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 2p / T,
the amplitude coefficients
a1, ..., aN
are non-negative, and the radian
phase angles satisfy 0 £ q1
, ..., qN
< 2p.
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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