wmtsa (version 1.1-1)

wavMRD: Calculate the detail sequences for wavelet transform crystals

Description

Let $\mathbf{W}_{j,n}$ be a discrete wavelet packet crystal where $j$ is the decomposition level and $n$ is the oscillation index. The detail sequence ${\mathcal{D}}_{j,n}$ is formed (essentially) by reconstructing the transform after zeroing out all other crystals except $\mathbf{W}_{j,n}$. The wavMRD function calculates the details for a DWT and MODWT in an optimized way.

Usage

wavMRD(x, level=NULL, osc=NULL)

Arguments

x

an object of class wavTransform.

level

an integer (vector) containing the decomposition level(s) corresponding to the crystal(s) to be decomposed. Default: If the input is of class wavTransform, then the default is to return the details at all levels of the transform, i.e., a full

osc

an integer (vector) containing the oscillation indices corresponding to the crystal(s) to be decomposed. Default: the default values are coordinated with that of the level argument.

Value

• an object of class WaveletMRD.

concept

class constructordetail function generationmultiresolution decompositionwavelet

References

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

See Also

wavMRDSum, reconstruct, wavDWT, wavMODWT.

Examples

## calculate various wavelet transforms of the 
## first difference of a linear chirp sequence 
x <- make.signal("linchirp", n=1024)
x.dwt <- wavDWT(x, n.levels = 3)
x.modwt <- wavMODWT(x, n.levels = 3)

## calculate the wavelet details for all crystals 
## of the DWT and MODWT 
wavMRD(x.dwt)
wavMRD(x.modwt)

## plot the wavelet details for levels 1 and 3 of 
## the MODWT 
plot(wavMRD(x.modwt, level = c(1,3)))

## plot the wavelet details for all levels of the 
## MODWT of a linear chirp. 
plot(wavMRD(x.modwt))