Description Usage Arguments Details References See Also Examples
Kolmogorov-Zurbenko Fourier Transform is an iterated Fourier transform.
1 2 3 | kzft(x, f=0, m=1, k=1)
coeff(m, k)
transfer_function(m, k, lamda = seq(-0.5,0.5,by=0.01), omega = 0 )
|
x |
The raw data |
f |
The frequency that KZFT is applied at. |
m |
The window size for transform |
k |
The number of iterations for applying the KZFT |
lamda |
The frequencies used for the calculating the transfer function. |
omega |
The frequency that KZFT is applied at. |
Kolmogorov-Zurbenko Fourier Transform (KZFT) is the Fourier transform applied over every segment of length m iterated k times. The argument alg="F" will use Fast Fourier Transforms written in C (fftw library). The alg="C" is a slow Fourier Transform but has the advantage of being able to handle missing values. It currently works in one dimension. The alg="R" is an R version of KZFT for experimental purposes.The coeff function generates the coefficients for the KZFT function.
You will introduce a phase shift and decrease the fidelity of the signal if the product of f*m is not an integer.
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.
Igor G. Zurbenko, Amy L. Potrzeba, Tidal Waves in Atmosphere and Their Effects, Acta Geophysica Volume 58, Number 2, 356-373
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 | # example taken from Wei Yang's KZFT package
# coefficients of kzft(201,5)
# function to calculate polnomial coefficients for kzft
## Not run:
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);
## End(Not run)
# 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 kzft(201,5) at frequency 0.025")
# example with missing values
set.seed(2)
period=101
f<-1/period
t<-1:2000
s<-1*sin(2*pi*f*t)
x<-s
noise<-3*rnorm(length(t))
x<-s+noise
m=101
rand_idx <- sample(t,100,replace=FALSE)
x[rand_idx]<-NA
x<-as.vector(na.omit(x))
system.time(z1<-kzft(x, m=m, k=1, f=f))
system.time(z2<-kzft(x, m=m, k=2, f=f))
system.time(z3<-kzft(x, m=m, k=3, f=f))
par(mfrow=c(2,2))
plot(x,type="l",main="Original time series",xlab="t", ylab="y")
lines(s,col="blue")
plot(2*Re(z1),type="l",main="kzft(101,1)",xlab="t", ylab="y", ylim=c(-6,6))
lines(s,col="blue")
plot(2*Re(z2),type="l",main="kzft(101,2)",xlab="t", ylab="y", ylim=c(-6,6))
lines(s,col="blue")
plot(2*Re(z3),type="l",main="kzft(101,3)",xlab="t", ylab="y", ylim=c(-6,6))
lines(s,col="blue")
par(mfrow=c(1,1))
|
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.