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- The periodic signal x(t) is shown in the following figure. It is a rectangular pulse repeated every 4 seconds. a) Write the mathematical representation of x(t) b) What is the Fourier Transform of x(t)? c) Sketch X(@), showing the important parameters. Make sure you show the magnitude of X(@) at w = 0.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.1-Fourier series. A- graph each of the following periodic functions. Graph at least 3 periods. P(+) = {², 0Specify the types of symmetry for the signals shown in Figure a,b,c,d. Specify also which terms in the trigonometric Fourier series are zero.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).a) Explain with the aid of sketches the meaning of the following terms, as related to periodic waveforms. i) Even symmetry i) Odd symmetry ii) Half wave symmetry b) Determine the Fourier series of the following function: - f(t) = 3 f(t) = 5 0can you solve this? Please write wellFor the signal f (t) = 2 cos²(t) + sin(4t) 1) Determine if the signal f (t) is a periodic signal or not. If it is periodic, find its period. 2) Determine if the signal f (t) is a power or an energy signal. Prove that. 3) Draw the amplitude spectrum of the signal f(t). 4) Draw two-sided magnitude spectrum of the signal f (t). 5) Calculate the power of the signal using frequency domain.1. Suppose you set the function generator to output the signal below: x(t) = 1.5 sin (2000 t t) The fundamental frequency of the signal is: а) 1000 Hz b) 2000 Hz c ) 1000 π Hz d) 2000π Hz 2. Suppose you set your function generator to input a “1.0 Vpp, 100kHz Square wave, no DC components" signal into a spectrum analyzer. At what frequency is the 2nd harmonic: a) 200 kHz b) 300 kHz c) 200 t kHz d) 300 t kHzSEE 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,