3) The signal y(t) is the step response of a LTl system. Answer the following questions and justify your answer. y(t) a...
Problem 3. Consider an LTIC system S. whose response to the unit-step function u(t) is as follows Slu(t)] Moreover, let the following input signal (t) go through the same LTIC system: r(t) 3 -2 1 Can you sketch/compute the output y(t) of the LTIC system S] to the input r(t) without using the impulse-response function h(t) of the system? Justify your answer!
0 for t<0 t-1 for 0sts2 16. The step response of a LTI system is given by y sep 1for 2sts3 0 for t 24 (a) Determine the impulse response of the system h() (b) Write the impulse response in terms of unit step functions.
3. For following input/output system relationships, determine the impulse response h(t). Clearly show all the steps arriving to your answer. p(-)x(1-)a L(2- r)x(1)dr-L*-1)x(1)dr (10 points) y(t) a. b. (10 points) y(t) -00 4. (10 points) An LTI system has the impulse response: h(t) = 4e-0.75(-1)[u(t + 4) - u(t - 10)]. this system Causal or Non-Causal? You must justify your answer. A correct answer with no justification worth only 4 points Is 3. For following input/output system relationships, determine the...
3. Impulse Response and Step Response. (25 pts) Consider the following LTI systems: • T1: Has input-output relationship yı(t) = -X1(t – 5) 1<t<4 • T2: Has impulse response hz(t) = { therwise • T3: Has step response s3(t) = -4u(t + 3) • T4: Has step response s4(t) = -tu(t) (a) (5 pts) What is the impulse response hi(t) of system Tj? (b) (10 pts) What is the step response sz(t) of system T2? Write it in terms of...
QUESTION 2 (12 marks) The step response of an LTI system is given by g(t) = (1 - e-3t)u(t) (a) Determine the impulse response, h(t), of the system. (b) Use the linearity and time invariance properties to determine the response of the system to the input x(t) = 38(t) + 2u(t – 2). (c) Determine the frequency response of the system H(jw). [Hint: Use the tables in the formula sheet]. (d) Hence determine the output y(t) for the input signal...
A system is given by: yt=5xt+1-3 Is the system BIBO stable? Justify Is the system memoryless? Explain Is the system causal? Explain Is the system time invariant? Justify Is the system linear? Justify What is the impulse response h(t) of the system? Is the system internally stable? If you could not figure out h(t) from part f, use the h(t) from the problem below. ht=5e-tut-u(t-4)
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)
5. Fourier Transform and System Response (12 pts) A signal æ(t) = (e-t-e-3t)u(t) is input to an LTI system T with impulse response h(t) and the output has frequency content Y(jw) = 3;w – 4w2 - jw3 (a) (10 pts) Find the Fourier transform H(jw) = F{h(t)}, i.e., the frequency response of the system. (b) (2 pts) What operation does the system T perform on the input signal x(t)?
Determine if the linear time-invariant continuous-time system with impulse response t 1 h(t) 0. t 1 is stable. Justify your answer
1. The signal x(t)- expl-a)u(t) is passed as the input to a system with impulse response h(t) -sin(2t)/(7t (a) Find the Fourier transform Y() of the output (b) For what value of α does the energy in the output signal equal one-half the input signal energy? Hint: use the duality property of Fourier Transform to obtain H(a