Normalized frequency

From Wikipedia, the free encyclopedia

Normalized frequency is a dimensionless quantity, obtained by taking the ratio between an actual frequency and a reference value, or a nominal value.

In an optical fiber, the normalized frequency, V (also called the V number), is given by

V = {2 \pi a \over \lambda} \sqrt{{n_1}^2 - {n_2}^2}\quad = {2 \pi a \over \lambda} \mathrm{NA},

where a is the core radius, λ is the wavelength in vacuum, n1 is the maximum refractive index of the core, n2 is the refractive index of the homogeneous cladding, and applying the usual definition of the numerical aperture NA.

In multimode operation of an optical fiber having a power-law refractive index profile, the approximate number of bound modes (the mode volume), is given by

{V^2 \over 2} \left( {g \over g + 2} \right)\quad,

where g is the profile parameter, and V is the normalized frequency, which must be greater than 5 for the approximation to be valid.

For a step index fiber, the mode volume is given by V2/2. For single-mode operation is required that V < 2.405, which is the first root of the Bessel function J0.

In digital signal processing, normalized frequency is the ratio of the frequency of a continuous time signal to the sampling frequency:

f_n = {f \over f_s} .

In other words, it is the signal frequency normalized to the sampling frequency.

Note that some DSP textbooks and some applications (mainly filter design procedures) use half of the sampling frequency as reference.

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