A linear time-invariant continuous-time system responds to the following inputs with the corresponding outputs: If x(t) = u(t), then y(t) = 2(1 − e¯¹) u(t) and if x(t): = cos t, then 1.414 cos(t - π/4). Find y(t) for the following inputs (Hint: Use Problem 1.23 for part (d)): y(t) = (a) x(t) = 2u(t) — 2u(t − 1) (b) x(t) = 4 cos(2(t - 2)) (c) x(t) = 5u(t) + 10 cos(2t)
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- Q1) For the two waveforms x(t) and h(t). a) Draw x(t) and h(t - t). b) Write down the expression for the intermediate function w(t). c) Evaluate the intermediate function w(t) for the values of t = -2,-1,0, 1, 2,3, 4, 5 and write your values in the given table. -2 -1 2 3. d) Plot the convolution of the two rectangular pulses y(t) = x(t) + h(t) shown. 2 y(t) O 15 -2 1 -1 0.5 -2 -1 2 1 t 2 4Write the mathematical description of the given continuous-time function below and perform the following operations. 1. x(t + 3) 2. x(t-1) 3. x(2t) 4. x(t/2) Show the details of your work. -1 x (t) 0 2Given the system below, find the steady-state error if R(s) %3D Y(s) R(s) 5 %3D s2 + 7s + 10
- Please adhere to the following instructions Turn in the assignment on time, you have one week from the day the assignment is given. • Provide solutions to problems in the order assigned Problem 1: Classify the following signals as energy or power signals, and find the normalized energy or normalized power of each: d. exp(j2nt) over (-∞Find the steady-state oscillations of y" + cy' + y = r(t) with c > 0 and r(t) as given. Note that the spring constant is k = 1. Show the details. In Probs. 14–16 sketch r(t). 16. r(t) = t if -1/2Sketch the function:X(t) = tu(t) - 3(t-2)u(t-2) + 2(t-3)u(t-3)How do you determine how much it goes up and down? What's the easiest way to go about drawing the graphs step by step?f(a,b,c,d) = m(2,3,6,7,8,9,12,13) f=aⓇc f = a + b * The following function can be represented by ....... f=ãⓇc f=a+c none of the mentionedFirst Örder System Assume that you are given a first order system below: C(s) 2(9 + 4) R(s) s+ 4(9 + 8) Answer the following questions: Manual Calculation Find the pole of the system and sketch it in an s-plane. Determine the time response, c(t) of the system for a unit step input, r(t). Then, sketch c(t) against time, t. From the time response, determine the rise time, Tr, settling time, T,, time constant, Tc, and steady-state error Then, show all of these time values in the sketch.Imagine we have a function f(t)=2u(t)+2r(t-1)-4r(t-2)+2r(t-3): a) Determine whether the function is Even or Odd or none of them?b) Find the Ev{f(t)} and Od{f(t)}c) Draw the even part and the odd part.Convolve the following continuous-time signals, assuming that T₁=1 sec. and T, -1.5 sec Plot the result -1 T 2T, h(t) KConvolve the following continuous-time signals, assuming that T₁-1 sec. and 7,-1.5 sec Plot the result X(7) T 27, (r) ÄA. Write a Matlab function to generate the following function f(t) ft) 1.5 0.5 -0.5 -1.5 -10 8 -2 0 2 10 Time [Second) Values 2.SEE MORE QUESTIONSRecommended textbooks for youIntroductory Circuit Analysis (13th Edition)Electrical EngineeringISBN:9780133923605Author:Robert L. BoylestadPublisher:PEARSONDelmar's Standard Textbook Of ElectricityElectrical EngineeringISBN:9781337900348Author:Stephen L. HermanPublisher:Cengage LearningProgrammable Logic ControllersElectrical EngineeringISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill EducationFundamentals of Electric CircuitsElectrical EngineeringISBN:9780078028229Author:Charles K Alexander, Matthew SadikuPublisher:McGraw-Hill EducationElectric Circuits. (11th Edition)Electrical EngineeringISBN:9780134746968Author:James W. Nilsson, Susan RiedelPublisher:PEARSONEngineering ElectromagneticsElectrical EngineeringISBN:9780078028151Author:Hayt, William H. (william Hart), Jr, BUCK, John A.Publisher:Mcgraw-hill Education,Introductory Circuit Analysis (13th Edition)Electrical EngineeringISBN:9780133923605Author:Robert L. BoylestadPublisher:PEARSONDelmar's Standard Textbook Of ElectricityElectrical EngineeringISBN:9781337900348Author:Stephen L. HermanPublisher:Cengage LearningProgrammable Logic ControllersElectrical EngineeringISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill EducationFundamentals of Electric CircuitsElectrical EngineeringISBN:9780078028229Author:Charles K Alexander, Matthew SadikuPublisher:McGraw-Hill EducationElectric Circuits. (11th Edition)Electrical EngineeringISBN:9780134746968Author:James W. Nilsson, Susan RiedelPublisher:PEARSONEngineering ElectromagneticsElectrical EngineeringISBN:9780078028151Author:Hayt, William H. (william Hart), Jr, BUCK, John A.Publisher:Mcgraw-hill Education,