Question

Consider a sawtooth waveform with saturation error at the top and bottom of the signal- essentially an undersampled square wave. Determine the Fourier Coefficients 

          Consider a sawtooth waveform with saturation error at the top and bottom of the signal- essentially an undersampled square wave. Determine the Fourier Coefficients
Consider a sawtooth waveform with saturation error at the top and bottom of the signal- essentially an undersampled square wave. Determine the Fourier Coefficients

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Transcript

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00:01 Hi in the given problem we know that the four year waveforms equation is given as f t is equal to a not plus sigma n is equal to 1 to infinity a n cos omega not t plus b n sine omega not t now a not is equal to 1 over t the integral of f t d t so this integral is zero is from 0 to 3 .5 this is 0 to 3 .5 now here this can be as 1 over 3 .5 integral from 0 to 0 .5 1 d t plus from 0 .5 to 1 d t plus from 0 .5 to 1 .5 minus t d t d t plus from 1 .5 to 2 .5 this is minus minus 5 d t and plus from 2 .5 to 3 .5 this is t d t so that everything get cancelled so this and this get cancelled so here the integral would be minus 1 .2857 so that's the value of a not now a and similarly a .n would be equal to 2 over 3 .5, 1 over n, sine times sign of 0 .5 n minus 5 over n, cos 2 .5n.
02:08 Now, and then similarly, b .n is equal to 2 over 3 .5 .1, 1 over n, cost, cost 0 .5 n minus 1 plus 5 over n cost 2 .5 n minus cos 1 .5n...
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