Rkzft {kza} | R Documentation |
Kolmogorov-Zurbenko Fourier Transform is an iterated Fourier transform.
Rkzft(x, m=100, k=1, f=NULL, dim=1)
x |
The raw time series |
m |
The window size for transform |
k |
The number of iterations for applying the KZFT |
f |
The frequency that KZFT is applied at. |
dim |
A value of 1 will return a vector of the given frequency and a value of 2 will return a matrix (spectra). |
Kolmogorov-Zurbenko Fourier Transform (KZFT) is the Fourier transform applied over every segment of length m iterated k times. If a frequency is not selected then the frequency with the largest amplitude is used. The approach taken here is to iterate fft to create a matrix of frequencies over time, another approach is to use matrices for the KZFT transform (see the KZFT package by Wei Yang in R).
This is the R scripted version of kzft, it does not use FFTW (see README).
I. G. Zurbenko, The spectral Analysis of Time Series. North-Holland, 1986.
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, J. Franklin Inst., 499-520, 2002.
R. H. Shumway, D. S. Stoffer, Time Series Analysis and Its Applications: With R Examples, Springer, 2006.
Wei Yang and Igor Zurbenko, kzft: Kolmogorov-Zurbenko Fourier Transform and Applications, R-Project 2007.
# example taken from Wei Yang's KZFT package # coefficients of kzft(201,5) # function to calculate polnomial coefficients for kzft #require(polynom) #coeff <- function(m, k) #{ # poly<-polynomial(rep(1,m)) # polyk<-poly^k # coef<-as.vector(polyk) # coef<-coef/m^k # M=(m-1)*k+1 # return(coef[1:M]) #} #a<-coeff(201,5); #t<-seq(1:1001)-501; #z<-cos(2*pi*0.025*t); #plot(z*a,type="l",xlab="Time", ylab="Coefficient", main="Coefficients of the kzft"); #lines(a); #lines(-1*a); # example taken from Wei Yang's KZFT package # transfer function of the kzft(201,5) at frequency 0.025 lamda<-seq(-0.1,0.1,by=0.001) tf1<-transfer_function(201,1,lamda,0.025) tf2<-transfer_function(201,5,lamda,0.025) matplot(lamda,cbind(log(tf1),log(tf2)),type="l",ylim=c(-15,0), ylab="Natural log transformation of the coefficients", xlab="Frequency (cycles/time unit)", main="Transfer function of Rkzft(201,5) at frequency 0.025") # example # signal with a frequency of 0.01 t<-1:1000 f<-10/1000 x<-cos(2*pi*f*t) + rnorm(length(t),0,3) system.time(z1<-Rkzft(x,m=200,k=1, dim=1)) system.time(z2<-Rkzft(x,m=200,k=2, dim=1)) system.time(z3<-Rkzft(x,m=200,k=3, dim=1)) par(mfrow=c(2,2)) plot(x,type="l",main="Original time series",xlab="t", ylab="y") plot(2*Re(z1),type="l",main="kzft(200,1)",xlab="t", ylab="y") plot(2*Re(z2),type="l",main="kzft(200,2)",xlab="t", ylab="y") plot(2*Re(z3),type="l",main="kzft(200,3)",xlab="t", ylab="y") par(mfrow=c(1,1))