Sampled Sinusoids

• Sampling corresponds to transforming the continuous time variable $t$ into a set of discrete times that are integer $n$ multiples of the sampling period $T_s$:
  $$t \longrightarrow nT_s.$$

• Integer $n$ corresponds to the index in the sequence.

• Continuous sinusoid:
  $$x(t) = A\sin(\omega t + \phi).$$

• Discrete sinusoid
  $$x(n) = A\sin(\omega nT_s + \phi),$$
  a sequence of numbers that may be indexed by $n$.