### Units

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

*sampling interval*in seconds.

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*). 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 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.*,

*amplitude*of a signal may be in any arbitrary units such as volts, sound pressure (SPL), and so on.

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Sinusoids

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Example