# Sampling

Consider 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

*Sampler*: [

_{T}*Reals*→

*Complex*] → [

*Integers*→

*Complex*]

where *T* is the **sampling period** (it has units of seconds/sample).
The **sampling frequency** is *f _{s}* = 1/

*T*, in units of samples/second (or sometimes Hz, cycles/second). If

*y*=

*Sampler*(

_{T}*x*) then for all

*n*in

*Integers*,

*y*(*n*) = *x*(*nT*).

**Exercise**: Verify that Sampler_{T} is linear
but not time invariant.