ENGINEERING CIRCUIT...(LL)>CUSTOM PKG.<
9th Edition
ISBN: 9781260540666
Author: Hayt
Publisher: MCG CUSTOM
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 17, Problem 6E
(a)
To determine
Find the value of the Fourier series coefficients
(b)
To determine
Sketch the function
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Please show all the steps and explanation.
QUESTION 3
a) Determine the Fourier series ao, an and bn of the periodic signal, x(t), illustrated
in Figure Q3(a). Then, calculate the first 3 non-zero harmonics of the series.
b)
where wo =
-T
x(t) =
ii.
x(t)
an
A
Knowing that the values of A = 1 and T = 4, put x(t) under the form:
n=3
+
Σ an cos(nwot) + bn sin(nwot)
n=1
T
4
T
2
-A
Figure Q3(a): Periodic signal
c)
The signal x(t) as described in b) is applied to a circuit whose transfer function
is given by:
Y(s)
0.25s
H(s) = =
x(s) 1 +0.25s
where X(s) and Y(s) are the Laplace transfer functions of the input x(t) and the
output y(t) of the circuit, respectively.
i.
Determine the gain and the phase of the circuit.
Find then the output of the circuit y(t). Explain and reflect on the results.
Could you please write clearly! Thank you
Chapter 17 Solutions
ENGINEERING CIRCUIT...(LL)>CUSTOM PKG.<
Ch. 17.1 - Let a third-harmonic voltage be added to the...Ch. 17.1 - A periodic waveform f(t) is described as follows:...Ch. 17.2 - Prob. 3PCh. 17.2 - Prob. 4PCh. 17.3 - Prob. 5PCh. 17.3 - Prob. 6PCh. 17.4 - Prob. 7PCh. 17.5 - Prob. 8PCh. 17.5 - Prob. 9PCh. 17.6 - Prob. 10P
Ch. 17.6 - Prob. 11PCh. 17.7 - Prob. 12PCh. 17.7 - Prob. 13PCh. 17.8 - Find (a) F5sin23t); (b) FAsin20t); (c)...Ch. 17.9 - Prob. 15PCh. 17.10 - Prob. 16PCh. 17 - Determine the fundamental frequency, fundamental...Ch. 17 - Plot multiple periods of the first, third, and...Ch. 17 - Calculate a0 for the following: (a) 4 sin 4t; (b)...Ch. 17 - Prob. 4ECh. 17 - Prob. 5ECh. 17 - Prob. 6ECh. 17 - Prob. 7ECh. 17 - With respect to the periodic waveform sketched in...Ch. 17 - Prob. 9ECh. 17 - Prob. 10ECh. 17 - A half-sinusoidal waveform is shown in Fig. 17.31,...Ch. 17 - Plot the line spectrum (limited to the six largest...Ch. 17 - Prob. 13ECh. 17 - Prob. 14ECh. 17 - Prob. 15ECh. 17 - Prob. 16ECh. 17 - Prob. 17ECh. 17 - Prob. 18ECh. 17 - The nonperiodic waveform g(t) is defined in Fig....Ch. 17 - Prob. 20ECh. 17 - Prob. 21ECh. 17 - Prob. 22ECh. 17 - Prob. 23ECh. 17 - Prob. 24ECh. 17 - Prob. 25ECh. 17 - Prob. 26ECh. 17 - Prob. 27ECh. 17 - Prob. 28ECh. 17 - Prob. 29ECh. 17 - Prob. 30ECh. 17 - Prob. 31ECh. 17 - Prob. 32ECh. 17 - Prob. 33ECh. 17 - Prob. 34ECh. 17 - Prob. 35ECh. 17 - Prob. 36ECh. 17 - Use the Fourier transform to obtain and plot the...Ch. 17 - Prob. 38ECh. 17 - Prob. 39ECh. 17 - Prob. 40ECh. 17 - For g(t) = 3etu(t), calculate (a) G(j); (b) ().Ch. 17 - Prob. 42ECh. 17 - Prob. 43ECh. 17 - Prob. 44ECh. 17 - Prob. 45ECh. 17 - Prob. 46ECh. 17 - Find F(j) if f(t) is given by (a) 2 cos 10t; (b)...Ch. 17 - Prob. 48ECh. 17 - Prob. 49ECh. 17 - Prob. 50ECh. 17 - Prob. 51ECh. 17 - Prob. 52ECh. 17 - Prob. 53ECh. 17 - If a system is described by transfer function h(t)...Ch. 17 - Prob. 55ECh. 17 - (a) Design a noninverting amplifier having a gain...Ch. 17 - Prob. 57ECh. 17 - Prob. 58ECh. 17 - Prob. 59ECh. 17 - Prob. 60ECh. 17 - Prob. 61ECh. 17 - Prob. 62ECh. 17 - Design an audio amplifier with gain of 10, using...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Could you help me solve this problem about signals and systems?Thank you.arrow_forward1 4 2T a) List all symmetries applicable to the periodic function shown above. b) Find the Fourier series av, an, and b, for f(t). c) Using the formula for the rms value of a periodic function, show that 6 = 12arrow_forward1. Find the continuous time Fourier series coefficients of the following continuous time periodic signal. Sketch the magnitude and phase spectrums separately. -2 x(1) 4 1 0 1 2 Fig. 1: A continuous time domain periodic signal.arrow_forward
