Concept explainers
Sketch the line spectrum for the waveform shown in Figure 17.31.
Answer to Problem 15E
The line spectrum for the given waveform is sketched as shown in Figure 1.
Explanation of Solution
Given data:
Refer to Figure 17.31 in the textbook.
Formula used:
Write the general expression for Fourier series expansion.
Write the general expression for Fourier series coefficient
Write the general expression for Fourier series coefficient
Write the general expression for Fourier series coefficient
Write the expression to calculate the fundamental angular frequency.
Here,
Calculation:
In the given Figure 17.31, the time period is
The function
Substitute 0.4 for T in equation (5) to find
Applying equation (6) in equation (2) to find
Simplify the above equation as follows,
For half wave symmetry and even symmetry,
For all values of ‘n’,
Applying equation (6) in equation (3) to find the value of coefficient
Consider the function,
Consider,
On differentiating the above expression,
Equation (8) will be follows,
In the above equation, consider,
By applying linearity,
In equation (10),
consider,
Let,
Equation (11) will be as follows,
Similarly, in equation (10),
consider,
Let,
Equation (12) will be as follows,
Substitute the values of m and l in equation (10) as follows,
Substitute the value of y in equation (9) as follows,
Therefore,
On applying the limits,
Simplify the equation as follows,
Simplify the equation as follows,
Substitute the value of
Converting the equation (1) which is in angular frequency into frequency.
Substitute the value of
By considering
For
For
The sketch for the line spectrum is shown in Figure 1.
Conclusion:
Thus, the line spectrum for the given waveform is sketched as shown in Figure 1.
Want to see more full solutions like this?
Chapter 17 Solutions
Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
- calculate the Fourier coefficients a0, an, and bn.arrow_forwardQues. 1. Find the complex exponential Fourier series representation of the following signals: (a) x(t) = 6cos(2w,t) (b) x(t) = cos²(t)arrow_forwardDetermine whether or not each of the signals is periodic. If a signal is periodic, determine the fundamental period. (a) (b) (c) (d) x(t) = Ev { sin(4π t) u(t)} x(t) = e(²t-n) x[n] = n=0 = cos os (n) cos (n) x[n]cos (n) = COSarrow_forward
- 1.51. Determine whether or not each of the following signals is periodic. If a signal is periodic, determine its fundamental period. (a) x(t)= cos 2t + 4 (b) x(t)= cos? t (c) x(t)= (cos 2rt)u(t) (d) x(t)= ejr! (e) x[n]= ejl(n/4)–a] 36 CHAPTER 1 Signals and Sys (f) x[n]= cos 8 п cos 2 (g) x[n]= cos (h) x[n]= cos 4 + sin 8 2 cos 2 %3Darrow_forward(a) Determine whether or not each of the following signals is periodic. If a signal is periodic, determine its fundamental period. (i) Ssin (ii) x(1)=2sin° (21)arrow_forwardplot the double - Sidleal amplitude spectrum of the Following periodic signal use this -in wot dt Cn X(t) 2 -3 3. -2arrow_forward
- What is the period of a signal with a frequency of 100 hertz?a) 10sB) 20sC) 10 msD) 5 msE) 20 msarrow_forward1. Given a halfwave rectifier with an RC load as shown below: |ic + iR ip Vo Vy = Vm sin(@t) Figure 1 Schematic diagram of a halfwave rectifier a) Using Fourier series find the components of Vo(t) by deriving the expression for Vadc, V, and V2 .arrow_forward7. For the signal, x(t) = log(cos(a*pi*t+d)) for a = 25 Hz, what is the time period of the signal, if periodic? a) 0.16s b) 0.08s c) 0.12s d) 0.04sarrow_forward
- 3. The current waveform of ia is shown in Fig. 1. If the amplitude is 10A, find the THD(Total Harmonic Distortion) of ia. (Fourier Series analysis is needed) ib 120°. -60% Fig. 1 Cot wt cotarrow_forwardFind whether the given signal is periodic and then fundamental period. Cos(0.01πn)arrow_forwardobtain the fourier series representation of the wavefom shown in image:arrow_forward
- 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,