wst                package:wavethresh                R Documentation

_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 _t_r_a_n_s_f_o_r_m.

_D_e_s_c_r_i_p_t_i_o_n:

     Computes the packet-ordered non-decimated wavelet transform
     (TI-transform). This algorithm is functionally equivalent to the
     time-ordered non-decimated wavelet transform (computed by 'wd'
     with the 'type="station"' argument).

_U_s_a_g_e:

     wst(data, filter.number=10, family="DaubLeAsymm", verbose=FALSE)

_A_r_g_u_m_e_n_t_s:

    data: A vector containing the data you wish to decompose. The
          length of this vector must be a power of 2.

filter.number: This selects the smoothness of wavelet that you want to
          use in the decomposition. By default this is 10, the
          Daubechies least-asymmetric orthonormal compactly supported
          wavelet with 10 vanishing moments.

  family: specifies the family of wavelets that you want to use. The
          options are "DaubExPhase" and "DaubLeAsymm".

 verbose: Controls the printing of "informative" messages whilst the
          computations progress. Such messages are generally annoying
          so it is turned off by default.

_D_e_t_a_i_l_s:

     The packet-ordered non-decimated wavelet transform is more
     properly known as the TI-transform described by Coifman and
     Donoho, 1995. A description of this implementation can be found in
     Nason and Silverman, 1995. 

     The coefficients produced by this transform are exactly the same
     as those produced by the 'wd' function with the 'type="station"'
     option _except_ in that function the coefficients are
     _time-ordered_. In the 'wst' function the coefficients are
     produced by a wavelet packet like algorithm with a _cyclic
     rotation_ step instead of processing with the father wavelet
     mirror filter at each level. 

     The coefficients produced by this function are useful in curve
     estimation problems in conjunction with the thresholding function
     'threshold.wst' and either of the inversion functions
     'AvBasis.wst' and 'InvBasis.wst' The coefficients produced by the
     'time-ordered non-decimated wavelet transform' are more useful for
     time series applications: e.g. the evolutionary wavelet spectrum
     computation performed by 'ewspec'.  Note that a time-ordered
     non-decimated wavelet transform object may be converted into a
     packet-ordered non-decimated wavelet transform object (and vice
     versa) by using the 'convert' function.

_V_a_l_u_e:

     An object of class: 'wst'. The help for the 'wst' describes the
     intricate structure of this class of object.

_R_E_L_E_A_S_E:

     Version 3.5.3 Copyright Guy Nason 1995

_S_e_e _A_l_s_o:

     'wst.object', 'threshold.wst', 'AvBasis.wst', 'InvBasis.wst',
     'filter.select', 'convert', 'ewspec', 'plot.wst',

_E_x_a_m_p_l_e_s:

     #
     # Let's look at the packet-ordered non-decimated wavelet transform
     # of the data we used to do the time-ordered non-decimated wavelet
     # transform exhibited in the help page for wd. 
     #
     #test.data <- example.1()$y
     #
     # Plot it to see what it looks like (piecewise polynomial)
     #
     #ts.plot(test.data)
     #
     # Now let's do the packet-ordered non-decimated wavelet transform.
     #
     #TDwst <- wst(test.data)
     #
     # And let's plot it....
     #
     #plot(TDwst)
     #
     # The coefficients in this plot at each resolution level are the same
     # as the ones in the non-decimated transform plot in the wd
     # help page except they are in a different order. For more information
     # about how the ordering works in each case see
     # Nason, Sapatinas and Sawczenko, 1998. 
     # 
     # Next example
     # ------------
     # The chirp signal is also another good example to use.
     #
     #
     # Generate some test data
     #
     #test.chirp <- simchirp()$y
     #ts.plot(test.chirp, main="Simulated chirp signal")
     #
     # Now let's do the packet-ordered non-decimated wavelet transform.
     # For a change let's use Daubechies extremal phase wavelet with 6
     # vanishing moments (a totally arbitrary choice, please don't read
     # anything into it).
     #
     #chirpwst <- wst(test.chirp, filter.number=6, family="DaubExPhase")
     #plot(chirpwst, main="POND WT of Chirp signal")

