dwpt                package:waveslim                R Documentation

(_I_n_v_e_r_s_e) _D_i_s_c_r_e_t_e _W_a_v_e_l_e_t _P_a_c_k_e_t _T_r_a_n_s_f_o_r_m_s

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

     All possible filtering combinations (low- and high-pass) are
     performed to decompose a vector or time series.  The resulting
     coefficients are associated with a binary tree structure
     corresponding to a partitioning of the frequency axis.

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

     dwpt(x, wf="la8", n.levels=4, boundary="periodic")
     idwpt(y, y.basis)
     modwpt(x, wf = "la8", n.levels = 4, boundary = "periodic")

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

       x: a vector or time series containing the data be to decomposed.
           This must be a dyadic length vector (power of 2). 

      wf: Name of the wavelet filter to use in the decomposition.  By
          default this is set to '"la8"', the Daubechies orthonormal
          compactly supported wavelet of length L=8 (Daubechies, 1992),
          least asymmetric family.  

n.levels: Specifies the depth of the decomposition.  This must be a
          number less than or equal to log(mbox{length}(x),2). 

boundary: Character string specifying the boundary condition.   If
          'boundary=="periodic"' the default, then the vector you
          decompose is assumed to be periodic on its defined interval,
           if 'boundary=="reflection"', the vector beyond its
          boundaries is assumed to be a symmetric reflection of itself. 

       y: 

 y.basis: 

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

     The code implements the one-dimensional DWPT using the pyramid
     algorithm (Mallat, 1989).

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

     Basically, a list with the following components 

    w?.?: Wavelet coefficient vectors.  The first index is associated
          with the scale of the decomposition while the second is
          associated with the frequency partition within that level.

 wavelet: Name of the wavelet filter used.

boundary: How the boundaries were handled.

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

     B. Whitcher

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

     Mallat, S. G. (1989) A theory for multiresolution signal
     decomposition: the wavelet representation, _IEEE Transactions on
     Pattern Analysis and Machine Intelligence_, *11*, No. 7, 674-693.

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

     Wickerhauser, M. V. (1994) _Adapted Wavelet Analysis from Theory
     to Software_, A K Peters.

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

     'dwt', 'modwpt', 'wave.filter'.

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

     data(mexm)
     J <- 4
     mexm.mra <- mra(log(mexm), "mb8", J, "modwt", "reflection")
     mexm.nomean <- ts(
       apply(matrix(unlist(mexm.mra), ncol=J+1, byrow=FALSE)[,-(J+1)], 1, sum), 
       start=1957, freq=12)
     mexm.dwpt <- dwpt(mexm.nomean[-c(1:4)], "mb8", 7, "reflection")

