Normalized frequency
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Normalized frequency is a dimensionless quantity, obtained by taking the ratio between an actual frequency and a reference value, or a nominal value.
Fiber optics
In an optical fiber, normalized frequency , V (also called the V number), is given by
- <math>V = {2 \pi a \over \lambda} \sqrt{{n_1}^2 - {n_2}^2}\quad,</math>
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
- <math>{V^2 \over 2} \left( {g \over g + 2} \right)\quad,</math>
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.
Digital signal processing
In digital signal processing, normalized frequency is the ratio of the frequency of a continuous time signal to the sampling frequency:
- <math> f_n = {f \over f_s} </math>
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.