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3. Impulse Response and Step Response. (25 pts) Consider the following LTI systems: • T1: 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...
(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...
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)
This is the information missing for part four 3. Impulae and Step Reaponae. (24 pta Consider the following LTT systema T: Has input-output relationship pi(t)-2) . Ta: Has impulke response ha),otheri . Th Has step respon" ss(t) = 4u(t + 1) * T. Han step response a4(t) = e-qa(t + 2) (a) (4 pts) What is the impulse respotse hi(t) of system T? What is the corresponding step response ai(t)? Show that h(t)(-2) and s(t)(t2) (b) (11 pts) What is...
(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....
Consider the LTI system with input ??(??) = ?? ?????(??) and the impulse response ?(??) = ?? ?2????(??). A. (3 points) Determine ??(??) and ??(??) and the ROCs B. (3 points) Using the convolutional property of the Laplace transform, determine ??(??), the Laplace transform of the output, ??(??) C. (3 points) From the answer of part B, find ??(??) 9 points) Consider the LTI system with input x(t)eu(t) and the impulse response h(t)-e-2u(t) A. 3 points) Determine X(s) and H(s)...
Consider an LTI system with the impulse response h(t) = e- . Is the system casual? Explain. Find and plot the output s(t) given that the system input is x(t) = u(t). Note that s(t) in this case is commonly known as the step response of the system. If the input is x(t) = u(t)-u(t-T). Express the output y(t) as a function of s(t). Also, explicitly write the output y(t) as a function of t. a) b) c)
2. Linearity Consider a system given with the following impulse response: (5%) h[n] 4u[1 a) Is the system LTI? b) Is it causal? c) Is it stable? 2. Linearity Consider a system given with the following impulse response: (5%) h[n] 4u[1 a) Is the system LTI? b) Is it causal? c) Is it stable?
A causal LTI system yields the following input output relationship. Find h(t), the impulse response of the system. (Hint: Try first to determine the output when the input is u(t)) a(t) y(t) LTT →t 2 2 Figure 1: An input-output pair
Help me do this problem step by step LSM1 Problem (50 pts) Consider a causal continuous-time LTI system with input-output relationship dt+)t). (a) Find the transfer function H(s) of the system and specify its ROC. (b) Find the impulse response h(t) of the system. (12 pts) (12 pts) (c) Using the convolution property of the Laplace transform, find the output y(t) of the system in response to the input (t)ut) e2-u(t 1 (26 pts)