% @(#)transfwave.hlq	19.1 (ESO-IPG) 02/25/03 13:34:20
%++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%.COPYRIGHT  (c)  1993 European Southern Observatory
%.IDENT      transfwave.hlq
%.AUTHOR     06-APR-93, IPG/ESO
%.KEYWORDS   MIDAS, help files, 
%.PURPOSE    On-line help file for the command: TRANSF/WAVE
%.VERSION    1.0  JS : Creation, 06-APR-93
%----------------------------------------------------------------
\se
SECTION./WAVE
\es\co
TRANSF/WAVE					   JS  06-APR-93
\oc\su
TRANSF/WAVE  Name_File_Image Name_File_Wavelet Which_Algorithm Nbr_Scale   
             [Cut_Off_Frequency] 
             compute a wavelet transform
\us\pu
Purpose:    
           Computes the wavelet transform of an image 
\up\sy
Syntax:     
           TRANSF/WAVE Name_File_Image  Name_File_Wavelet 
                       [Which_Algorithm] [Nbr_Scale] [Cut_Off_Frequency] 
\ys\pa
           Name_File_Image = Name of the image

\ap\pa
           Name_File_Wavelet = Name of the file which contains the wavelet
                transform

\ap\pa
           Which_Algorithm = Algoritm number (1 to 8)\\
                1: a trous algorithm with a linear scaling function; the 
                   wavelet function is the difference betwwen two resolutions\\
                2: a trous algorithm with a B3-spline scaling function; the 
                   wavelet function is the difference betwwen two resolutions\\
                3: algorithm using the Fourier transform: without any 
                   reduction of the samples between two scales the Fourier 
                   transform of the scaling function is a b3-spline the 
                   wavelet function is the difference between two resolution\\
                4: pyramidal algorithm in the direct space, with a linear 
                   scaling function\\
                5: pyramidal algorithm in the direct space, with a b3-spline 
                   scaling function\\
                6: algorithm using the Fourier transform:
                   with a reduction of the samples between two scales the 
                   Fourier transform of the scaling function is a b3-spline the
                   wavelet function is the difference between two resolution\\
                7: algorithm using the Fourier transform:
                   with a reduction of the samples between two scales
                   the Fourier transform of the scaling function is a b3-spline
                   the wavelet function is the difference between the square of
                   two resolutions\\
                8: Mallat's Algorithm with biorthogonal filters.\\
\\
                   2 is the default value.
\ap\pa
           Nbr_Scale = Number of scales of the wavelet transform.
                3 is the default value.
\ap\pa
           Cut_Off_Frequency = 0.1 ... 0.5; default 0.5. The Cut_Off_Frequency 
                is necessary for algorithms using the Fourier transform. In 
                other cases, it is ignored. This value defined the cut-off 
                frequency of the scaling function.
\ap\see
See also: 
           HEADER/WAVE, RECONS/WAVE, VISUAL/WAVE            
\ees\no
Note:       
           For the first three algorithms, there is no reduction of the
           number of samples. Then the size of the wavelet transform is
           equal to that of the image  multiplied by the scale number.
           For the algorithms 4 to 7, the number of samples is equal to
           (NxN + N/2xN/2 + N/4xN/4 + ...).
           For the last algorithm, the wavelet transform size is equal
           to the image's one.
\\
           The last algorithm is the only one which is not isotropic.
\on\exs
Examples:
\ex
           TRANSF/WAVE  image1 wave_image1 5 4 
           Computes the wavelet transform of image1 with 4 scales by
           the pyramidal algorithm in the direct space. The result
           is saved in the file wave_image1.
\xe \sxe

