wtlib.par.lib

su 的源代码库

WTLIB - Functions for wavelet transforms

wt_cascade - generate the mother wavelet and scaling function
fhierfromcd - calculates f(x,z) hierarchically from CD (wavelet coefficients)
wto1d - wavelet transform operator, 1D
wto1dset - setup wavelet operators
wt1 - 1D wavelet transform
wtn - n-D wavelet transform

Function prototypes:
void wt_cascade(WtFilter *wfilt,WtSizes *wtsizes);
void fhierfromcd(float *f,float *cd,
     WtFilter *wfilt,WtSizes *wtsizes,int justDC);
void wto1d(float *cd,int npoints,enum ToCorD tocord,
     WtFilter *wfilt);
void wto1dset(WtFilter *wfilt,WtSizes *wtsizes);
void wt1(float *cd,enum ToCorD tocord,int npoints,
     WtFilter *wfilt,WtSizes *wtsizes,int idim);
void wtn(float *cd,enum ToCorD tocord,
     	WtFilter *wfilt,WtSizes *wtsizes, int dconly);

wt_cascade:
Input:
WtFilter *wfilt		pointer to wavelet operator (filter)
WtSizes  *wtsizes	pointer to sizes of the wavelet operator

Returns:
wfilt->psi		pointer to mother wavelet
wfilt->phi		pointer to scaling function

fhierfromcd:
Input:
float *cd		pointer to wavelet coefficients
WtFilter *wfilt		pointer to wavelet operator (filters)
WtSizes *wtsizes	pointer to wavelet sizes
int justDC		flag =1 do DC (zero frequency)

Returns:
float *f		pointer to function f(x,z)

wto1d:
Input:
float *cd		pointer to wavelet coefficients, or f(x)
int npoints		size of the input signal
enum ToCorD tocord	=ToC inverse  or =ToD  forward transform
WtFilter *wfilt		pointer to wavelet operator (filters)

Returns:
float *cd		pointer to f(x) or to wavelet coefficients

wto1dset:
Input:
WtFilter *wfilt		pointer to wavelet filter
WtSizes *wtsizes	pointer to wavelet filter sizes

Return:
wfilt->order		order of Daubechies wavelet
wtsizes->sizes		sizes of the wavelet operator

wt1:
Input:
float *cd		pointer to wavelet coeff. or input f(x)
enum ToCorD tocord	=ToC (invers) =ToD (forward) wavelet transform
int npoints		size of signal f(x) or cd
WtFilter *wfilt		pointer to wavelet operator (filters)
WtSizes *wtsizes	pointer to wavelet sizes
int idim		index for dimension

Returns:
float *cd		pointer to input f(x) or to wavelet coefficients

wtn:
Input:
float *cd		pointer to n-D wavelet coeff, or f(x_1,..,x_n)
enum ToCorD tocord	=ToC (inverse) =ToD (forward) wavelet transform
WtFilter *wfilt		pointer to wavelet operator (filters)
WtSizes *wtsizes	pointer to wavelet sizes 
int dconly		keep and transform back form mra dc component only

Returns:
float *cd		pointer to f(x_1,...,x_n) or n-D wavelet coeffs.
Notes:
wt_cascade:
Generate data sets phi[0..lengthphi-1] or psi[0..lengthphi-1].
phi or psi[i] = \phi or \psi (i>>MaxLevel).

fhierfromcd:
Once we have the wavelet coefficients cd, we could applied a	     
inverse wavelet transform to reconstruct the function f, this     
is the ordinary way to view the reconstructed f. A good alternative
is to make the "MRA display", which is to show f hierarchically.  
In "MRA display", the DC is put on the upper-left corner, and higher
frequency rectanges are on the lower-right corner.		     

wto1d:
1D wavelet transform operator, used to apply multi-dimensional  
wavelet transform, in which data of each dimension is extracted 
and 1D wavelet transform (forward: tocord==ToD; backward: tocord 
==ToC) is applied to this 1-D data. Before using wto1d, we must 
call wto1dset to set up the wavelet filters.			   
							   
wto1dset:
This subroutine initialize the wavelet filters for wavelet
transform operator wto1d. According to the order you choose
in your main (wtsizes->order=4 up to 20), wto1dset set up
the filter to be the Daubechies wavelet of this order/length. 
This subroutine will be need before calling wt1 or wtn. 

wt1:
1D wavelet transform. cd[1..npoints] as the discrete values of a 1D
function f(x) will be replaced by its wavelet transform if tocord
==ToD, or the wavelet coefficients cd[1..npoints] will be replaced
by the inverse wavelet transform, thus to obtain the reconstructed
f. The size of f npoints MUST be an integer power of 2.

wtn:
Given a n-D discrete values cd[...] of a n-D function f(x_1,...,x_n)
n-D wavelet transform will be applied if tocord==ToD; or given
a n-D wavelet coefficients of an n-D function, inverse wavelet
transform will be applied to reconstruct the n-D function f. Must
call wto1dset before calling wtn.
References:
Daubechies, I., 1988, Orthonormal Bases of Compactly Supported
Wavelets, Communications on Pure or Applied Mathematics, Vol. XLI,
909-996.

Z. Meng & J. Scales, Multi-resolution Analysis with wavelet 	  
transform: An application to 2-D tomography, CWP-223, 1996    

W. Press et al., Numberical Recipes in C (second edition),     
Cambridge University Press, 1988				   
Author:
CWP: Zhaobo Meng, Colorado School of Mines, Sept 1996
Modified: Carlos E. Theodoro, Colorado School of Mines, Jun 97