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ralab::base::filter::utilities::Mexican_Hat2< TReal > Struct Template Reference

Mexican hat wavelet Version 2. More...

#include <mexhat.hpp>

Inheritance diagram for ralab::base::filter::utilities::Mexican_Hat2< TReal >:

Public Member Functions

 Mexican_Hat2 (TReal mu, TReal sigma)
 
TReal operator() (TReal x)
 

Protected Attributes

TReal mu_
 
TReal sigma_
 

Detailed Description

template<typename TReal>
struct ralab::base::filter::utilities::Mexican_Hat2< TReal >

Mexican hat wavelet Version 2.

For Gaussian of the same amplitude and matching withs, generates response of same amplitude.

\begin{eqnarray*} T_1 &= {1 \over {\sigma}}\\ T_2 &= \left( 1 - {t^2 \over \sigma^2} \right)\\ T_3 &= e^{-t^2 \over 2\sigma^2}\\ \psi(t) &= T_1 \cdot T_2 \cdot T_3 \end{eqnarray*}

 Note, the change in the Term \form#9 compared with the Mexican_Hat functor.

Definition at line 81 of file mexhat.hpp.

Constructor & Destructor Documentation

§ Mexican_Hat2()

template<typename TReal >
ralab::base::filter::utilities::Mexican_Hat2< TReal >::Mexican_Hat2 ( TReal  mu,
TReal  sigma 
)
inline
Parameters
mumean
sigmastandard deviation

Definition at line 83 of file mexhat.hpp.

Member Function Documentation

§ operator()()

template<typename TReal >
TReal ralab::base::filter::utilities::Mexican_Hat2< TReal >::operator() ( TReal  x)
inline

Definition at line 91 of file mexhat.hpp.

References ralab::base::filter::utilities::Mexican_Hat< TReal >::mu_, and ralab::base::filter::utilities::Mexican_Hat< TReal >::sigma_.

92  {
93  TReal two = TReal(2);
94  TReal t1( 1 / sigma_ );
95  TReal t2(1 - pow( x-mu_ , two)/ pow(sigma_,two ) );
96  TReal t3( exp(-pow((x-mu_) , two )/( 2 * pow( sigma_, two ) ) ) );
97  return( t1 * t2 * t3 );
98  }
KernelTraitsBase< Kernel >::space_type::abscissa_type x

Member Data Documentation

§ mu_

template<typename TReal >
TReal ralab::base::filter::utilities::Mexican_Hat2< TReal >::mu_
protected

Definition at line 100 of file mexhat.hpp.

§ sigma_

template<typename TReal >
TReal ralab::base::filter::utilities::Mexican_Hat2< TReal >::sigma_
protected

Definition at line 101 of file mexhat.hpp.


The documentation for this struct was generated from the following file: