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Find the exponential Fourier series of a function that has the following trigonometric Fourier series coefficients:
Take T = 2π.
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Chapter 17 Solutions
EBK FUNDAMENTALS OF ELECTRIC CIRCUITS
- Given a periodic signal x(t) with Fourier series coefficients a Let y(t)-Dd/dt [(x(t)] (derivative) and y(t) has Fourier series coefficients by Select one: O bk=jkwo + ak None of the answers bk= -j k wo ak bx jk ak bx jk wo ak Next pagarrow_forwardFind the Fourier series representation of the periodic function below. Then, evaluate the first few terms of the series up to n = 4 if x = 0.905. Round off the final answer to five decimal places. Add your answer -3.0+ -1.0+ -9.0 -8.0-7.0-6.0 -5.0-4.0-3.0-2.0-1.0 -1.0- -2.0+ -3.0+ 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 ______ ...arrow_forwardAssume that there is a Fourier series converging to the function f(t) defined by the graph below -3 a. Determine the period and the mathematical function of the f(t). b. Determine if the above function is an even or odd function c. Determine the coefficients in this Fourier series. d. Use Matlab to plot the fourier series function and overlay it to the the original function. Select the number of terms n corresponding to your last 2 digits of your NIM.arrow_forward
- :älium Jlas alla For the signal shown in figure below, find A- The complex exponential Fourier series B- Draw the spectrum of x(t) upto the eighth harmonic (n= +8) .Please, upload the file of your answer X(t) 1 -2 -1 -1/4 1/4arrow_forwardExpand the following function into Fourier's series upto 10 terms f(x) = 1+ x2 - narrow_forwardA periodic continuous time signal x(t) with period T0=9 is shown in Figure-1.a. Calculate the Fourier Series representation of x(t), find the Fourier Seriescoefficients.b. Calculate the Fourier Series representation of the following signals:x(t-1)x(-t)dx/dtarrow_forwardH.W: Calculate the Fourier series for the waveform -16 n² π² Ans. ao 1 & an=" 0 -2π & an= -TT H.W: Calculate the Fourier series for the waveform 2π² - Ans. a, = 4(-1)" n² 3 TT 2π ^f(t) ABA sint at n = odd at n = even 2π ↑f(t) 2π AM NA 11 (1) = 1² f(t)₁ 4π² -2π MAKA sss. -2π -T -2n-it -2π-n -3 -2π 2π ہلے f(t) cos t AKA 3 4πarrow_forwardQ1. Find the Fourier Series in Exponential format T 2. f(t) = 0. 4 4 and f(t) has a period of T. otherwisearrow_forwardGiven a periodic signal x(t) with period T= 2 and Fourier series coefficients ak. Let y(t) = x(-t) with Fourier series coefficients bk, Select one: O a. O b. O c. bk = a-k bk = ak/2 bk = O d. bk = 2ak akarrow_forwardSolve the following five Problems. Problem 1: Consider the waveform shown below. Assume o=1 a. Determine the complex exponential Fourier series of f(t). b. Determine the trigonometric Fourier series of f). f(t) otarrow_forward24 92 1492 ww 12 92 Figure #4 The circuit shown in Figure #4 shows the inductive and capacitive reactances of a series RLC circuit at the second harmonic of the complex input voltage "e". The Fourier series of "e" given by: F(t) = 15 – 36/r[ Sin377t – ½ Sin754t-¹/3 Sin1131t – ¼ Sin1508t -..] a. What is the frequency of the waveform? b. What is the amplitude of the third harmonic? c. What is the magnitude of the direct current component? d. Determine the apparent power consumed by the circuit e. Hence or otherwise, determine the power factor of this circuit.arrow_forwardConsider the Fourier series for the periodic function: x(t) = sin(t) + sin(t) The Fourier coefficient C1 of the exponential series is: Select one: O 0.5e j7/2 O 0.5 O 0.5e/2arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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