wavIndex: Boundary and interior wavelet coefficient identification

In wmtsa: Wavelet Methods for Time Series Analysis

Description

The boundary wavelet and scaling coefficients are those subject to circular filtering operations. This function returns the range of indices which span the interior (or nonboundary) wavelet and scaling coefficients. If approximate zero phase filters are used in the wavelet trsnsform input then the shift factors needed to bring the coefficients to (approximate) zero phase are also returned.

Usage

wavIndex(x)

Arguments

x	an object of class wavTransform or wavBoundary. The transform type must be a DWT or MODWT.

Value

a list the indices locating the interior and boundary coefficients as well as the the zero phase shift factors need for each level of the transform.

References

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

See Also

wavDWT, wavMODWT.

Examples

## calculate the coefficient indices for a MODWT 
## of a simple time series 
wavIndex(wavMODWT(1:8, wavelet="s8"))

Example output

$interior
$interior$low
d1 d2 d3 s1 s2 s3 
 8  0  0  8  0  0 

$interior$high
d1 d2 d3 s1 s2 s3 
 8  0  0  8  0  0 

$interior$length
d1 d2 d3 s1 s2 s3 
 1  0  0  1  0  0 


$boundary
$boundary$length
d1 d2 d3 s1 s2 s3 
 7  8  8  7  8  8 


$all
$all$length
d1 d2 d3 s1 s2 s3 
 8  8  8  8  8  8 


$shift
$shift$dwt
d1 d2 d3 s1 s2 s3 
-2 -2 -3 -1 -2 -2 

$shift$modwt
 d1  d2  d3  s1  s2  s3 
 -4 -11 -25  -3  -9 -21 

$shift$dwpt
w1.0 w1.1 w2.0 w2.1 w2.2 w2.3 w3.0 w3.1 w3.2 w3.3 w3.4 w3.5 w3.6 w3.7 
  -1   -2   -2   -2   -3   -2   -2   -3   -3   -2   -3   -3   -3   -2 

$shift$modwpt
w1.0 w1.1 w2.0 w2.1 w2.2 w2.3 w3.0 w3.1 w3.2 w3.3 w3.4 w3.5 w3.6 w3.7 
  -3   -4   -9  -11  -12  -10  -21  -25  -27  -23  -24  -28  -26  -22 

wmtsa documentation built on May 2, 2019, 6:50 p.m.