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Step of 6 1.008E Refer to Figure 1.5 in the textbook for square wave signal. The Fourier series for the signal is, sin 3 Calculate the total power, P = RT 1 = RT = RT = RT = RT P = R (1) Step of 6 Calculate the total power by summing the contribution of each harmonic P R = R R R 4V = + 2R π 2R 2R = R 9 25 ) 8 11 = R 9 25 )] Step of 6 The value of is nearly equal to 1. Consider the calculation of the infinite series in the parentheses has a sum that approaches π² 8 Therefore, the total power will be as follows: P R 8 P (2) R From equations (1) and (2), it is clear that the two approaches are equal. Step of 6 Calculate the fraction of energy in its fundamental. = 0.81 Therefore, the fraction of energy in its fundamental, E, is 0.81 Calculate the fraction of energy in its first five harmonics. = 9 1 = 0.93 Therefore, the fraction of energy in its first five harmonics, is 0.93 Step of 6 Calculate the fraction of energy in its first seven 8 111 E, = 9 25 0.95 Therefore, the fraction of energy in its first seven harmonics, E, is 0.95 Calculate the fraction of energy in its first nine harmonics. E, 8 1111 9 25 49 = 0.96 Therefore, the fraction of energy in its first nine harmonics, E, is 0.96 Step of 6 Calculate the fraction of energy in its first three harmonics. E, π 8 0.9 90% Hence, the fraction of energy in its first three harmonics, E, is 90% Therefore, 90% of the energy of the square wave is in the first 3