VF_deconvolveVD_deconvolveVE_deconvolve
FunctionDeconvolution
Syntax C/C++#include <VFstd.h>
void VF_deconvolve( fVector Y, fVector Flt, fVector X, fVector Rsp, ui size );
C++ VecObj#include <OptiVec.h>
void vector<T>::deconvolve( vector<T> Flt, const vector<T>& X, const vector<T>& Rsp );
Pascal/Delphiuses VFstd;
procedure VF_deconvolve( Y, Flt, X, Rsp:fVector; size:UIntSize );
DescriptionX is assumed to be the result of a convolution of some "true" profile with the response function Rsp; a deconvolution is attempted and stored in Y. A filter Flt is also calculated; if more than one vector is to be deconvolved with the same Rsp, use VF_deconvolve only once and use the filter Flt thus obtained to deconvolve other vectors by calling VF_filter. The response has to be stored in Rsp in wrap-around order: the elements for zero and positive times (or whatever the independent variable is) are stored as Rsp0 to Rspsize/2 and the elements for negative times as Rspsize/2+1 to Rspsize-1.
You may wish to use VF_rotate or VF_reflect to obtain the correct order when constructing the response vector.

X, Y, Rsp, and Flt must all be of the same size, which has to be an integer power of 2. X may be overwritten by Y, Rsp may be overwritten by Flt, but X and Flt as well as Y and Rsp have to be distinct from each other.

Mathematically, Flt is the inverse of the Fourier transform of Rsp. If the Fourier transform of Rsp contains elements equal to zero, all information is lost for the respective frequency and no reconstruction is possible. The best one can do in this case is to accept this loss and to deconvolve only up to those frequencies where still something is left to be reconstructed.
You are therefore advised not to use this function blindly but rather to inspect the Fourier transform of Rsp and decide what to do on the basis of your specific application. If you wish to use this function nevertheless, you may rely on the automatic editing of the filter, built into VF_deconvolve. Thereby, Flt is set to zero (instead of infinity) at those frequences where all information has been lost. You may set the threshold for this implicit editing by VF_setRspEdit. In order to retrieve the threshold actually set, use VF_getRspEdit.

This deconvolution is based on the implicit assumption that X is periodic; if this is not the case, see the description of VF_convolve about how to avoid end effects.

About special versions with the prefixes VFp_,  VFs_ and VFl_, consult chapter 4.8.

Error handlingIf size is not a power of 2, VF_FFT (on which VF_deconvolve is based) complains "Size must be an integer power of 2" and the program is aborted.
If, by VF_setRspEdit, you specified Trunc.Re = Trunc.Im = 0, SING errors may occur that are handled by setting Flt to ±HUGE_VAL at the respective frequency. During multiplication with the transform of X, this may lead to unhandled floating-point overflow errors (in case your guess of Rsp was wrong and there is some information left at the frequencies where you thought it was not).
Return valuenone
See alsoVF_filter,   VF_convolve,   VF_FFT,   VF_xcorr,   VF_spectrum

VectorLib Table of Contents  OptiVec home