Sampling, Frequencies of Sampled Sinusoid

Cuthbert Nyack
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 in red.
Sampled signal is in magenta.
Spectrum component at ws - w is in orange.
Component at ws + w is in yellow.
Component at 2ws - w is in green.
and Component at 2ws + w is in cyan.
Notice that all signals fit the sampled signal as the sampling time or frequency is changed..

The applet below is similar, this time showing w, Nws - w and Nws + w.