As a more interesting and informative example, note from the relation
In[20]:=
w = f T
that when we increase f by 1/T, the new discrete-time frequency is
In[21]:=
(f+ 1/T) T = fT + 1 = w + 1
It follows that the samples will not change. To illustrate this:
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A=1; f=1; p=0; T = 1/5;
p1 = PlotSampledSinusoid[10];
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f = 1 + 1/T;
p2 = PlotSampledSinusoid[10];
These two input continuous-time sinusoids result in the same set of samples. This is called aliasing, meaning that two signals result in the same set of samples. We say that the second sinusoid's frequency is too high for the sampling rate. In fact, we require that
In[24]:=
w = f T < 0.5, or 2f < 1/T
The way this is commonly stated: The sampling rate 1/T must be more than twice the frequency of the sinusoid.
More generally, if an input continuous-time signal consists of a superposition of sinusoids, no aliasing occurs in the sampling if the highest-frequency sinusoid has frequency less than half the sampling rate.
Up to Sampling and aliasing