- I need the answer as soon as possiblearrow_forward4. Consider the following periodic waveform (t). It is desired to find its Fourier series representations, where a = 10, b = 2. x(t) b ... a -a 0 a a За 2a t Σ 2 2 (a) Find the complex-exponential representation. Specifically, find the coefficient x and x ( 0). [Hine: e=(-1) for any integer n] 20 24 2 -jn +jna) - 2π 1-e 2m η πarrow_forwardQuestion 1 (a) Let x[n] be a real periodic signal with period N and Fourier coefficients ak. (i) Show that if N is even, at least two of the Fourier coefficients within one period of ak are real. (ii) Show that if N is odd, at least one of the Fourier coefficients within one period of ak is real. (b) Find the closed-form expression of the convolution of the sequences x(n) = (0.6)nu(n) and h(n) = (0.5)nu(n). (c) ) A system with input x(t) and output y(t) is defined by the equation y(t) = sin[x(t)]. Determine whether this system is invertible. %3Darrow_forward
- Electrical Engineering Department Signal and Systems (10641373) Discussion problems Instructor: Jamal Khrousheh Summer 2020 Q1) a) For periodic signal shown find: ao , a1 ,a2 , bı, b2 Yin -1 1 b) Find the complex Fourier series coefficients X(t) = sin (40m)cos (20m) forarrow_forwarda) Determine the Fourier series coefficients of x(t) given below. b) Plot the magnitude spectrum of x(1), |X(H)I- c) Let y(t) is the output of a filter, when x(t) is the input and H(f) is the frequency response of the filter. Determine y(t) when x(t) is passed through the following filters (T = 0.25). i) H() %3D2 П() - 3 < f <0 0arrow_forwardQ3 Consider the following three continuous-time signals with fundamental period of T=1/2: x(t) = cos(4 7 t) y(1) = sin(4 z t) z(1) = x(1)y(0) (a) Determine the Fourier series coefficients of x(t). (b) Determine the Fourier series coefficients of y(t) (c) Using the results of part (a) and (b), along with multiplication property of the continuous-time Fourier series, to determine the Fourier series coefficients of z(1)=x(t)y(1). (d) Determine the Fourier series coefficients of z(t) through direct expansion of z(1) in trigonometric form, and compare your result with that of part (c).arrow_forwardQ3(a) Suggest any two limitations of Fourier Series. (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. 2A f (t) = 4A (cos2wt cos4wt + 3 x 5 cos6wt + cos8wt + 7 x 9 1х3 5 x 7 π (c) Obtain the Compact trigonometric Fourier series of 6sin8t + 3cos8t. (d) Obtain the Fourier transform of a rectangular function. Also sketch its magnitude spectrum.arrow_forwardSpecify 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.arrow_forwardEENG226-Signals and Systems Please solve it very quickly ??arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)Electrical EngineeringISBN:9780133923605Author:Robert L. BoylestadPublisher:PEARSON
Delmar's Standard Textbook Of ElectricityElectrical EngineeringISBN:9781337900348Author:Stephen L. HermanPublisher:Cengage Learning
Programmable Logic ControllersElectrical EngineeringISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education
Fundamentals of Electric CircuitsElectrical EngineeringISBN:9780078028229Author:Charles K Alexander, Matthew SadikuPublisher:McGraw-Hill Education
Electric Circuits. (11th Edition)Electrical EngineeringISBN:9780134746968Author:James W. Nilsson, Susan RiedelPublisher:PEARSON
Engineering ElectromagneticsElectrical EngineeringISBN:9780078028151Author:Hayt, William H. (william Hart), Jr, BUCK, John A.Publisher:Mcgraw-hill Education,
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:PEARSON
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:9781337900348
Author:Stephen L. Herman
Publisher:Cengage Learning
Programmable Logic Controllers
Electrical Engineering
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:9780078028229
Author:Charles K Alexander, Matthew Sadiku
Publisher:McGraw-Hill Education
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:9780134746968
Author:James W. Nilsson, Susan Riedel
Publisher:PEARSON
Engineering Electromagnetics
Electrical Engineering
ISBN:9780078028151
Author:Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:Mcgraw-hill Education,