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simth::JakesRng

simth::JakesRng Class Reference

Jakes distributed random number generator. More...

#include <phrand.h>

Inheritance diagram for simth::JakesRng:

simth::RandomGeneratorGsl simth::RandomGenerator List of all members.

Public Member Functions

 JakesRng (double df_max)
virtual double get () const
double get_inl () const
double maxDoppler () const

Detailed Description

Jakes distributed random number generator.

This class returns a random variate which is distributed according to a Jakes distribution for a maximum doppler frequence $f_{max}$. This means the symmetric distribution is upper and lower bounded by the value $T=f_{max}$ which we call T for simplicity. The distribution of the random variate as returned by get() is

\[ p(x) = \left\{ \begin{array}{cl} \frac{1}{\pi}\frac{1/T}{\sqrt{1-(x/T)^2}} & \mbox{for } |x|\leq T \\ 0 & \mbox{elsewhere} \end{array} \right. \]

This distribution has a mean value of zero and a variance $\sigma_j^2$ of

\[ \sigma_j^2=\frac{T^2}{2} \]

A random variable with this distribution results if one takes the cosine or sine of a uniformly-$[-\pi,\pi]$ distributed random variable.

Constructor & Destructor Documentation

simth::JakesRng::JakesRng (  double  df_max  ) 
 

Class constructor with maximal doppler frequency as arguments.

Parameters:
df_max Maximum doppler frequency i.e. maximum value of the Jakes distribution.

Member Function Documentation

virtual double simth::JakesRng::get (   )  const [virtual]
 

Returns a random variate from the Jakes distribution.

Implements simth::RandomGenerator.

double simth::JakesRng::get_inl (   )  const [inline]
 

Inline version of get().

double simth::JakesRng::maxDoppler (   )  const [inline]
 

Returns the maximal doppler frequency.

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