The signal u(t) is a full-rectified sine wave with periodic varying amplitude, whose graph is given below. This signal can be written as a complex Fourier series: w(1) =Σ Against u(t) as QM5. What is the coefficient Ao for this series? None of the options k|1|09|k 03 AA 00
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- In the Fourier Series an and bn (for any n) are found by multiplying the signal by the nth harmonic (i.e. cos nx or sin nx), and then integrating. This works because multiplying any sinusoid (signal) by a sine or cosine results in a curve with an integral of A if the harmonic (n) is NOT present in the original signal. This process (multiplying the signal by a sinusoid of known frequency and integrating) is called A/ Reminder: Fourier Series: f(x)= ao + Σ(ancosx + b sinx), for all nA square wave has an amplitude of 2 and a fundamental frequency of 27 rad/sec. It is centered around t = 0, and it is symmetric around the time axis. a. Find the first 5 non-zero terms in the trigonometric Fourier series. b. Express terms as an exponential Fourier series.Find at least three nonzero terms (including ao and at least two cosine terms and two sine terms if they are not all zero) of the Fourier series for the given function, and sketch at least three periods of the function. Which of the following is the Fourier series for the given function? f(x) = 2 O A. f(x) = O B. f(x)= π 4 O D. f(x)= π 4 NI 2 π O c. f(x) = 2 π 2 π + π 4 - π 4 π COS X- COS X- - sin x + COS X- - 4 9μ 4 9μ 4 9₁ 4 - cos 3x... - - sin x- π 4 9μ cos 3x - ... sin 3x + . cos 3x - ... + 4 - sin x + π 4 9μ 4 9μ sin 3x - ... sin 3x + ... f(x) = -X ≤x<0 X 0≤xFind the Fourier series representation of the even extension of the function f(x) = = mx + b dm + b Then, find the value of an if m= 9.7, b = 6.93, d = 5, and n = 11. Round off the final answer to five decimal places. if 0 < xFind at least three nonzero terms (including ao and at least two cosine terms and two sine terms if they are not all zero) of the Fourier series for the given function, and sketch at least three periods of the function. Which of the following is the Fourier series for the given function? O A. f(x)= O B. f(x) = O C. f(x)= 9 18 + 2 9 9 2 9 ——— OD. f(x) = - 2 - + π 18 F π 18 π 18 π 6 sin x + - sin 3x + ... π cos x X- sin x- COS X + 6 π 6 π 6 - π cos 3x - ... sin 3x - ... cos 3x + ... - 18 π 6 sin x - - sin 3x - ... π f(x) = {: 0 9 ≤x≤0 0≤xA 4-bit digital pulse 0110 is repeating itself every 4 seconds as shown in Figure 5. Find the trigonometric Fourier series representing the pulse. Specify if there is any restriction on n. 0 110. +t seconds 0 1 23 45 67 8 Figure 5The plot below shows a full wave rectified sine wave, with a resulting amplitude of 5 and a period of π. Determine the Fourier series expansion of the full wave rectified sine wave below.SHOW complete solution. If f(x) = x3 + x is a periodic function with period 2π, then the Fourier series will have the properties such asa. a0 = 0b. an = 0 c. bn = 0d. bn = 1Find the Exponential Fourier Series of the function below; TT T A time TP4 Derive the Fourier Series of Following signal (2 = x 010 = 7 mont *5m2 2 = x x(1)₁ V NNN -A altanut tot sulev 0H.W 5: Find the coefficient of Fourier series of the following voltage waveform. fo -T -T/2 T/2 -E IbraheemFind the Fourier series representation of the even extension of the function ƒ(x)= Then, find the value of a0 if c = 7.7, and b = 6.6. Round off the final answer to five decimal places. ex+b Sex 4c+b if 0SEE MORE QUESTIONSRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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