mwd                package:wavethresh                R Documentation

_D_i_s_c_r_e_t_e _m_u_l_t_i_p_l_e _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 discrete multiple wavelet transform
     (DMWT). Using an adaption of Mallat's pyramidal algorithm. The
     DMWT gives vector wavelet coefficients.

_U_s_a_g_e:

     mwd(data, prefilter.type = "default", filter.type = "Geronimo",
             bc ="periodic", verbose = FALSE)

_A_r_g_u_m_e_n_t_s:

    data: A vector containing the data you wish to decompose. The
          length of this vector must be a power of 2 times the
          dimension of the DMWT (multiplicity of wavelets).

prefilter.type: This chooses the method of preprocessing required. The
          arguments will depend on filter.type, but "default" will
          always work.

filter.type: Specifies which multi wavelet filter to use, The options
          are "'Geronimo'" (dimension 2) or "'Donovan3'" (dimension 3).
          The latter has not been tested fully and may contain bugs.
          See the function 'mfilter.select' for further details.

      bc: specifies the boundary handling. If 'bc=="periodic"' the
          default, then the function you decompose is assumed to be
          periodic on its 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.

 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:

     The code implements Mallat's pyramid algorithm adapted for
     multiple wavelets using Xia, Geronimo, Hardin and Suter, 1996. The
     method takes a data vector of length '2^J*M', and preprocesses it.
     This has two effects, firstly it puts the data into matrix form
     and then filters it so that the DMWT can operate more efficiently
     Most of the technical details are similar to the single wavelet
     transform except for the matrix algebra considerations, and the
     prefiltering process. See Downie and Silverman (1998) for further
     details and how this transform can be used in a statistical
     context.

_V_a_l_u_e:

     An object of class 'mwd'.

_R_E_L_E_A_S_E:

     Version 3.9.6 (Although Copyright Tim Downie 1996)

_S_e_e _A_l_s_o:

     'accessC.mwd', 'accessD.mwd', 'draw.mwd', 'mfirst.last',
     'mfilter.select', 'mwd.object', 'mwr', 'plot.mwd', 'print.mwd',
     'putC.mwd', 'putD.mwd', 'summary.mwd', 'threshold.mwd', 'wd',
     'wr.mwd'.

_E_x_a_m_p_l_e_s:

     #
     # Generate some test data
     #
     #test.data <- example.1()$y
     #ts.plot(test.data)
     #
     # Decompose test.data with multiple wavelet transform and
     # plot the wavelet coefficients
     #
     #tdmwd <- mwd(test.data)
     #plot(tdmwd)
     #[1] 1.851894 1.851894 1.851894 1.851894 1.851894 1.851894 1.851894
     #
     # You should see a plot with wavelet coefficients like in
     #this-is-escaped-codenormal-bracket62bracket-normal but at each coefficient position
     # there are two coefficients in two different colours one for each of
     # the wavelets at that position.
     #
     # Note the scale for each level is returned by the function.

