### 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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