wd.object             package:wavethresh             R Documentation

_W_a_v_e_l_e_t _d_e_c_o_m_p_o_s_i_t_i_o_n _o_b_j_e_c_t_s

_D_e_s_c_r_i_p_t_i_o_n:

     These are objects of classes 

     'wd'

     They represent a decomposition of a function with respect to a
     wavelet basis (or tight frame in the case of the (time-ordered)
     non-decimated wavelet decomposition).

_D_e_t_a_i_l_s:

     To retain your sanity the C and D coefficients should be extracted
     by the 'accessC' and 'accessD' functions and inserted using the
     'putC' and 'putD' functions (or more likely, their methods),
     rather than by the `$' operator.

     Mind you, if you want to muck about with coefficients directly,
     then you'll have to do it yourself by working out what the
     fl.dbase list means (see 'first.last' for a description.)

     Note the _time-ordered non-decimated wavelet transform_ used to be
     called the _stationary wavelet transform_. In fact, the
     non-decimated transform has several possible names and has been
     reinvented many times. There are two versions of the non-decimated
     transform: the coefficients are the same in each version just
     ordered differently within a resolution level. The two transforms
     are 

     \textbullet{The function 'wd'() with an argument 'type="station"'
     computes the _time-ordered_ non-decimated transform (see Nason and
     Silverman, 1995) which is useful in time-series applications (see
     e.g. Nason, von Sachs and Kroisandt, 1998).} \textbullet{The
     function 'wst'() computes the packets ordered non-decimated
     transform is useful for curve estimation type applications (see
     e.g. Coifman and Donoho, 1995). }

_V_a_l_u_e:

     The following components must be included in a legitimate `wd'
     object. 

       C: a vector containing each level's smoothed data. The wavelet
          transform works by applying both a smoothing filter and a
          bandpass filter to the previous level's smoothed data. The
          top level contains data at the highest resolution level. Each
          of these levels are stored one after the other in this
          vector. The matrix 

          fl.dbase$first.last.c

          determines exactly where each level is stored in the vector.
          Likewise, coefficients stored when the NDWT has been used
          should only be extracted using the ``access'' and ``put''
          functions below.

       D: wavelet coefficients. If you were to write down the discrete
          wavelet transform of a function then these D would be the
          coefficients of the wavelet basis functions. Like the C, they
          are also formed in a pyramidal manner, but stored in a linear
          array. The storage details are to be found in 

          fl.dbase$first.last.d

          Likewise, coefficients stored when the NDWT has been used
          should only be extracted using the ``access'' and ``put''
          functions below. 

 nlevels: The number of levels in the pyramidal decomposition that
          produces the coefficients. If you raise 2 to the power of
          nlevels you get the number of data points used in the
          decomposition.

fl.dbase: The first last database associated with this decomposition.
          This is a list consisting of 2 integers, and 2 matrices. The
          matrices detail how the coefficients are stored in the C and
          D components of the `wd.object'. See the help on 'first.last'
          for more information. 

  filter: a list containing the details of the filter that did the
          decomposition

    type: either *wavelet* indicating that the ordinary wavelet
          transform was performed or *station* indicating that the
          time-ordered non-decimated wavelet transform was done.

    date: The date that the transform was performed or the wd was
          modified.

      bc: how the boundaries were handled

_G_E_N_E_R_A_T_I_O_N:

     This class of objects is returned from the 'wd' function to
     represent a (possibly time-ordered non-decimated) wavelet
     decomposition of a function. Many other functions return an object
     of class wd.

_M_E_T_H_O_D_S:

     The wd class of objects has methods for the following generic
     functions: 'plot', 'threshold', 'summary', 'print', code{draw}.

_R_E_L_A_E_A_S_E:

     Version 3.5.3 Copyright Guy Nason 1994

_S_e_e _A_l_s_o:

     'wd', 'wst'

