Concept explainers
Find the Fourier series representation of the signal shown in Fig. 17.64.
Figure 17.64
Find the Fourier series representation of the signal shown in Figure 17.64.
Answer to Problem 26P
The Fourier series representation
Explanation of Solution
Given data:
Refer to Figure 17.64 in the textbook.
Formula used:
Write the expression to calculate the fundamental angular frequency.
Here,
Write the general expression to calculate trigonometric Fourier series of
Here,
Write the expression to calculate the dc component of the function
Write the expression to calculate Fourier coefficients.
Calculation:
The given waveform is drawn as Figure 1.
Refer to the Figure 1. The Fourier series function of the waveform is defined as,
The time period of the function in Figure 1 is,
Substitute
Substitute
Simplify the above equation to find
Substitute
Simplify the above equation to find
Simplify the above equation to find
Substitute
Simplify the above equation to find
Simplify the above equation to find
Substitute
Conclusion:
Thus, the Fourier series representation
Want to see more full solutions like this?
Chapter 17 Solutions
EBK FUNDAMENTALS OF ELECTRIC CIRCUITS
- The inverse Fourier Transform of delta(omega) isa) 1/2 pib) 2 pic) 1/pid) piarrow_forwardCOMPUTE FOURIER SERIES ( NEED NEAT HANDWRITTEN SOLUTION ONLY OTHERWISE DOWNVOTE).arrow_forwardQ2) Explain the i) ii) iii) The difference between power signal and energy signal (with equations) Parsival Theorem The Fourier seriesarrow_forward
- Determine the complex exponential Fourier series representation for the signal below. x(t) = sin(6t+¹/3) Show the details of your work. Write your answer on a white typewriting paper, scan it in JPEG format, and paste it into the space provided below.arrow_forwardDetermine the Fourier Transform of the following signals: 1. x(n) = (1/5)n u(n-5)arrow_forwardA portion of a repetitive voltage (E(t)) waveform is :shown below. Find The type of waveform ?symmetry а. ?b. Fourier coefficient an ?c. Fourier coefficient bn ?d. The average voltage is Note: please show your <<arrow_forwarduse dire ct Fourier transform formula o prove thès 80 ejwt CS Scanned with CamScarnerarrow_forwardA sinusoidal voltage Vi(t)=20Sin(wt) is passed through half wave rectifier , find 1-The period T 2- The dc value of output 3-The first harmonics of output voltage using Fourier seriesarrow_forwardWhich of the statements given below is false? A) Harmonics of a voltage or current are found with the help of fourier analysis B) In Fourier analysis of double symmetry current waveform sin (wht) harmonics are zero C) None D) In the current waveform with half-wave symmetry, even harmonics are zero E) In most power electronics circuits, the higher the harmonic frequency, the higher the harmonic amplitude.arrow_forwardConsider the periodic signal r(t) shown below: x(t) (a) Derive the Fourier series coefficients a for the signal x(t). To receive full credit, you must show all work. (In other words, you can use a table to check your results, but you will not receive full credit unless you show how the coefficients are derived.) (b) The signal x(t) (shown on the previous page) is the input to an LTI system with the frequency response H(jw) shown below (magnitude and phase plots): |H(jw)| LH(jw) = - 10 -207 -107T +107 +207 Determine the output y(t) of this system when the input is æ(t). 2.arrow_forwardFind the Inverse Fourier Transform x(t) of each signal X(w) given below. X(w) = -4 sinc² (4) X(w) = sinc(πw) 2w X(w) = (7) rect (24) X(w) = A(2w)arrow_forwardCompute the discrete time Fourier series (DTFS) of the following signal and plot its magnitude response x[n] = 8[n] + 8[n – 1] – 8[n + 1] %3Darrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- 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 Education
- Fundamentals 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,