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


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.,



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Sinusoids
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