Compute the convolution y(t)=x(t)*h(t) of the following signals. a. x(1)=e"u(t+5); b. x(1)=(+1)[u(t+1)-u(t)]+ (-t+1)[u(t)-u(t-1)]; h(t)=u(t)-u(t-2)+e²*&t-3). h(t)=e"u(-2t).
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- Calculate y(t)=x(t)*v(t) using the convolution integral for the continuous signals x(t) and v(t) given in the figure below. Write the result of y(t) as a piecewise function. Also, show the result in an approximate way by drawing a graph.When the unit step function is applied to the system input given the block diagram below, the output response takes the value c (0.2) = 0.11 fort = 0.2 s and c (infinity) = 0.333 for t = infinity. What is the steady-state error of the system? calculateWhen the unit step function is applied to the input of the system whose block diagram is given below, the output response takes the value c (0.2) = 0.11 for t = 0.2 s and c (infinity) = 0.333 for t = infinity. What is the steady-state error of the system? calculate.
- The mathematical models of some continuous time systems are given above. x(t) is the input signal of the system, and y(t) is the output signal of the system. Which of the following systems is linear and which is nonlinear?A continuous-time LTI system is described by d^2y(t)/dt^2 + 4[dy(t)/dt] + 3y(t) = 2dx(t)/dt + 4x(t). Assuming zero initial condition, find out the response y(t) of the above system for the input x(t) = e^(−2t)u(t).Experiment 1: Laplace transforms, Inverse Laplace transforms, and Applications Theoretical background (Provide the relevant concept s concerning the experiment.) I want Theoretical background for this experiment without Plagiarism
- If G(s) = 1 / (s + 2), find the response c(t) if the input r(t) = u(t), a unit step, assuming zero initial condition.Signal and system The mathematical model of a system is y" (t) + ay'(t) + by(t) = a (t) + ca (t) where a=1, b=2 and c=1. 1) Find zeros and poles of the system. 2) Show them onto the S-Plane (the complex plane) 3) Discuss the BIBO stability of the system.2) In the circuit shown in Fig. 1, the capacitor is initially charged to V0 volts and the switch isclosed at t = 0. Obtain the current, i(t), for t> 0 using the Laplace transform.
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