waveletshift.dwt: Find Circular Shift of DWT Wavelet Coefficients

In wavelets: Functions for Computing Wavelet Filters, Wavelet Transforms and Multiresolution Analyses

Description

Finds circular shift of DWT wavelet coefficients at a specified level, for a specified filter length.

Usage

waveletshift.dwt(L, j, N = NULL)

Arguments

L	Length of wavelet transform filter used.
j	Level of DWT wavelet coefficients to be shifted.
N	Length of original time series sample.

Details

This function computes the circular shift associated with a wavelet transform filter of length L and level j. L must be of even length.

Each coefficient's index will be circularly shifted forward by the value outputted. For example, if we have a vector of DWT wavelet coefficients (with NAs inserted) with indices 1,2,3,4,5,6,7,8 and the value outputted from the function waveletshift.dwt is 2, the new order of the vector of aligned DWT wavelet coefficients would be 7,8,1,2,3,4,5,6.

If N is specified, the function will output the "shift" Modulo N. Because the shift is circular, the value outputted when N is specified is equivalent to the case when N is not specified.

This function calculates the absolute value of vjG in formulas (114c) in Wavelet Methods for Time Series Analysis by Percival and Walden (2000). (And optionally vjG Modulo N)

Value

shift

Circular shift for specified level of DWT wavelet coefficients for a specified filter length.

Author(s)

Kelvin Ma, [e-mail]

References

Percival, D. B. and A. T. Walden (2000) Wavelet Methods for Time Series Analysis, Cambridge University Press.

See Also

scalingshift.dwt and plot.dwt

Examples

# Finding the circular shift for a wavelet transform filter of length 8,
# pertaining to DWT Wavelet Coefficients of level 5.
waveletshift.dwt(8, 5)

# If the sample size of the original time series is of length 1024.
waveletshift.dwt(8, 5, N = 1024)

Example output

[1] 109
[1] 109

wavelets documentation built on March 26, 2020, 6:50 p.m.