|x(t) = a0||+ a1 cos (wot + q1) + a2 cos (2wot + q2)|
|+ ... + aN cos (Nwot + qN)|
where the fundamental frequency
is 2p /T rad/sec,
the amplitude coefficients
a1, ..., aN
are non-negative, and the radian
phase angles satisfy 0 £ q1
, ..., qN
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
n) are shown. (If the dc-component is negative,
a0 < 0,
then |a0| is shown in
the magnitude spectrum and an angle of
is shown in the phase spectrum.) To see a table of the coefficients, click
1. Sketch a signal that has a large fundamental frequency component, but small small dc-component and small higher harmonics.
2. Sketch a signal that has large dc and fundamental frequency components, but small higher harmonics.
3. Sketch a signal that has small dc and fundamental frequency components, but large second harmonic.
4. Sketch a signal that has a small fundamental frequency component, but large dc component and large second harmonic.
5. Describe how you would construct a signal that has small dc and fundamental frequency components, but large second, third, and fourth harmonics.
Original applet by Steve Crutchfield, update by Hsi Chen Lee.