Sampling a Sinusoid

Let x : Reals ® Reals be such that for all t Î Reals,

x(t) = cos(2p f t).

Here, f is the frequency, in units of Hertz. Let y = SamplerT (x). Then for all n in Integers,

y(n) = cos(2p f nT).

Units

f
   cycles/second
2p
   radians/cycle
n
   samples
T
   seconds/sample
2p f
   radians/second
2p fT
   radians/sample
2p fnT
   radians