Find the inverse Fourier transform of the rectangular pulse spectrum defined as, X(e® ) = 1 ; |0| < 1 = 0 ; %3D
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- c) Given that X(@) = S x(t)e-jøt dt where X(@) is the direct Fourier transform of x(t), and x(t) the inverse Fourier transform of X(@). From this definition, find the Fourier transforms of each of the two (2) signals depicted in Figure 4(c). |x(1) x(1) 2 Figure 4(c)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 coefficients a_0, a_k, and b_k of the following function: f(x) = 1-x, 0<=x<2, f(x+2) = f(x).
- Q1- Find the Fourier Coefficients using Fourier series x(n) = (...,-1, 2, 1, 2, -1, 0,-1,2, 1, 2,...} %3DQ1// Find the Fourier series coefficients of the wave function shown below: + x, if -n3-12. Repres x(t) = e-4 %3D over the interval (-1, 1) using: (a) The exponential Fourier series (b) The trigonometric Fourier series (c) Sketch the function to which either Fourier series convergesExample 2 •What are the Fourier Series Coefficients (FSC) of this signal: (1) f = sin2 (2nt) + sin(2nt) LA Time,Q2: Find The Fourier series for the function defined by 4Q2: Find The Fourier series for the function defined by 0Problem 3 Find the Fourier Transform of y(t) = cos(100nt – 1/4). Plot the spectrum (Fourier %3| transform) of the signal. Problem 4 Find the Fourier Transform of z(t) = 2 sin(500nt + 2n/3). Plot the spectrum (Fourier transform) of the signal.a) Find v(t) in terms of Amplitude and phase form b) Find the response vo(t) using Fourier series in the circuit shown, draw frequency spectrum for until four non zero terms of the output Remember: n for this problem is series n (1,2,3 ...) v(t) v(t) = 104 ∑( n=1 n=odd | + w 5 Ohm 20 NT 5 cos3nt - 3 NT 30²) sin3.nt 5 ohm 15 1+ Ba) Calculate the inverse Fourier transform of the function, f(t) if F(ω) =200(jω+1)/jω(jω+10)(2jω+4) b)By using Fourier transform method, determine the current, i(t) as shown in Figure 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,