wt::Convolution Class Reference

Implements the overlap-add covolution[3] of a signal with several filter kernels of the same size, each being shorter that the signal. More...

#include <convolution.hh>

Public Member Functions
	Convolution (const CMatrix &kernels, size_t subSample=1)
	Constructor. More...
virtual	~Convolution ()
	Destructor. More...
template<class iDerived , class oDerived >
void	apply (const Eigen::DenseBase< iDerived > &signal, Eigen::DenseBase< oDerived > &out)
	Performs the convolution of the signal passed by signal with the kernels passed to the constructor. More...
size_t	kernelLength () const
	Returns the length of the kernels. More...
size_t	numKernels () const
	Returns the number of kernels. More...
size_t	subSampling () const
	Returns the sub-sampling assinged to the convolution operation. More...
void	setSubSampling (size_t subSample)
	Sets the sub-sampling assinged to the convolution operation. More...

Protected Attributes
size_t	_K
	The number of kernels. More...
size_t	_M
	The lenght of the kernels. More...
CMatrix	_kernelF
	Holds the Fourier transformed of the kernels. More...
CVector	_part
	Working vector for the forward-transform of an piece of the input signal. More...
FFT	_fwd
	The in-place FFT transform of a (zero-padded) signal part. More...
CMatrix	_lastRes
	Second halfs of the back-transformed, filtered singals. More...
CMatrix	_work
	Working memory for backward transformation of filtered signals. More...
FFT	_rev
	Backward transformation. More...
size_t	_subSampling
	Possible subsampling for the kernels. More...

Detailed Description

Implements the overlap-add covolution[3] of a signal with several filter kernels of the same size, each being shorter that the signal.

As all kernels share the same size, hence the forward FFT of a piece of the input signal must be computed only once. This speeds up the convolution slightly. Further, assuming K kernels of size M and a signal length of N samples. The direct FFT convolution cost would be , not including the costs of computing the FFTs of the kernels.

Using the overlap-add method, the costs are , which results into a benifit if .

Constructor & Destructor Documentation

Convolution::Convolution	(	const CMatrix &	kernels,
		size_t	subSample = 1
	)

Constructor.

The complex matrix kernels specifies the convolution filters to be used. Every colum specifies a filter kernel.

Convolution::~Convolution ( )

virtual

Destructor.

Member Function Documentation

template<class iDerived , class oDerived >

void wt::Convolution::apply ( const Eigen::DenseBase< iDerived > &  signal, Eigen::DenseBase< oDerived > &  out  )

inline

Performs the convolution of the signal passed by signal with the kernels passed to the constructor.

The results are stored in the columns of the array out. Hence, given a signal with N samples and K kernels, the output must be pre-allocated as a NxK array/matrix.

size_t wt::Convolution::kernelLength ( ) const

inline

Returns the length of the kernels.

size_t wt::Convolution::numKernels ( ) const

inline

Returns the number of kernels.

void wt::Convolution::setSubSampling ( size_t  subSample )

inline

Sets the sub-sampling assinged to the convolution operation.

size_t wt::Convolution::subSampling ( ) const

inline

Returns the sub-sampling assinged to the convolution operation.

Member Data Documentation

FFT wt::Convolution::_fwd

protected

The in-place FFT transform of a (zero-padded) signal part.

size_t wt::Convolution::_K

protected

The number of kernels.

CMatrix wt::Convolution::_kernelF

protected

Holds the Fourier transformed of the kernels.

CMatrix wt::Convolution::_lastRes

protected

Second halfs of the back-transformed, filtered singals.

size_t wt::Convolution::_M

protected

The lenght of the kernels.

CVector wt::Convolution::_part

protected

Working vector for the forward-transform of an piece of the input signal.

FFT wt::Convolution::_rev

protected

Backward transformation.

size_t wt::Convolution::_subSampling

protected

Possible subsampling for the kernels.

This property of the convolution is not computed or handled by the convolution itself, instead it is a property that can be assigned to it. I.e. kind of meta-data for the convolution operation.

CMatrix wt::Convolution::_work

protected

Working memory for backward transformation of filtered signals.

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The documentation for this class was generated from the following files:

• /Users/hannes/Uni/Wavelet/wt/lib/convolution.hh
• /Users/hannes/Uni/Wavelet/wt/lib/convolution.cc