2. Determine the function of time, a(t), for each of the following Laplace transforms and their associated regions of convergenice: )부부, Rds) > 1 d)승부 R1(s) >-1 3. Consider an LTI systern with input r(t)-ε-lu(t) and impulse response h(t)-e-2u(t). (a) Determine the Laplace transforms of ar(t)...
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