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Angular frequency

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Angular frequency ω (in radians per second), is larger than frequency ν (in cycles per second, also called Hz), by a factor of 2π. This figure uses the symbol ν, rather than f to denote frequency.

A sphere rotating around an axis. Points farther from the axis move faster, satisfying ω = v / r.

In physics, angular frequency "ω" (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit time (for example, in rotation) or the rate of change of the phase of a sinusoidal waveform (for example, in oscillations and waves), or as the rate of change of the argument of the sine function. Angular frequency (or angular speed) is the magnitude of the vector quantity angular velocity.^[1]

One revolution is equal to 2π radians, hence^[1][2]

$${\displaystyle \omega ={\frac {2\pi }{T}}={2\pi f},}$$

where:

• ω is the angular frequency (measured in radians per second),
• T is the period (measured in seconds),
• f is the ordinary frequency (measured in hertz) (sometimes symbolised with ν).

Contents

• 1Units
• 2Examples
  • 2.1Circular motion
  • 2.2Oscillations of a spring
  • 2.3LC circuits
• 3Terminology
• 4See also
• 5References and notes
  
  

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Full width at half maximum

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Full width at half maximum

In a distribution, full width at half maximum (FWHM) is the difference between the two values of the independent variable at which the dependent variable is equal to half of its maximum value. In other words, it is the width of a spectrum curve measured between those points on the y-axis which are half the maximum amplitude. Half width at half maximum (HWHM) is half of the FWHM if the function is symmetric. The term full duration at half maximum (FDHM) is preferred when the independent variable is time.

FWHM is applied to such phenomena as the duration of pulse waveforms and the spectral width of sources used for optical communications and the resolution of spectrometers. The convention of "width" meaning "half maximum" is also widely used in signal processing to define bandwidth as "width of frequency range where less than half the signal's power is attenuated", i.e., the power is at least half the maximum. In signal processing terms, this is at most −3 dB of attenuation, called half-power point or, more specifically, half-power bandwidth. When half-power point is applied to antenna beam width, it is called half-power beam width.

Contents

• 1Specific distributions
  • 1.1Normal distribution
  • 1.2Other distributions
• 2See also
• 3References
• 4External links
  
  

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