![6. If a LTI DT system as h[n]-(-(2/3)(-0 ?) + (5/3)(075)a[n] and the n]--1.5-n-1], use both Z-trans system. given by the sequence sforms and convolution to obtain the output vizl of the sample response input to this system is](http://img.homeworklib.com/questions/eea99e40-0d96-11ec-a964-1bd139e73129.png?x-oss-process=image/resize,w_560)
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6. If a LTI DT system as h[n]-(-(2/3)(-0 ?)" + (5/3)(075)"a[n] and the n]--1.5-n-1], use both...
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...
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...
5. Use the BZT to obtain the output of a system described by the unit sample response h[r11-4-n-l] when the input is the sequence ln)-025". Use MATLAB to plot the output sequence that results...
5. Use the BZT to obtain the output of a system described by the unit sample response h[r11-4-n-l] when the input is the sequence ln)-025". Use MATLAB to plot the output sequence that results, 6. Use the BZT to obtain the output of a system described by the unit sample response h[n] [n-l] when the input is the sequence xln]-2"ul-i]
5. Use the BZT to obtain the output of a system described by the unit sample response h[r11-4-n-l] when the...
Question 2: Consider the following DT signal: g[n] = 2 "u[-n – 3] * a[n+3], a)...
Question 2: Consider the following DT signal: g[n] = 2 "u[-n – 3] * a[n+3], a) Find the convolution sum in the time domain (show all the necessary steps). b) Consider an LTI system with an input of x[n] and impulse response of h[n] as given below: 2, if n = -1 1, if n=0 x[n] = 3-2, if n=1 3, if n=2 -4, if n=3 3, if n = -1 1, if n=0,2 h[n] = 2, if n =...
(Convolution DT) consider the following LTI system with input x[n] and output y[n]: (a) sketchbthe input...
(Convolution DT) consider the following LTI system with input x[n] and output y[n]: (a) sketchbthe input signal x[n] = (1/2)^n(u[n])
Discrete-time convolution. Use of shift invariance for LTI systems. A discrete-time LTI system is described the...
Discrete-time convolution. Use of shift invariance for LTI systems. A discrete-time LTI system is described the its impulse response h[n]. h[n] = (5)"u[n]. n-3 1 An input x[n] = u[n – 4) is applied. The output of the system y[n] is given by: x[r] – 54 G)" ()") un 14 The correct answer is not provided gắn] = [16(5)” – 54(5) ] n] y[n] = [16()" – 54(+)"] uſn – 4
5 pts D Question 1 A system has the following impulse response: .2 Sample number, n From the choices below, select the frequency response of this system. H (eju)-e(1.5 ) (2 sin( 1.5ώ) +...
5 pts D Question 1 A system has the following impulse response: .2 Sample number, n From the choices below, select the frequency response of this system. H (eju)-e(1.5 ) (2 sin( 1.5ώ) + 4 sin(0.δώ)) H (ee) = e-j(1.5e-5) (cos( 1.5 ) +2 cos(0.54)) @ H (ee)-e-n1.si) (sin( 1.54) t. 2 sin(0.δώ)) (sin(l.50) +4sin(0.0) H (ee)-e-j(1.5i) (2 cos( 1.5ώ) + 4 cos(0.5a)) H (efo)-e-n1.5u) (cos( 1.50) + 2 cos(0.50)) https://rmitinstructure.comcoursesy 5 pts DQuestion 2 A system has the following...
eatu(t), (a >0), is 6(t). Find the response 5. The response of an LTI system to...
eatu(t), (a >0), is 6(t). Find the response 5. The response of an LTI system to e of the system to r(t)= eat cos (Bt)u (t). You have to express the response in terms of 5(t), u (t), sine function, and exponential function. (20 pts) -ly(t)), where * denotes convolution operator. (3) ()[() ]- dt d d Hint: dt
eatu(t), (a >0), is 6(t). Find the response 5. The response of an LTI system to e of the system to...
2) An LTI DT system is defined by the difference equation: y[n] = -0.4yIn - 1]...
