Consider an LTI system: dy(t) +2y(t) = 3x(t) and H(jk 12) = dt 3 2+jk 12...
The input and output of a causal LTI system are related by the diff. eq: d^2y(t)/dt^2 + 5dy(t)/dt + 6y(t) = 2x(t) a. Find impulse response of the system b. What is the response of the system if 2x(t) = e^(-2t)u(t)
Problem #2 Consider a continuous-time LTI system given by: dy[ + 2y(t) = x(t). Using the Fourier transform, find the output y(t) to each of the following input signals: (a) x(t) = e-'u(t), and (b) x(t) = u(t).
Question given an LTI system, characterized by the differential equation d’y() + 3 dy + 2y(t) = dr where x(t) is the input, and y(t) is the output of the system. a. Using the Fourier transform properties find the Frequency response of the system Hw). [3 Marks] b. Using the Fourier transform and assuming initial rest conditions, find the output y(t) for the input x(t) = e-u(t). [4 Marks] Bonus Question 3 Marks A given linear time invariant system turns...
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...
Q5. The measured input-output pair of for an LTI system is observed as follows: LTI system imput: x(t)-1+2cos(t)+5cos (2t)+4cos(t) LTI system output: y(t)-3+cos(t) +6cos(3t) For a new input x(t) = 1+2*cos(t)+5.5*cos(2t)+4*cos(3t), the conrespondding output is observed in the form of y (t)-A+Bcos(t)+Ccos (2t)+Dcos(3t). Determine the values of coefficients of A, B, C, and D A- D- Submit Answer Tries 0/3
3. (l’+2° +1²=4') Topic: Laplace transform, CT system described by differential equations, LTI system properties. Consider a differential equation system for which the input x(t) and output y(t) are related by the differential equation d’y(t) dy(t) -6y(t) = 5x(t). dt dt Assume that the system is initially at rest. a) Determine the transfer function. b) Specify the ROC of H(s) and justify it. c) Determine the system impulse response h(t).
d’y(t) 4x(t) = + 3 dy(t) - +2y(t) dt2 +34 dt For the system presented in Part 2, sketch its input/output block diagram including any feedback loops. Be explicit in whether you are presenting this figure in a time- domain or s-domain representation.
3. Consider a linear time invariant system described by the differential equation dy(t) dt RCww + y(t)-x(t) where yt) is the system's output, x(t) ?s the system's input, and R and C are both positive real constants. a) Determine both the magnitude and phase of the system's frequency response. b) Determine the frequency spectrum of c) Determine the spectrum of the system's output, y(r), when d) Determine the system's steady state output response x()-1+cos(t) xu)+cost)
(a) LTI Systems. Consider two LTI subsystems that are connected in series, where system Tl has step response s1(t)=u(t-1)-u(t-5) and system T2 has impulse response h2t = e-3tu(t). Find the overall impulse response h(t). Hint: you will need to find h1(t) first (b)Fourier Series. The input signal r(t) and impulse response h(t) of an LTI system are as follows:x(t) = sin(2t)cos(t)-ej3t +2 and h(t) = sin(2t)/t Use the Fourier Series method to find the output y(t) (c)Parseval's Identity and Theorem. Consider the system in the...
slove the system eqution: d^3y(t)/dt^3 - 2 d^2y(t)/dt^2 - 5 dy(t)/dt +6 y(t) = 2 d^2u(t)/dt^2 +du(t)/dt +u(t) A) compute the transfer function Y(s)/U(s)? B)Find inverse Laplace for y(t) and x(t)? C) find the final value of the system? D)find the initial value of the system? Please solve clearly with steps.