(Frequency response of CT LTI systems): You want to design a system whose unit impulse response has the form:
(Frequency response of CT LTI systems): You want to design a system whose unit impulse response has the form:
h(t) =u(t) - u(t - N).
Find all possible values of N >0 such that when the input signal x(t) = cos(πt), the output signal y(t) = 0 for all t.
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(Frequency response of CT LTI systems): You want to design a system whose unit impulse response has the form:
3. Suppose that the frequency response of an LTI system is given by (a) What is...
3. Suppose that the frequency response of an LTI system is given by (a) What is the impulse response hinl) of the system? (b) Suppose that the input signal has the form zin-Ae'? n. For what values of ?0 in the range -r S will we have yn0 for all n? (c) Find the output y[n] of the system for the input x[n] = 3 + ?[n-2] cos(0.5?n 0.25m
Q1) Consider an LTI system with frequency response (u) given by (a) Find the impulse response h(0) for this system. [Hint: In case of polynomial over pohnomial frequency domain representation, we...
Q1) Consider an LTI system with frequency response (u) given by (a) Find the impulse response h(0) for this system. [Hint: In case of polynomial over pohnomial frequency domain representation, we analyce the denominator and use partial fraction expansion to write H() in the form Then we notice that each of these fraction terms is the Fourier of an exponentiol multiplied by a unit step as per the Table J (b) What is the output y(t) from the system if...
Consider that a CT system with unit impulse response h(t)=u(t) is excited by the input signal...
Consider that a CT system with unit impulse response h(t)=u(t) is excited by the input signal defined as 0,<-3 t +3,-3<t < 0 x(t) = { t -- +3,0 < t < 6 0,t> 6 Find the output of the system and plot it. (10 points)
2.7.5 The impulse response of a continuous-time LTI system is given by h(t) = f(t) -...
2.7.5 The impulse response of a continuous-time LTI system is given by h(t) = f(t) - et u(t). (a) What is the frequency response H (w) of this system? (b) Find and sketch H(w). (c) Is this a lowpass, bandpass, or highpass filter, or none of those? 2.7.6 The impulse response of a continuous-time LTI system is given by h(t) = S(t – 2). (This is a delay of 2.) (a) What is the frequency response H (w) of this...
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...
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...
The unit impulse response and the input to an LTI system are given by: h(t) u(t)...
The unit impulse response and the input to an LTI system are given by: h(t) u(t) - u(t - 4) x(t) e2[u(t)-u(t - 4)] x(t) 1 y(t) h(t) 1. Determine the output signal, i.e.y(t), you may use any method. 2. Is this system memoryless? Why? 3. Is this system causal? Why? 4. Is this system BIBO stable? Why?
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...
4. Consider a CT LTI system whose impulse response is given by h(t)( 3) (t 2))...
4. Consider a CT LTI system whose impulse response is given by h(t)( 3) (t 2)) (a) Sketch h(t), and label a mportant points. 2 2. b) Is the system causal? Circle your answer. No justification needed yes r ノ(c) Is the system stable? Circle your answer. No justification needed. or no ye d) Suppose the input to the system is r(t) ut 5). Over what range of t is the system output not equal to 0? Circle your answer....
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...
3. Suppose that the frequency response of an LTI system is given by (a) What is the impulse response hinl) of the system? (b) Suppose that the input signal has the form zin-Ae'? n. For what values of ?0 in the range -r S will we have yn0 for all n? (c) Find the output y[n] of the system for the input x[n] = 3 + ?[n-2] cos(0.5?n 0.25m
Q1) Consider an LTI system with frequency response (u) given by (a) Find the impulse response h(0) for this system. [Hint: In case of polynomial over pohnomial frequency domain representation, we analyce the denominator and use partial fraction expansion to write H() in the form Then we notice that each of these fraction terms is the Fourier of an exponentiol multiplied by a unit step as per the Table J (b) What is the output y(t) from the system if...
Consider that a CT system with unit impulse response h(t)=u(t) is excited by the input signal defined as 0,<-3 t +3,-3<t < 0 x(t) = { t -- +3,0 < t < 6 0,t> 6 Find the output of the system and plot it. (10 points)
2.7.5 The impulse response of a continuous-time LTI system is given by h(t) = f(t) - et u(t). (a) What is the frequency response H (w) of this system? (b) Find and sketch H(w). (c) Is this a lowpass, bandpass, or highpass filter, or none of those? 2.7.6 The impulse response of a continuous-time LTI system is given by h(t) = S(t – 2). (This is a delay of 2.) (a) What is the frequency response H (w) of this...
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...
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...
The unit impulse response and the input to an LTI system are given by: h(t) u(t) - u(t - 4) x(t) e2[u(t)-u(t - 4)] x(t) 1 y(t) h(t) 1. Determine the output signal, i.e.y(t), you may use any method. 2. Is this system memoryless? Why? 3. Is this system causal? Why? 4. Is this system BIBO stable? Why?
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...
4. Consider a CT LTI system whose impulse response is given by h(t)( 3) (t 2)) (a) Sketch h(t), and label a mportant points. 2 2. b) Is the system causal? Circle your answer. No justification needed yes r ノ(c) Is the system stable? Circle your answer. No justification needed. or no ye d) Suppose the input to the system is r(t) ut 5). Over what range of t is the system output not equal to 0? Circle your answer....
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...
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