Fourier Series Approximation

For a continuous-time, T-periodic signal x(t), the N-harmonic Fourier series approximation can be written as

x(t) = a0 + a1 cos (wot + q1) + a2 cos (2wot + q2)
+ ... + aN cos (nwot + qN)

where the fundamental frequency wo is 2 pi / T, the amplitude coefficients a1, ..., aN are >= 0, and the radian phase angles satisfy 0 <= q1, ..., qN <= 2 pi. To explore the Fourier series approximation, select a labeled signal, use the mouse to sketch one period of a signal, or use the mouse to modify a selected signal. Specify the number of harmonics, N, and click "Calculate." The approximation will be shown in red. In addition, the magnitude spectrum (a plot of an vs. n) and phase spectrum (a plot of qn vs. n) are shown. To see a table of the coefficients used, click "Show."

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