1 2 b m 0 m 1 2 where a a m and b m are the

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= 1 , 2 , ... b m = 0 , m = 1 , 2 , ... where a 0 , a m and b m are the coefficients corresponding to DC, the sines and the cosines respectively. The figures below show the signal being built up in steps starting with the fundamental and adding higher harmonics one by one. As the last figure in the series shows, the sawtooth ripple contains a large DC, a fundamental, and every harmonic but with a magnitude that diminishes with the index of the harmonic. In most (but not every) engineering application, it is good enough to think of the sawtooth as DC+fundamental frequency. 1
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Fig. 1: Frequency domain - Only 1st harmonic used Fig. 2: Time domain signal v ( t ) = 1 + sin (2 πf in ) 2 π ( f in ) RC - Only 1st harmonic used. Fig. 3: Frequency domain - Only 1st and 2nd harmonics used 2
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Fig. 4: Time domain signal v ( t ) = 1 + sin (2 πf in ) 2 π ( f in ) RC + sin (4 πf in ) 4 π ( f in ) RC - Only 1st and 2nd harmonics used Fig. 5: Frequency domain - Only 1st, 2nd and 3rd harmonics used 3
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Fig. 6: Time domain signal v ( t ) = 1 + sin (2 πf in ) 2 π ( f in ) RC + sin (4 πf in ) 4 π ( f in ) RC + sin (6 πf in ) 6 π ( f in ) RC - Only 1st, 2nd and 3rd harmonics used Fig. 7: Frequency domain - Only 1st, 2nd, 3rd and 4th harmonics used 4
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Fig. 8: Time domain signal v ( t ) = 1 + sin (2 πf in ) 2 π ( f in ) RC + sin (4 πf in ) 4 π ( f in ) RC + sin (6 πf in ) 6 π ( f in ) RC + sin (8 πf in ) 8 π ( f in ) RC - Only 1st, 2nd, 3rd and 4th harmonics used Fig. 9: Time domain signal - First 100 harmonics used 5
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