EECS20N: Signals and Systems

Sampling a Sinusoid

Let x : Reals → Reals be such that for all t ∈ Reals,

x(t) = cos(2π f t).

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

y(n) = cos(2π f nT).

Units

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