Fourier Series Approximation |
For a continuous-time, T-periodic signal x(t), the N-harmonic Fourier series approximation can be written as
x(t) = a_{0} | + a_{1} cos (w_{o}t + q_{1}) + a_{2} cos (2w_{o}t + q_{2}) |
+ ... + a_{N} cos (nw_{o}t + q_{N}) |
where the fundamental frequency w_{o} is 2 pi / T, the amplitude coefficients a_{1}, ..., a_{N} are >= 0, and the radian phase angles satisfy 0 <= q_{1}, ..., q_{N} <= 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 a_{n} vs. n) and phase spectrum (a plot of q_{n} vs. n) are shown. To see a table of the coefficients used, click "Show."