6. (20 pts) Foran LTI system, when (t)=A(t)+6(t+1),n(t)-Au(-1- t); when (t)-26(t + 1) + δ(t)in(t) =...
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...
Problem 6 (20 pts) Suppose that the impulse response of a causal LTI system has a Laplace transform which is given by 5+1 H(3) and that the input to this system is x(t) = ell! $+ 25 +2 a) Determine the Laplace transform of the output y(t), along with its associated region of convergence. (12 pts) b) Determine the output y(t). (8 pts)
Problem 4(20 pts) A linear time-invariant (LTI) system responds to x, () with y (t) as shown (a) Sketch the system's response, y2(t), to the input x2(t) (b) Sketch the system's response, y3(t), to the input X3(t). (c) Sketch the input X4(t)s x1(t) + x2(t) + x3(t). (d) Sketch the system's response, y(t) to the input x(t) As required, annotate your sketch when slope changes occur 0 1 2 3 4 5 6 7 8 012 3 45 6 7...
The output of an LTI system is yı(t) when xy(t) is the input. System yı(t) -1 1 The output of the system is yz(t) when x2(t) is the input. x (t) 3 N yz(t) System Express yz(t) in terms of yı(t) using the following format yz(t) = a, y(t-by) + a2 yı(t-b2)
3. Problem 3: (20 pts) Figure 1: Problem 3 An LTT system consisting of two LTI subsystems are shown in the Figure 1. Let the frequency responses of the two subsystems h, and hy be defined as: SMC5 HGW) = H ) = 10 otherwise 10 otherwise Let z(t) = 4008°() +-* sin(3) be the input into the system. (a) Determine , 's and wi's such that z(t) = d.get (10 pts) (b) Use the property of LTI system with...
Suppose the signal x[n] = δ[n-1] + cos(nn/6+ π/4) is input to the LTI system described by the equation y[n][n] +r|n - 0.5yn -. Determine a closed-form expression for yn]
Suppose the signal x[n] = δ[n-1] + cos(nn/6+ π/4) is input to the LTI system described by the equation y[n][n] +r|n - 0.5yn -. Determine a closed-form expression for yn]
(e) Consider an LTI system with impulse response h(t) = π8ǐnc(2(t-1). i. (5 pts) Find the frequency response H(jw). Hint: Use the FT properties and pairs tables. ii. (5 pts) Find the output y(t) when the input is (tsin(t) by using the Fourier Transform method. 3. Fourier Transforms: LTI Systems Described by LCCDE (35 pts) (a) Consider a causal (meaning zero initial conditions) LTI system represented by its input-output relationship in the form of a differential equation:-p +3讐+ 2y(t)--r(t). i....
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,...
1. (20 p) Compute and sketch the output y(t) of the continuous-time LTI system with impulse response h(t) = el-tuſt - 1)for an input signal x(t) = u(t) - ut - 3). 2. (20p) Consider an input x[n] and an unit impulse response h[n] given by n-2 x[n] = (4)”- u[n – 2] h[n] = u(n + 2] Determine and plot the output y[n] = x[n] *h[n].
An LTI system, with an input g(t) and an output y(t), is represented with the following state and output matrices. Assuming a zero-state condition, identify the steady state error if the system is subject to a unit step function. [x1 [x2. ) = [] : [22] + [3] AND y = [2 -1) [x3] + [2]g 4. 0 2 1 3 5