2) An LTI DT system is defined by the difference equation: y[n] = -0.4yIn - 1] + x[n]. a) Derive the impulse response of the system. (2 pt) b) Determine if the system is BIBO stable. (1 pt) c) Assuming initial conditions yl-1) = 1, derive the complete system response to an input x[n] = u[n] - u[n-2), for n > 0.(2 pt) d) Derive the zero-state system response to an input z[n] = u[n] - 2u[n - 2] +...
Problem 3 Assume a system function of an LTI system is H(-) =(257-6 The input to...
Problem 3 Assume a system function of an LTI system is H(-) =(257-6 The input to the system x(n) = 3"u(n). Assuming y(n) and Y(z) are the Z-transform pair, and y(n) is the output of the above system: a) determine Y(z) assuming ROC of H(z) is z/>3 b) Determine y(n) by inverting Y(z) using the method of residuals (assuming ROC of H(z) is [z/>3) c) What is the ROC of a stable system given by H(z) ? d) What is...
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...
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...
5. Use the BZT to obtain the output of a system described by the unit sample response h[r11-4-n-l] when the input is the sequence ln)-025". Use MATLAB to plot the output sequence that results, 6. Use the BZT to obtain the output of a system described by the unit sample response h[n] [n-l] when the input is the sequence xln]-2"ul-i]
5. Use the BZT to obtain the output of a system described by the unit sample response h[r11-4-n-l] when the...
Question 2: Consider the following DT signal: g[n] = 2 "u[-n – 3] * a[n+3], a) Find the convolution sum in the time domain (show all the necessary steps). b) Consider an LTI system with an input of x[n] and impulse response of h[n] as given below: 2, if n = -1 1, if n=0 x[n] = 3-2, if n=1 3, if n=2 -4, if n=3 3, if n = -1 1, if n=0,2 h[n] = 2, if n =...
Discrete-time convolution. Use of shift invariance for LTI systems. A discrete-time LTI system is described the its impulse response h[n]. h[n] = (5)"u[n]. n-3 1 An input x[n] = u[n – 4) is applied. The output of the system y[n] is given by: x[r] – 54 G)" ()") un 14 The correct answer is not provided gắn] = [16(5)” – 54(5) ] n] y[n] = [16()" – 54(+)"] uſn – 4
5 pts D Question 1 A system has the following impulse response: .2 Sample number, n From the choices below, select the frequency response of this system. H (eju)-e(1.5 ) (2 sin( 1.5ώ) + 4 sin(0.δώ)) H (ee) = e-j(1.5e-5) (cos( 1.5 ) +2 cos(0.54)) @ H (ee)-e-n1.si) (sin( 1.54) t. 2 sin(0.δώ)) (sin(l.50) +4sin(0.0) H (ee)-e-j(1.5i) (2 cos( 1.5ώ) + 4 cos(0.5a)) H (efo)-e-n1.5u) (cos( 1.50) + 2 cos(0.50)) https://rmitinstructure.comcoursesy 5 pts DQuestion 2 A system has the following...
eatu(t), (a >0), is 6(t). Find the response 5. The response of an LTI system to e of the system to r(t)= eat cos (Bt)u (t). You have to express the response in terms of 5(t), u (t), sine function, and exponential function. (20 pts) -ly(t)), where * denotes convolution operator. (3) ()[() ]- dt d d Hint: dt
eatu(t), (a >0), is 6(t). Find the response 5. The response of an LTI system to e of the system to...
2) An LTI DT system is defined by the difference equation: y[n] = -0.4yIn - 1] + x[n]. a) Derive the impulse response of the system. (2 pt) b) Determine if the system is BIBO stable. (1 pt) c) Assuming initial conditions yl-1) = 1, derive the complete system response to an input x[n] = u[n] - u[n-2), for n > 0.(2 pt) d) Derive the zero-state system response to an input z[n] = u[n] - 2u[n - 2] +...
Problem 3 Assume a system function of an LTI system is H(-) =(257-6 The input to the system x(n) = 3"u(n). Assuming y(n) and Y(z) are the Z-transform pair, and y(n) is the output of the above system: a) determine Y(z) assuming ROC of H(z) is z/>3 b) Determine y(n) by inverting Y(z) using the method of residuals (assuming ROC of H(z) is [z/>3) c) What is the ROC of a stable system given by H(z) ? d) What is...
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