The discrete Fourier series (DFS) summation is defined from 0 to N-1, where N represents the fundamental period of the signal. This contrasts with the continuous Fourier series (CFS), which extends from negative infinity to positive infinity. The DFS utilizes a finite summation, while the CFS employs an infinite summation, particularly evident when expressed in terms of sine and cosine functions or complex exponentials (e^inx).
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The summation goes from n=0 to infinity in case of Fourier series in terms of sin(nx) and cos(nx). In terms of einx, it goes from - infinity to infinity.Ahmad Kishki said:Why is the summation for the discrete Fourier series from 0 to N-1 (where N is the fundamental period of the signal) wheras it goes from minus infiniti to infiniti for continuous Fourier series...Thank you