2. Find the fourier transform G(jw) for the function g(t) { where a is a positive constant g(t) = e-at t> 0 t≤0
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2. Find the fourier transform G(jω) for the function g(t)
g(t) =
(
e−at t > 0
0 t ≤ 0
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- 1) An aperiodic continuous time signal x(t) is shown in Figure-1.Computeand draw the Fourier Transform X(w). Hint: Consider the two cases t>0 and t0 x(f)Q2. Suppose f(t) is represented by Figure Q2. Determine the Fourier Transform of the function using the derivative property. Abs -4 -3 -2 -1 0 1 2 3 4 5 6 Figure Q2Q2-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)Cos3t
- 3 Consider the circuit shown below. Find the Fourier transform of vole), where R1=30 0 R2-60 C=50 mF 1,(t)=2e-3u(t) A R13 R2 i, ww3) Given G(f) below is the Fourier transform for a pulse function. a) What is the area under the pulse function? b) Find the value of T? please justify your answers. 025 02 0 15 0.1 0.05 -20 -10 10 20a) Figure 4 below shows a rectangular pulse. i. Derive the Fourier transform for x(t) using integration. ii. Sketch X(@). Label all the important information on the sketching. i. Predict what happens to the DC level as the pulse gets broader while the peak amplitude is maintained at A. x(t) A Activate Window t T T Go to Settings to activ Figure 4 Windows.
- 4-For the follow signal: L 0 < t< 2K It. L y = f(t) = 2K < tDetermine the Fourier transform for the signal x(t) given in Figure Q1(a). An arbitrary system has impulse response given h(t) = e−²tu(t). If the signal x(t) is passed through the system, determine the output signal y(t) using Fourier analysis. jw _jw e 2 -e 2 Hint: sinc() jw = 2 -1 x(t) Figure Q1(a)Q2/ Skitch the following aperiodic waveform in the time domain and calculate it is Fourier transform. - 22t3 2 %3D otherwise %3DSketch or graph and then find the Fourier series for the given function f(x). Show the details of your work -{: 1 0Q1) 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/ For the function shown below, find the trigonometric Fourier series form. f(t) = t2 - ASEE 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,