Explanation Given data: The given waveform is shown in Figure 1. Calculation: The waveform repeats itself after every 10 ms . Hence, the time period T of the given waveform is 10 ms . The conversion from ms to s is given as, 1 ms = 1 × 10 − 3 s The conversion from 10 ms to s is given as, 10 ms = 10 × 10 − 3 s The observed result from the given diagram is, f ( t ) = − f ( − t ) f ( t ) = − f ( t − T 2 ) The above properties show that the given waveform is half wave symmetric. Therefore, the value of the coefficients a 0 and a n are 0 . The value of the coefficients b n is given as, b n = { 8 T ∫ 0 T 4 f ( t ) sin n ω 0 t d t , n = odd 0 , n = even The value of the fundamental radian frequency is given as, ω 0 = 2 π T Substitute 10 × 10 − 3 s for T in the above equation. ω 0 = 2 π 10 × 10 − 3 s = 200 π rad / s The value of the coefficient b n is calculated as, b n = 8 T ∫ 0 T 4 f ( t ) sin n ω 0 t d t Substitute 10 × 10 − 3 s for T , 200 π rad / s for ω 0 and 10 for f ( t ) in the above equation. b n = 8 10 × 10 − 3 s ∫ 0 10 × 10 − 3 s 4 10 sin n ( 200 π rad / s ) t d t = 800 ∫ 0 2.5 × 10 − 3 s 10 sin n ( 200 π ) t d t = 800 ∫ 0 1 × 10 − 3 s 10 sin n ( 200 π ) t d t + ∫ 1 × 10 − 3 s 2

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Fourier Series

Most of the incidents studied in the field of Engineering and Science as a function of time. For example, current and voltage are in the alternating current circuit. These occasional activities can be analyzed in the activity components (fundamental freq…

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Chapter 17, Problem 22E

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The value of a0, an and bn for 1≤n≤10 for the given waveform.

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Chapter 17, Problem 21E

Chapter 17, Problem 23E

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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. 3P Ch. 17.2 - Prob. 4P Ch. 17.3 - Prob. 5P Ch. 17.3 - Prob. 6P Ch. 17.4 - Prob. 7P Ch. 17.5 - Prob. 8P Ch. 17.5 - Prob. 9P Ch. 17.6 - Prob. 10P

Ch. 17.6 - Prob. 11P Ch. 17.7 - Prob. 12P Ch. 17.7 - Prob. 13P Ch. 17.8 - Find (a) F5sin23t); (b) FAsin20t); (c)...Ch. 17.9 - Prob. 15P Ch. 17.10 - Prob. 16P Ch. 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. 4E Ch. 17 - Prob. 5E Ch. 17 - Prob. 6E Ch. 17 - Prob. 7E Ch. 17 - With respect to the periodic waveform sketched in...Ch. 17 - Prob. 9E Ch. 17 - Prob. 10E Ch. 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. 13E Ch. 17 - Prob. 14E Ch. 17 - Prob. 15E Ch. 17 - Prob. 16E Ch. 17 - Prob. 17E Ch. 17 - Prob. 18E Ch. 17 - The nonperiodic waveform g(t) is defined in Fig....Ch. 17 - Prob. 20E Ch. 17 - Prob. 21E Ch. 17 - Prob. 22E Ch. 17 - Prob. 23E Ch. 17 - Prob. 24E Ch. 17 - Prob. 25E Ch. 17 - Prob. 26E Ch. 17 - Prob. 27E Ch. 17 - Prob. 28E Ch. 17 - Prob. 29E Ch. 17 - Prob. 30E Ch. 17 - Prob. 31E Ch. 17 - Prob. 32E Ch. 17 - Prob. 33E Ch. 17 - Prob. 34E Ch. 17 - Prob. 35E Ch. 17 - Prob. 36E Ch. 17 - Use the Fourier transform to obtain and plot the...Ch. 17 - Prob. 38E Ch. 17 - Prob. 39E Ch. 17 - Prob. 40E Ch. 17 - For g(t) = 3etu(t), calculate (a) G(j); (b) ().Ch. 17 - Prob. 42E Ch. 17 - Prob. 43E Ch. 17 - Prob. 44E Ch. 17 - Prob. 45E Ch. 17 - Prob. 46E Ch. 17 - Find F(j) if f(t) is given by (a) 2 cos 10t; (b)...Ch. 17 - Prob. 48E Ch. 17 - Prob. 49E Ch. 17 - Prob. 50E Ch. 17 - Prob. 51E Ch. 17 - Prob. 52E Ch. 17 - Prob. 53E Ch. 17 - If a system is described by transfer function h(t)...Ch. 17 - Prob. 55E Ch. 17 - (a) Design a noninverting amplifier having a gain...Ch. 17 - Prob. 57E Ch. 17 - Prob. 58E Ch. 17 - Prob. 59E Ch. 17 - Prob. 60E Ch. 17 - Prob. 61E Ch. 17 - Prob. 62E Ch. 17 - Design an audio amplifier with gain of 10, using...

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