In this book, time is always in physical units of *seconds*
(s), while time or is in units of *samples* (counting
numbers having no physical units). Time is a continuous real
variable, while discrete-time in samples is integer-valued. The
physical time corresponding to time in samples is given by

For *frequencies*, we have two physical units: (1)
*cycles per second* and (2) *radians per second*. The
name for cycles per second is *Hertz* (Hz) (though in the past it
was *cps*, which is more mnemonic). One cycle equals
radians, which is 360 degrees (). Therefore, Hz is the
same frequency as radians per second (rad/s). It is easy to
confuse the two because both radians and cycles are pure numbers, so
that both types of frequency are in physical units of inverse seconds
(s
).

For example, a *periodic signal* with a period of (Greek
``tau'') seconds has a frequency of Hz, and a radian
frequency of
rad/s. The sampling rate, , is the
reciprocal of the sampling period , *i.e.*,

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