waveslim (version 1.12)

shift.2d: Circularly Shift Matrices from a 2D MODWT

Description

Compute phase shifts for wavelet sub-matrices based on the ``center of energy'' argument of Hess-Nielsen and Wickerhauser (1996).

Usage

shift.2d(z, wf, inv=FALSE)

Arguments

z

2D MODWT object

wf

Character string for wavelet filter.

inv

Boolean value on whether to perform the forward or inverse operation.

Value

• 2D MODWT object with circularly shifted coefficients.

Details

The "center of energy" technique of Wickerhauser and Hess-Nielsen (1996) is employed to find circular shifts for the wavelet sub-matrices such that the coefficients are aligned with the original series. This corresponds to applying a (near) linear-phase filtering operation.

References

Hess-Nielsen, N. and M. V. Wickerhauser (1996) Wavelets and time-frequency analysis, Proceedings of the IEEE, 84, No. 4, 523-540. Percival, D. B. and A. T. Walden (2000) Wavelet Methods for Time Series Analysis, Cambridge University Press.

See Also

phase.shift, modwt.2d.

Examples

G1 <- G2 <- dnorm(seq(-512/4,512/4,length=512))
G <- 100 * zapsmall(G1 %o% G2)
J <- 6
G <- modwt.2d(G, "la8", J)
names.modwt <- c(t(sapply(c("LH","HL","HH"), paste, 1:J, sep="")), 
                 paste("LL", J, sep=""))
n <- 50
par(mfrow=c(3,3), mar=c(5,4,4,2)/1.9, pty="s")
for(i in names.modwt[1:9])
  image(G[[i]][256 + -n:n, 256 + -n:n], axes=FALSE, col=rainbow(128), main=i)
Gs <- shift.2d(G, "la8")
for(i in names.modwt[1:9])
  image(Gs[[i]][256 + -n:n, 256 + -n:n], axes=FALSE, col=rainbow(128), main=i)