kzw {kzft}R Documentation

Kolmogorov-Zurbenko Wavelet

Description

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

Usage

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")

Arguments

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)

Details

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.

References

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.

See Also

kzft, kzp, kztp.

Examples

# 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")

[Package kzft version 0.15 Index]