compgrot             package:wavethresh             R Documentation

_C_o_m_p_u_t_e _e_m_p_i_r_i_c_a_l _s_h_i_f_t _f_o_r _t_i_m_e _o_r_d_e_r_e_d _n_o_n-_d_e_c_i_m_a_t_e_d _t_r_a_n_s_f_o_r_m_s.

_D_e_s_c_r_i_p_t_i_o_n:

     Computes the empirical shift required for time-ordered
     non-decimated transform coefficients to bring them into time
     order.

_U_s_a_g_e:

     compgrot(J)

_A_r_g_u_m_e_n_t_s:

       J: The 'number of levels' in the non-decimated transform where
          coefficients are to be time-aligned.

_D_e_t_a_i_l_s:

     Time-ordered non-decimated transform coefficients when raw are not
     in exact time alignment due to the phase of the underlying
     wavelet. This function returns the shifts that are necessary to
     apply to each resolution level in the transform to bring back each
     set of time-ordered coefficients into time alignment. Note that
     the shifts returned are approximate shifts which work for any
     Daubechies wavelet. More accurate shifts can be computed using
     detailed knowledge of the particular wavelet used. 

     Each shift is "to the left". I.e. higher indexed coefficients
     should take the place of lower-indexed coefficients. Periodic
     boundaries are assumed. 

     This realignment is mentioned in Walden and Contreras Cristan,
     (1997) and Nason, Sapatinas and Sawczenko, (1998).

_V_a_l_u_e:

     A vector containing the shifts that need to be applied to each
     scale level to return them to the correct time alignment.

     There are 'J' entries in the vector. The first entry corresponds
     to the shift required for the finest level coefficients (i.e.
     level 'J-1') and the last entry corresponds to the coarsest level
     (i.e. level 0). Entry 'j' corresponds to the shift required for
     scale level 'J-j'.

_R_E_L_E_A_S_E:

     Version 3.6 Copyright Guy Nason 1997

_N_o_t_e:

     GROT was the shop started by Reginald Perrin. Unfortunately, GROT
     stands for "Guy ROTation".

_S_e_e _A_l_s_o:

     'wst', 'wst.object', 'wpst', 'wpst.object'.

_E_x_a_m_p_l_e_s:

     #
     # Let's see how the resolution levels have to be shifted 
     #
     #compgrot(4)
     #[1]  2  6 15 31
     #
     # In other words. Scale level 3 needs to be shifted two units.
     # Scale level 2 needs to be shifted 6 units
     # Scale level 1 needs to be shifted 15 units
     # Scale level 0 needs to be shifted 31 units.

