mfilter.select          package:wavethresh          R Documentation

_P_r_o_v_i_d_e _f_i_l_t_e_r _c_o_e_f_f_i_c_i_e_n_t_s _f_o_r _m_u_l_t_i_p_l_e _w_a_v_e_l_e_t_s.

_D_e_s_c_r_i_p_t_i_o_n:

     This function returns the filter coefficients necessary for doing
     a discrete multiple wavelet transform (and its inverse).

_U_s_a_g_e:

     mfilter.select(type = "Geronimo")

_A_r_g_u_m_e_n_t_s:

    type: The name for the multiple wavelet basis. The two possible
          types are "Geronimo" and "Donovan3"

     .

_D_e_t_a_i_l_s:

     This function supplies the multiple wavelet filter coefficients
     required by the 'mwd' function.

     A multiple wavelet filter is somewhat different from a single
     wavelet filter. Firstly the filters are made up of matrices not
     single coefficients. Secondly there is no simple expression for
     the high pass coefficients G in terms of the low pass coefficients
     H, so both sets of coefficients must be specified. Note also that
     the transpose of the filter coefficients are used in the inverse
     transform, an unnecessary detail with scalar coefficients. There
     are two filters available at the moment. Geronimo is the default,
     and is recommended as it has been checked thoroughly. Donovan3
     uses three orthogonal wavelets described in Donovan et al. but
     this coding has had little testing. 

     See Donovan, Geronimo and Hardin, 1996 and Geronimo, Hardin and
     Massopust, 1994. 

     This function fulfils the same purpose as the 'filter.select'
     function does for the standard DWT 'wd'.

_V_a_l_u_e:

     A list is returned with the following eight components which
     describe the filter:

    type: The multiple wavelet basis type string.

       H: A vector containing the low pass filter coefficients.

       G: A vector containing the high pass pass filter coefficients.

    name: A character string containing the full name of the filter.

    nphi: The number of scaling functions in the multiple wavelet
          basis.

    npsi: The number of wavelet functions in the multiple wavelet
          basis.

      NH: The number of matrix coefficients in the filter. This is
          different from length(H).

  ndecim: The decimation factor. I.e. the scale ratio between two
          successive resolution levels.

_R_E_L_E_A_S_E:

     Version 3.9.6 (Although Copyright Tim Downie 1995-6)

_S_e_e _A_l_s_o:

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

_E_x_a_m_p_l_e_s:

     #This function is currently used by `mwr' and `mwd' in decomposing and
     #reconstructing, however you can view the coefficients.
     #
     # look at the filter coefficients for Geronimo multiwavelet
     #
     #mfilter.select()
     #$type:
     #[1] "Geronimo"
     #
     #$name:
     #[1] "Geronimo Multiwavelets"
     #
     #$nphi:
     #[1] 2
     #
     #$npsi:
     #[1] 2
     #
     #$NH:
     #[1] 4
     #
     #$ndecim:
     #[1] 2
     #$H:
     # [1]  0.4242641  0.8000000 -0.0500000 -0.2121320  0.4242641  0.0000000
     # [7]  0.4500000  0.7071068  0.0000000  0.0000000  0.4500000 -0.2121320
     #[13]  0.0000000  0.0000000 -0.0500000  0.0000000
     #
     #$G:
     # [1] -0.05000000 -0.21213203  0.07071068  0.30000000  0.45000000 -0.70710678
     #
     # [7] -0.63639610  0.00000000  0.45000000 -0.21213203  0.63639610 -0.30000000
     #[13] -0.05000000  0.00000000 -0.07071068  0.00000000

