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- In the following, write out the Fourier series for the following. You should do the integrals yourself (show the steps), rather than just asking a program for the result. A. A triangular wave: -p < x < 0, f(x) = 0 0 < x < p, f(x) = x B. A half-wave rectifier -p < x < 0, f(x) = 0, 0 < x < p, f(x) = sin xQUESTION 7 A waveform f(t) is described by the Fourier series given below. Which of these choices correctly describes the symmetry of the function? ftt) = 2/3 -[cos(w.t)-cos(5Sw.t) +cos(7w,t) - cos(1lw,t) +cos(13w,t) + ..] O A. Odd symmetry, half-wave symmetry, non-zero average value. O B. Half-wave symmetry, zero average value. O C. Even symmetry, quarter-wave symmetry, zero average value. O D. Even symmetry, half-wave symmetry, zero average value.Q2: Find the Fourier series of the function. for a>t>0 for 2n >t > TI 2 f(t) = -2 }
- For the signal f(t) = 8 cos(nt) sin(2nt) %3D 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 one-sided magnitude spectrum of the signal f(t). 5) Calculate the power of the signal using frequency domain.Q3: Find b, in Fourier series for the signal shown in the figure below: Where x(t) =t s.t. -11 Ii. ln. f g O * :The answer is What kind of functions is the funetion shown in this figure? a) Even b) Odd c) Neither odd nor even d) None of them a b d e f g O * ;The answer is What is the value of (d.) for Fourier Cosine Series of the function /(x) - /2 w/2Example: Determine the complex Fourier series for the function f(t) =t in the range 0Q2-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)Cos3tElectrical Engineering p x(t) 1 1 3 Consider the above figure which shows one period of the periodic signal r(t). Draw the magnitude and phase spectrum of x(t) for all frequencies between -0.5 Hz and 0.5 Hz. Also, write an approximation for r(t) as a sum of cosine functions for frequencies up to 0.5 Hz. Note that you do not need to write a closed form infinite sum.Q1/ For the function shown below, find the trigonometric Fourier series form. f(t) = t2 - Ad. It is a periodic signal with a fundamental period T=2/3 -] What is the second harmonic frequency of the following signal? 5 x(t) = are %3D of k=0 Select one: a. 97/2 b. 3/2 c. 3n/2 d. 37Formula: Fourier Series of a Full-wave rectified sinusoidal signal is given by the equation: 4A (cos2wt cos4wt cos6wt + 5 х7 2A cos8wt f(t) + 3х5 + π 1х3 7x 9 (b) A full-wave rectified sinusoidal signal has a peak amplitude A of 6 V and a time period of 2 ms. Using Fourier Series, (i) calculate the frequencies and the amplitudes (magnitudes) for the first four even harmonics and dc; (ii) sketch the magnitude spectrum of this signal for the first four even harmonics and dc.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,