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How is a trigonometric Fourier series represented?

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in Signals and Systems by (1.2m points)
How is a trigonometric Fourier series represented?

(a) A0 +∑[ancos(w0t)+ ansin(w0t)]

(b) ∑[ancos(w0t)+ ansin(w0t)]

(c) A0 *∑[ancos(w0t)+ ansin(w0t)]

(d) A0 +∑[ancos(w0t)+ ansin(w0t)]  + sinwt

The question was asked in my homework.

Asked question is from Fourier Series in division Fourier Series of Signals and Systems

1 Answer

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by (42.1k points)
Right option is (a) A0 +∑[ancos(w0t)+ ansin(w0t)]

Explanation: A0 + ∑[ancos(w0t)+ ansin(w0t)] is the correct representation of a trigonometric Fourier series. Here  A0 = 1/T∫x(t)dt and an =2/T∫x(t)cos(w0t)dt and bn= 2/T∫x(t)sin(w0t)dt.

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