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![bC1 = (4)^4 [] = [u] (+39-3 [n-4) a [n] *h [n] y [n] = 20 Ž *177 h (t-T7 mm UGT) Ź 6,7-3 4[7-43 (14*** u () T-3 u [T-4] (62)](http://img.homeworklib.com/questions/f1b1a0d0-2289-11eb-9687-75eda24166e8.png?x-oss-process=image/resize,w_560)
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Discrete-time convolution. Use of shift invariance for LTI systems. A discrete-time LTI system is described the...
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.
CONVOLUTION - Questions 4 and 5 4. Consider an LTI system with an impulse response h(n)...
CONVOLUTION - Questions 4 and 5 4. Consider an LTI system with an impulse response h(n) = [1 2 1] for 0 <n<2. If the input to the system is x(n) = u(n)-un-2) where u(n) is the unit-step, calculate the output of the system y(n) analytically. Check your answer using the "conv" function in MATLAB. 5. Consider an LTI system with an impulse response h(n) = u(n) where u(n) is the unit-step. (a) If the input to the system is...
A causal discrete-time LTI system is described by the equation
A causal discrete-time LTI system is described by the equationwhere z is the input signal, and y the output signal y(n) = 1/3x(n) + 1/3x(n -1) + 1/3x(n - 2) (a) Sketch the impulse response of the system. (b) What is the dc gain of the system? (Find Hf(0).) (c) Sketch the output of the system when the input x(n) is the constant unity signal, x(n) = 1. (d) Sketch the output of the system when the input x(n) is the unit step signal, x(n)...
Name: 10. [8 points] Consider a discrete-time LTI system with input x[n] and out- put y[n]....
Name: 10. [8 points] Consider a discrete-time LTI system with input x[n] and out- put y[n]. When the input signal x[n] = (6)" is applied to the system, the output signal is y[n] = 0 for all n When the input signal xn] (3)" u[n] is applied to the system, the output signal is y[n] = A 8[n] + 2 (5)" u[n] for all n, where A is a constant number a) Find A. b) Find the impulse response of...
Consider a discrete-time LTI system with impulse response hn on-un-1), where jal < 1. Find the...
Consider a discrete-time LTI system with impulse response hn on-un-1), where jal < 1. Find the output y[n] of the system to the input x[n] = un +1].
Problem 3) Two discrete-time LTI systems are connected in cascade. The first system is defined by...
Problem 3) Two discrete-time LTI systems are connected in cascade. The first system is defined by its frequency response: H(e-1+and the second system is (a) Determine the frequency response for the overall cascade system. Simplify your (c) Write down the difference equation that relates the output y[n] to the input x[n]. defined by its impulse response: hln]-n-n-+n-2]-n-3] answer as far as possible. (b) Determine and plot the impulse response h[n] for the overall cascade system.
6) Consider a discrete-time LTI system with impulse response h[n] = response h[n] = ( 1)...
6) Consider a discrete-time LTI system with impulse response h[n] = response h[n] = ( 1) u[n]. Use Fourie transforms to determine the response of this system to the input x[n] = ml + un).
Problem 4. Use the convolution integral to find the response y(t) of the LTI system with...
Problem 4. Use the convolution integral to find the response y(t) of the LTI system with impulse response h(t) to input x(t) a) x(I)-2expl_2t)u(t) , h(1)-expl-t)u(t)
The unit-sample response of a DT LTI system is h[n], shown below. Use linearity and time-invariance...
The unit-sample response of a DT LTI system is h[n], shown
below.
Use linearity and time-invariance to find the response of the
system to each of the inputs below.
(a) x[n] = δ[n] − δ[n − 3]
(b) x[n] = u[n]
(c) x[n] = 3δ[n] − 2(δ[n + 1] + δ[n − 1]) + δ[n + 2] + δ[n −
2]
Problem 3. The unit-sample response of a DT LTI system is hn], shown below. h[n] 2, 0,1 h[n-1, -2...
Use MATLAB to compute the convolution as a sum ofechoes of the input signal x[n] = cos () with th...
Use MATLAB to compute the convolution as a sum ofechoes of the input signal x[n] = cos () with the impulse response h[n]1.5un un - 6]) of an LTI system S. Is the output periodic? Why or why not? Please explain.
Use MATLAB to compute the convolution as a sum ofechoes of the input signal x[n] = cos () with the impulse response h[n]1.5un un - 6]) of an LTI system S. Is the output periodic? Why or why not?...
CONVOLUTION - Questions 4 and 5 4. Consider an LTI system with an impulse response h(n) = [1 2 1] for 0 <n<2. If the input to the system is x(n) = u(n)-un-2) where u(n) is the unit-step, calculate the output of the system y(n) analytically. Check your answer using the "conv" function in MATLAB. 5. Consider an LTI system with an impulse response h(n) = u(n) where u(n) is the unit-step. (a) If the input to the system is...
Name: 10. [8 points] Consider a discrete-time LTI system with input x[n] and out- put y[n]. When the input signal x[n] = (6)" is applied to the system, the output signal is y[n] = 0 for all n When the input signal xn] (3)" u[n] is applied to the system, the output signal is y[n] = A 8[n] + 2 (5)" u[n] for all n, where A is a constant number a) Find A. b) Find the impulse response of...
Consider a discrete-time LTI system with impulse response hn on-un-1), where jal < 1. Find the output y[n] of the system to the input x[n] = un +1].
Problem 3) Two discrete-time LTI systems are connected in cascade. The first system is defined by its frequency response: H(e-1+and the second system is (a) Determine the frequency response for the overall cascade system. Simplify your (c) Write down the difference equation that relates the output y[n] to the input x[n]. defined by its impulse response: hln]-n-n-+n-2]-n-3] answer as far as possible. (b) Determine and plot the impulse response h[n] for the overall cascade system.
6) Consider a discrete-time LTI system with impulse response h[n] = response h[n] = ( 1) u[n]. Use Fourie transforms to determine the response of this system to the input x[n] = ml + un).
Problem 4. Use the convolution integral to find the response y(t) of the LTI system with impulse response h(t) to input x(t) a) x(I)-2expl_2t)u(t) , h(1)-expl-t)u(t)
The unit-sample response of a DT LTI system is h[n], shown
below.
Use linearity and time-invariance to find the response of the
system to each of the inputs below.
(a) x[n] = δ[n] − δ[n − 3]
(b) x[n] = u[n]
(c) x[n] = 3δ[n] − 2(δ[n + 1] + δ[n − 1]) + δ[n + 2] + δ[n −
2]
Problem 3. The unit-sample response of a DT LTI system is hn], shown below. h[n] 2, 0,1 h[n-1, -2...
Use MATLAB to compute the convolution as a sum ofechoes of the input signal x[n] = cos () with the impulse response h[n]1.5un un - 6]) of an LTI system S. Is the output periodic? Why or why not? Please explain.
Use MATLAB to compute the convolution as a sum ofechoes of the input signal x[n] = cos () with the impulse response h[n]1.5un un - 6]) of an LTI system S. Is the output periodic? Why or why not?...
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