Sampling, Frequencies of Sampled Sinusoid.
The periodicity of the spectrum of a sampled sinusoidal signal means that
it can be represented as an infinite number of signals all of
the same amplitude. If the unsampled signal frequency is
w and the sampling frequency is
ws then the frequencies
in the spectrum of the sampled signal occur at w
and nws ± w
for all n.
This effect is shown in the applet below.
Unsampled signal at w is
Sampled signal is in magenta.
Spectrum component at
ws - w is in
ws + w is in
2ws - w is in
and Component at
2ws + w is in
Notice that all signals fit the sampled signal as the sampling time or frequency
The applet below is similar, this time showing w,
Nws - w and
Nws + w.
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© 2000 Cuthbert A. Nyack.