irregwd              package:wavethresh              R Documentation

_I_r_r_e_g_u_l_a_r _w_a_v_e_l_e_t _t_r_a_n_s_f_o_r_m (_d_e_c_o_m_p_o_s_i_t_i_o_n).

_D_e_s_c_r_i_p_t_i_o_n:

     This function performs the irregular wavelet transform as
     described in the paper by Kovac and Silverman.

_U_s_a_g_e:

     irregwd(gd, filter.number=2, family="DaubExPhase", bc="periodic", verbose=FALSE)

_A_r_g_u_m_e_n_t_s:

      gd: A grid structure which is the output of the 'makegrid'
          function.

filter.number: This selects the smoothness of wavelet that you want to
          use in the decomposition. By default this is 2, the
          Daubechies extremal phase orthonormal compactly supported
          wavelet with 2 vanishing moments.

  family: specifies the family of wavelets that you want to use. Two
          popular options are "DaubExPhase" and "DaubLeAsymm" but see
          the help for 'filter.select' for more possibilities.

      bc: specifies the boundary handling. If 'bc="periodic"' the
          default, then the function you decompose is assumed to be
          periodic on it's interval of definition, if 'bc="symmetric"'
          then the function beyond its boundaries is assumed to be a
          symmetric reflection of the function in the boundary. The
          symmetric option was the implicit default in releases prior
          to 2.2.

 verbose: Controls the printing of "informative" messages whilst the
          computations progress. Such messages are generally annoying
          so it is turned off by default.

_D_e_t_a_i_l_s:

     If one has irregularly spaced one-dimensional regression data
     (t,y), say. Then the function 'makegrid' interpolates this to a
     regular grid and then the standard wavelet transform is used to
     transform the interpolated data. However, unlike the standard
     wavelet denoising set-up the interpolated data, y, values are
     correlated. Hence the wavelet coefficients of the interpolated
     will be correlated (even after using an orthogonal transform).
     Hence, in particular, the variance of each wavelet coefficient may
     well be different and so this routine also computes those
     variances using a fast algorithm (related to the two-dimensional
     wavelet transform). 

     When thresholding with 'threshold.irregwd' the threshold function
     makes use of the information about the variance of each
     coefficient to modify the variance locally on a coefficient by
     coefficient basis.

_V_a_l_u_e:

     An object of class 'irregwd' which is a list with the following
     components. 

       C: Vector of sets of successively smoothed versions of the
          interpolated data (see description of equivalent component of
          'wd.object' for further information.)

       D: Vector of sets of wavelet coefficients of the interpolated
          data at different resolution levels. (see description of
          equivalent component of 'wd.object' for further information.)

       c: Vector that aids in calculation of variances of wavelet
          coefficients (used by 'threshold.irregwd').

 nlevels: The number of resolution levels. This depends on the length
          of the data vector. If length(data)=2^m, then there will be m
          resolution levels. This means there will be m levels of
          wavelet coefficients (indexed 0,1,2,...,(m-1)), and m+1
          levels of smoothed data (indexed 0,1,2,...,m).

fl.dbase: There is more information stored in the C and D than is
          described above. In the decomposition ``extra'' coefficients
          are generated that help take care of the boundary effects,
          this database lists where these start and finish, so the
          "true" data can be extracted.

  filter: A list containing information about the filter type: Contains
          the string "wavelet" or "station" depending on which type of
          transform was performed.

      bc: How the boundaries were handled.

    date: The date the transform was performed.

_R_E_L_E_S_A_S_E:

     3.9.4 Code Copyright Arne Kovac 1997

_S_e_e _A_l_s_o:

     'makegrid', 'wd', 'wr.wd', 'accessC', 'accessc', 'accessD',
     'putD', 'putC', 'filter.select', 'plot.irregwd',
     'threshold.irregwd'.

_E_x_a_m_p_l_e_s:

     #
     # See full example at the end of the help for makegrid. 
     #

