imodwt               package:wavelets               R Documentation

_I_n_v_e_r_s_e _M_a_x_i_m_a_l _O_v_e_r_l_a_p _D_i_s_c_r_e_t_e _W_a_v_e_l_e_t _T_r_a_n_s_f_o_r_m

_D_e_s_c_r_i_p_t_i_o_n:

     Computes the inverse maximal overlap discrete wavelet transform
     for a maximal overlap discrete wavelet transform that was obtained
     from a univariate or multivariate time series.

_U_s_a_g_e:

     imodwt(wt, fast=TRUE)

_A_r_g_u_m_e_n_t_s:

      wt: A 'modwt' object.

    fast: A logical flag which, if true, indicates that the inverse
          pyramid algorithm is computed with an internal C function.
          Otherwise, only R code is used in all computations.

_D_e_t_a_i_l_s:

     The inverse discrete wavelet transform is computed via the inverse
     pyramid algorithm, using pseudocode written by Percival and Walden
     (2000), p. 101.

_V_a_l_u_e:

     An object with class and attributes equivalent to the original
     series that was used to compute the MODWT.  In general, the output
     will be equivalent to the original series (i.e. X =
     imodwt(modwt(X))), however when thresholding or shrinkage methods
     are used on the 'modwt' object, the output of 'imodwt' may differ
     from the original series.

_A_u_t_h_o_r(_s):

     Eric Aldrich. ealdrich@gmail.com.

_R_e_f_e_r_e_n_c_e_s:

     Percival, D. B. and A. T. Walden (2000) _Wavelet Methods for Time
     Series Analysis_, Cambridge University Press.

_S_e_e _A_l_s_o:

     'dwt', 'modwt', 'idwt'.

_E_x_a_m_p_l_e_s:

     # obtain the two series listed in Percival and Walden (2000), page 42
     X1 <- c(.2,-.4,-.6,-.5,-.8,-.4,-.9,0,-.2,.1,-.1,.1,.7,.9,0,.3)
     X2 <- c(.2,-.4,-.6,-.5,-.8,-.4,-.9,0,-.2,.1,-.1,.1,-.7,.9,0,.3)

     # combine them and compute MODWT
     newX <- cbind(X1,X2)
     wt <- modwt(newX, n.levels=3, boundary="reflection")

     # compute the inverse MODWT
     invX <- imodwt(wt)

     # compare
     newX
     invX

