kzw                   package:kzft                   R Documentation

_K_o_l_m_o_g_o_r_o_v-_Z_u_r_b_e_n_k_o _W_a_v_e_l_e_t

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

     Kolmogorov-Zurbenko Wavelet is calculated based on
     Kolmogorov-Zurbenko Fourier transform.

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

     kzw(x,f1=1/length(x),f2=0.5,delta.f=1/length(x),t1=1,t2=length(x),
     delta.t=1,n,k=3,method="zero")
     kzww(x,f1=1/length(x),f2=0.5,delta.f=1/length(x),t1=1,t2=length(x),
     delta.t=1,m,k=3,method="zero")

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

       x: A vector of the time series

      f1: left bound of sampling frequency

      f2: right bound of sampling frequency

 delta.f: samplling frequency interval

      t1: left bound of time

      t2: right bound of time

 delta.t: time interval

       n: Multiple of the period

       m: Length of the window size

       k: Number of iterations of the KZFT

  method: Methods of extending time series at both ends.It is either
          zero (adding zeroes) or repeat (symmetrically repeat the time
          series)

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

     Kolmogorov-Zurbenko Wavelet is calculated based on
     Kolmogorov-Zurbenko Fourier transform. KZW maybe considered as a
     nonparametric version of wavelet transform. It does not need to
     have parametric base functions. Since it is based on the
     Kolmogorov-Zurbenko Fourier transform, it is strongly robust with
     respect to noise and information in different frequencies. It also
     has a very high resolution property. There are two versions of KZW
     in this package. There is no difference between these two
     functions except the definition of the window size. In kzw, the
     window size is a multiplication of the period which is one over
     the frequency of interest. In kzww, the window size is fixed for
     all interested frequencies.

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

     I. G. Zurbenko, 1986: The spectral Analysis of Time Series.
     North-Holland, 248 pp.

     I. G. Zurbenko, P. S. Porter, Construction of high-resolution
     wavelets, Signal Processing 65: 315-327, 1998.

     R. Neagu, I. G. Zurbenko, Tracking and separating non-stationary
     multi-component chirp signals, Journal of Franklin Institute 339:
     499-520, 2002.

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

     'kzft', 'kzp', 'kztp'.

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

     # example
     t=1:999
     p1=rep(10,333)
     p2=rep(20,333)
     p=c(p1,p2,p1)
     f=1/p

     x=sin(2*pi*f*t)+rnorm(999,0,1)
     plot(t,x,type='l')

     kzw.x=kzw(x,30/999,120/999,1/999,1,999,1,7,5)
     ff=30:120/999
     contour(t,ff,kzw.x$em)
     lines(t,f,col="red")

