ind the Fourier series for K f(x) = 0, -2
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- 8. What is the Fourier transform of e-lt cos(t)? (A) 1 (B) (C) (D) 2 1+02² 1+02² 1 1+(2-1)²Electrical Engineering p x(t) 1 1 3 Consider the above figure which shows one period of the periodic signal r(t). Draw the magnitude and phase spectrum of x(t) for all frequencies between -0.5 Hz and 0.5 Hz. Also, write an approximation for r(t) as a sum of cosine functions for frequencies up to 0.5 Hz. Note that you do not need to write a closed form infinite sum.Problem 4. Given the signal x(t) in Figure 2, find the followings [show all details] x(t) 5 -4T 4T Figure 2: Signal x(t) Хо [Hint: For the triangular waveform, Co 2Xo and Cr where X, is the amplitude] (nk)2 2 1) Fourier coefficients (i.e., CR) of the exponential form for x(t). 2) The Harmonic Series for the signal x(t).
- Q2: Find The Fourier series for the function defined by 4 < x< 0 1 09. Prove the following Fourier Transform properties: x(t) dn · x(t) x(t – a) ej2n fot . x(t) X(f) = F[x(t)] (jw)" · X (f) e-jwa , X(f) X(f – fo) 1 x(a· t) |a| +00 | X1 (t) · x2 (t – t) · dt X1(t) · X2(t)1. Determine the Fourier transform of the following functions: a. x(n) = 3" u(n) b. x(n) = -0.55" u(-n - 2)Q1/ For the function shown below, find the trigonometric Fourier series form. f(t) = t2 - APlot the signal x(t) = 3, 7cos(272t) x [u(t – 0) – u(t – 3)]. IMPORTANT: Pay attention to the frequency of the signal when drawing. Write values of amplitude and time axis. Sloppy drawings are invalid.). Calculate the Fourier Transform of - 1Question 4. The Fourier transform of ƒ(t) is F(w) = 5e-6jw wj 3 2 + Using the Convolution Theorem, find ƒ(t) in the form f(t) = A H(tto)ect+D and enter the values of the constants A, to, C and D, as integers. Enter A: Enter to: Enter c: Enter D: 0000b) Consider the two (2) periodic signals shown in Figure 4(b). Find the compact trigonometric Fourier Series for that periodic signal. x(t) -4 -3 -2 -1 0 1 x(t) t2 -4 -3 -2 -1 0 1 2 3 4 Figure 4 (b)In the following, write out the Fourier series for the following. You should do the integrals yourself (show the steps), rather than just asking a program for the result. A. A triangular wave: -p < x < 0, f(x) = 0 0 < x < p, f(x) = x B. A half-wave rectifier -p < x < 0, f(x) = 0, 0 < x < p, f(x) = sin xSEE 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,