![6 Impulse Response Let h(t) denote the response of a system for which the input signal is the unit-impulse t 0: he(t) = t [a(t) _ u(t-1)] + 2a(t-2), for t > 0.](http://img.homeworklib.com/questions/6360d270-466c-11eb-b3bb-ddeb68072cef.png?x-oss-process=image/resize,w_560)
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6 Impulse Response Let h(t) denote the response of a system for which...
Problem 1: Let the impulse response of an LTI system be given by 0 t< h(t)...
Problem 1: Let the impulse response of an LTI system be given by 0 t< h(t) = 〉 1 0 < t < 1 0 t>1 Find the output y(t) of this system if the input is given by a) x(t) = 1 + cos(2nt) b) x(t)-cos(Tt) c) x(t) sin (t )l d) x(t) = 1 0 < t < 10 0 t 10 e) x(t) = δ(t-2)-5(t-4) f) a(t)-etu(t) Problem 2: For the same LTI system in Problem 1,...
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)
Please dont use Laplace or Fourier A linear time-invariant continuous-time system has the impulse response h(t)...
Please dont use Laplace or Fourier
A linear time-invariant continuous-time system has the impulse response h(t) = (sin(t) + e-t) u(t) (a) Compute the step response s(t) for all 20. (b) Compute the output response y(t) for all t > 0 when the input is u(t)-(t-2) with no initial energy in the system.
7. Let h(T) =T,IT <1 (and equal to zero otherwise) be an impulse response function of...
7. Let h(T) =T,IT <1 (and equal to zero otherwise) be an impulse response function of a WSS process. Find its transfer function (v).
3. Let X be a random variable and denote by Mx(t) its MGF. Prove that, for...
3. Let X be a random variable and denote by Mx(t) its MGF. Prove that, for any t > 0, we have P[X >Mx(t)e
2. For the linear time-invariant systems with impulse responses given below, determin if the system is...
2. For the linear time-invariant systems with impulse responses given below, determin if the system is BIBO stable or BIBO unstable. (a) h)--21-3)lu)-u(t-5)] (b) h(t)--for t > 2 and h(t) = 0 for t < 2 (c) h(t)-cos tu(t) (d) h(t) coste 'u(t) t -1
Ouestion 1 (10%) The circuit shown in Fig. 1 is at steady state before t-0s. Determine...
Ouestion 1 (10%) The circuit shown in Fig. 1 is at steady state before t-0s. Determine v(t) and i(t) for>0. 3Ω 60 |(t) 12 u() 22 ) 12Ω Fig. 1
6. Let X(e2) be the DTFT of a signal nl which is known to be zero...
6. Let X(e2) be the DTFT of a signal nl which is known to be zero for n < 0 and n > 3. We know X(eim) for four values of N as follows X (ejm)0, X(en/2) X(eT/2)5 5j, X(ej0) 10, 55j = = = (a) Find n. (Hint: Compute the IDFT) (b) Find X(ei?)
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...
b(t) 1. Consider the system described by: 2. Consider the sy uuu It tet i(t) =...
b(t) 1. Consider the system described by: 2. Consider the sy uuu It tet i(t) = 0 -1 ] y(t) = (1 out) u(t) , 0, \t <1 (1, t > 1 a) Find the state transition matrix and the impulse response matrix of the system. 2D) Determine whether the system is (i) completely state controllable, (ii) differentially control lable, (iii) instantaneously controllable, (iv) stabilizable at time to = 0. (c) Repeat part (b) for to = 1. gd) Determine...
Problem 1: Let the impulse response of an LTI system be given by 0 t< h(t) = 〉 1 0 < t < 1 0 t>1 Find the output y(t) of this system if the input is given by a) x(t) = 1 + cos(2nt) b) x(t)-cos(Tt) c) x(t) sin (t )l d) x(t) = 1 0 < t < 10 0 t 10 e) x(t) = δ(t-2)-5(t-4) f) a(t)-etu(t) Problem 2: For the same LTI system in Problem 1,...
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)
Please dont use Laplace or Fourier
A linear time-invariant continuous-time system has the impulse response h(t) = (sin(t) + e-t) u(t) (a) Compute the step response s(t) for all 20. (b) Compute the output response y(t) for all t > 0 when the input is u(t)-(t-2) with no initial energy in the system.
7. Let h(T) =T,IT <1 (and equal to zero otherwise) be an impulse response function of a WSS process. Find its transfer function (v).
3. Let X be a random variable and denote by Mx(t) its MGF. Prove that, for any t > 0, we have P[X >Mx(t)e
2. For the linear time-invariant systems with impulse responses given below, determin if the system is BIBO stable or BIBO unstable. (a) h)--21-3)lu)-u(t-5)] (b) h(t)--for t > 2 and h(t) = 0 for t < 2 (c) h(t)-cos tu(t) (d) h(t) coste 'u(t) t -1
Ouestion 1 (10%) The circuit shown in Fig. 1 is at steady state before t-0s. Determine v(t) and i(t) for>0. 3Ω 60 |(t) 12 u() 22 ) 12Ω Fig. 1
6. Let X(e2) be the DTFT of a signal nl which is known to be zero for n < 0 and n > 3. We know X(eim) for four values of N as follows X (ejm)0, X(en/2) X(eT/2)5 5j, X(ej0) 10, 55j = = = (a) Find n. (Hint: Compute the IDFT) (b) Find X(ei?)
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...
b(t) 1. Consider the system described by: 2. Consider the sy uuu It tet i(t) = 0 -1 ] y(t) = (1 out) u(t) , 0, \t <1 (1, t > 1 a) Find the state transition matrix and the impulse response matrix of the system. 2D) Determine whether the system is (i) completely state controllable, (ii) differentially control lable, (iii) instantaneously controllable, (iv) stabilizable at time to = 0. (c) Repeat part (b) for to = 1. gd) Determine...
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