Find the Fourier scries of the function f(x) = |x| for -1 < x <1.
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- 2.35. Show that the Fourier transform of x(t) = e-² is X(f) = e-f². This is an example of a signal whose Fourier transform is of the same functional form as the signal itself. [Hint: Complete the square in the exponent of the Fourier transform integral and use Se-au² du = √/α.]Q1) A- Two signals x₁(t) and x₂ (t) having Fourier transforms X₁(f) and X₂(f)shown in figure (1) are combined to form 10-4 X₁(f) 10-4 X₂(f) ÄI f -5 kHz 0 5 kHz -10 kHz 0 10 kHz Figure (1) spectral of x₁ (t) and x₂ (t) y(t) = x₁(t) + 2x₂ (t) cos 2nfet fc = 20.000 kHz a) Find the bandwidth of the signal y(t) b) Given y(t), How could you separate x₁ (t) and 2x₂ (t) cos 2n fet?Q1) A- Two signals x₁(t) and x₂(t) having Fourier transforms X₁(f) and X₂(f)shown in figure (1) are combined to form 10-4 X₁(f) 10-4 X₂(f) XI f -5 kHz 0 5 kHz -10 kHz 0 10 kHz Figure (1) spectral of x₁ (t) and x₂ (t) y(t) = x₁(t) + 2x₂ (t) cos 2nfet fe= 20.000 kHz a) Find the bandwidth of the signal y(t) b) Given y(t), How could you separate x₁ (t)and2x₂ (t) cos 2nfct?
- Signal v(t) can be graphically illustrated as in Figure Q4 (b)(i): v(t) (i) (ii) (iii) -10 50 -4-3h 3 3 Figure Q4 (b)(i) Write the mathematical expression of v(t) Based on answer in Q4 (b)(i) and using suitable Fourier Transform property, determine the Fourier Transform of signal v(t) 27 Solve the Fourier Transform of signal z(t) shown in Figure Q4 (b)(iii) using the solution in Q4 (b)(ii) 25 -21-1 3 3 Зл TT 21 3 3 Figure Q4 (b)(iii)Fourier transform of the signal ejwo(t-to). Select one: a. 27 S(@ + wo) e-jWoto O b. 27 8(w – w.) e-iWato C. 27 8(w – wo) e jWo d. None of the answers e. 271 8(w + @) e W.h(t) 4 Q1: For the signal h(t), shown in figure beside. 1- i) Find Fourier Transform H(w) ii) Sketch amplitude and phase spectrum of H(w) -1
- H.W. 2 D Find the Fourier expansion for the Function interyad -stQ2-A) Find Inverse Fourier transform of 6 f(t) : 3+jw Q2-B) Find the power of the following signal f(t) = (4 – cos t)Cos3ti) Find the Fourier transform for the signal x(t) given in Figure 1. ii) system has impulse response given h(t) = e-2tu(t). If the signal x(t) ispassed through the system, determine the output signal y(t) using Fourier analysis jw jw e 2 -e Hint: sinc (e) jaFind the Fourier transform of the given function. x) = {e²³¹² if — e2iz if - 1Q2-A) Find Inverse Fourier transform of f(t) jn [4 + G+j10w8(@)] 3+jw Q2-B) Find the power of the following signal f(t) = (4 – cos t)Cos3tA discrete-time signal x[n] has a period of N> 2. Which of the following is/are always true about the signal's Fourier coefficients? Statement I: Ck = CN+k Statement II: ||Ck+1|| = ||CN_k_1||| Statement III: Zck+2 = - LC₂N-k-2 O a. I and II only O b. I, II, and III O C. Od. II and III only I and III onlySEE 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,