tukeywindow {bspec}

Compute windowing functions for spectral time series analysis.

Description

Several windowing functions for spectral or Fourier analysis of time series data are provided.

Usage

tukeywindow(N, r = 0.1)
squarewindow(N)
hannwindow(N)
welchwindow(N)
trianglewindow(N)
hammingwindow(N, alpha=0.543478261)
cosinewindow(N, alpha=1)
kaiserwindow(N, alpha=3)

Arguments

N

the length of the time series to be windowed

r

the Tukey window's parameter, denoting the its "non-flat" fraction.

alpha

additional parameter for Hamming-, cosine-, and Kaiser-windows.

Details

Windowing of time series data, i.e., multiplication with a tapering function, is often useful in spectral or Fourier analysis in order to reduce "leakage" effects due to the discrete and finite sampling. These functions provide windowing coefficients for a given sample size N.

Value

A vector (of length N) of windowing coefficients.

Author(s)

Christian Roever, [e-mail]

References

Harris, F. J. On the use of windows for harmonic analysis with the discrete Fourier transform. Proceedings of the IEEE, 66(1):51–83, 1978. doi: 10.1109/PROC.1978.10837

Press, W. H., Teukolsky, S. A., Vetterling, W. T., Flannery, B. P. Numerical recipes in C. Cambridge University Press, 1992.

See Also

welchPSD, empiricalSpectrum

Examples

# illustrate the different windows' shapes:
N <- 100
matplot(1:N,
        cbind(cosinewindow(N),
              hammingwindow(N),
              hannwindow(N),
              kaiserwindow(N),
              squarewindow(N),
              trianglewindow(N),
              tukeywindow(N,r=0.5),
              welchwindow(N)),
        type="l", lty="solid", col=1:8)
legend(N, 0.99, legend=c("cosine","hamming","hann","kaiser",
                         "square","triangle","tukey","welch"),
       col=1:8, lty="solid", xjust=1, yjust=1, bg="white")

# show their effect on PSD estimation:
data(sunspots)



spec1 <- welchPSD(sunspots, seglength=10, windowfun=squarewindow)
plot(spec1$frequency, spec1$power, log="y", type="l")

spec2 <- welchPSD(sunspots, seglength=10, windowfun=tukeywindow, r=0.25)
lines(spec2$frequency, spec2$power, log="y", type="l", col="red")

spec3 <- welchPSD(sunspots, seglength=10, windowfun=trianglewindow)
lines(spec3$frequency, spec3$power, log="y", type="l", col="green")