Normalized frequency

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, 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 ,

where a is the core radius, λ is the wavelength in vacuum, n₁ is the maximum refractive index of the core, and n₂ is the refractive index of the homogeneous cladding:

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

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

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

For a step index fiber, the mode volume is given by V²/2. For single-mode operation, V < 2.405.

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}}

i.e. 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.

References