getpacket.wst           package:wavethresh           R Documentation

_G_e_t _p_a_c_k_e_t _o_f _c_o_e_f_f_i_c_i_e_n_t_s _f_r_o_m _a _p_a_c_k_e_t _o_r_d_e_r_e_d _n_o_n-_d_e_c_i_m_a_t_e_d _w_a_v_e_l_e_t _o_b_j_e_c_t (_w_s_t).

_D_e_s_c_r_i_p_t_i_o_n:

     This function extracts and returns a packet of coefficients from a
     packet-ordered non-decimated wavelet object ('wst') object. The
     'wst' objects are computed by the 'wst' function amongst others.

_U_s_a_g_e:

     getpacket.wst(wst, level, index, type="D", aspect, ...)

_A_r_g_u_m_e_n_t_s:

     wst: Packet-ordered non-decimated wavelet object from which you
          wish to extract the packet from.

   level: The resolution level of the coefficients that you wish to
          extract.

   index: The index number within the resolution level of the packet of
          coefficients that you wish to extract.

    type: This argument must be either "'C'" or "'D'". If the argument
          is "'C'" then non-decimated father wavelet coefficients
          corresponding to the packet that you want are returned. If
          the argument is "'D'" then non-decimated mother wavelet
          coefficients are returned. 

  aspect: 

     ...: 

_D_e_t_a_i_l_s:

     The 'wst' function produces a packet-ordered non-decimated wavelet
     object: 'wst'. The coefficients in this structure can be organised
     into a binary tree with each node in the tree containing a packet
     of coefficients. 

     Each packet is obtained by repeated application of the usual DG
     quadrature mirror filter with both even and odd dyadic decimation.
     See the detailed description given in Nason and Silverman, 1995. 

     This function enables whole packets of coefficients to be
     extracted at any resolution level. The index argument chooses a
     particular packet within each level and thus ranges from 0 to
     2^{J-j} for j=0,..., J-1. Each packet corresponds to the wavelet
     coefficients with respect to different origins. 

     Note that both mother and father wavelet coefficient at different
     shifts are available by using the type argument.

_V_a_l_u_e:

     A vector containing the packet of packet-ordered non-decimated
     wavelet coefficients that you wished to extract.

_R_E_L_E_A_S_E:

     Version 3.9 Copyright Guy Nason 1998

_S_e_e _A_l_s_o:

     'wst', 'wst.object',

_E_x_a_m_p_l_e_s:

     #
     # Take the packet-ordered non-decimated transform of some random data 
     #
     #MyWST <- wst(rnorm(1:512))
     #
     # The above data set was 2^9 in length. Therefore there are
     # coefficients at resolution levels 0, 1, 2, ..., and 8.
     #
     # The high resolution coefficients are at level 8.
     # There should be 256 coefficients at level 8 in index location 0 and 1.
     #
     #length(getpacket(MyWST, level=8, index=0))
     #[1] 256
     #length(getpacket(MyWST, level=8, index=1))
     #[1] 256
     #
     # There are also 256 FATHER wavelet coefficients at each of these two indices
     # (origins)
     #
     #length(getpacket(MyWST, level=8, index=0, type="C"))
     #[1] 256
     #length(getpacket(MyWST, level=8, index=1, type="C"))
     #[1] 256
     #
     # There should be 4 coefficients at resolution level 2
     #
     #getpacket(MyWST, level=2, index=0)
     #[1] -0.92103095  0.70125471  0.07361174 -0.43467375
     #
     # Here are the equivalent father wavelet coefficients
     #
     #getpacket(MyWST, level=2, index=0, type="C")
     #[1] -1.8233506 -0.2550734  1.9613138  1.2391913

