SamplingConsider a continuous-time signal x : Reals → Complex. Computers, and digital hardware in general, have difficulty dealing with such signals. An integral part of what it means to be digital is that actions occur in discrete steps, not as a continuous evolution. Computers, however, can manipulate a closely related signal that is constructed by sampling the continuous-time signal.
A sampler is a system
where T is the sampling period (it has units of seconds/sample). The sampling frequency is fs = 1/T, in units of samples/second (or sometimes Hz, cycles/second). If y = SamplerT (x) then for all n in Integers,
y(n) = x(nT).
Exercise: Verify that SamplerT is linear but not time invariant.