scalingshift.dwt: Find Circular Shift of DWT Scaling Coefficients

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

Description

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

Usage

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

Arguments

L	Length of wavelet transform filter used.
j	Level of DWT scaling 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 scaling coefficients (with NAs inserted) with indices 1,2,3,4,5,6,7,8 and the value outputted from the function scalingshift.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 vjH in formulas (114c) in Wavelet Methods for Time Series Analysis by Percival and Walden (2000). (And optionally vjH Modulo N)

Value

shift

Circular shift for specified level of DWT scaling 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

waveletshift.dwt and plot.dwt

Examples

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

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

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