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- Chapter One Fourier Series Third Year Q1: Find the phase angle form of the Fourier series for the function define by f(t)=4-t, 04. Sketch f(r), the Fourier series of f(x), the Fourier sine series of f(r), and the Fourier cosine series of f (x): S 2 * 0.Please answer all subparts for like either dislike is ready.. Please all subparts in short..If the specific problem does not include instruction in rounding off, express your answer (nonterminating or repeating decimal) using 10 digits as seen in your scientific calculator.error, including expr Q1: Solve or choose the best answer. 1- The Fourier transform of the signal 8(t+1) +8(t-1) is a. 2/(1+jw) b. 2/(1-jw)) /C. 2 cos @ d. 2 sin w 2- For a periodic signal f(t) = 30 sin 1000t + 10 cos 3000t + 6 sin (5000t + 4), the fundamental frequency in rad/s is - i. 1000 ii. 3000 iii. 500 iv. 5000 3- The 1. ii. and notation errors, trigonometric Fourier series of an even function does not have The de term. The cosine terms iii. The sine terms iv. The odd harmonic terms 4- Find the possible values of a and b in the expression u(x, t) = = cos (at) sin (bx) such that it satisfies the wave equation. 5- The Inverse Fourier transform of the л(w-4л) + л8(w+4л) is_ i. 21 (1-сos 4rt) ii. π (1-сos 4rt) iii. 1 + cos 4лt iv. 2 x (1 + cos 4rt) 6- The value of 24 dz, where c: |z-j2| = 1 is will be: z²+4 i. 0 ii. π/2 iii. π iv. 1/5 of time Both sinh(z) and cosh(z) are entire functions. Neither sinh(z) nor cosh(z) are entire functions. signal 278(W) + 7- For a complex variable…1-Fourier series. A- graph each of the following periodic functions. Graph at least 3 periods. P(+) = {², 0Find the Fourier series representation of the periodic function below if k = 19 and m = 9. Then, evaluate the first few terms ofthe series up to n = 7 at x = 4.44.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).Find the Fourier series of f(x) as given over one period and sketch f(x) and partial sums: 4. f(x)= 3x² (-n < x < n)Recommended 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,