multiwave (version 1.0)

DWTexact: Exact discrete wavelet decomposition

Description

Computes the discrete wavelet transform of the data using the pyramidal algorithm.

Usage

DWTexact(x, filter)

Arguments

x

vector of raw data

filter

Quadrature mirror filter (also called scaling filter, as returned by the scaling_filter function)

Value

dwt

computable Wavelet coefficients without taking into account the border effect.

indmaxband

vector containing the largest index of each band, i.e. for $j > 1$ the wavelet coefficients of scale $j$ are $\code{dwt}(k)$ for $k in [\code{indmaxband}(j-1)+1,\code{indmaxband}(j)]$ and for $j=1$, $\code{dwt}(k)$ for $k in [1,\code{indmaxband}(1)]$.

Jmax

largest available scale index (=length of indmaxband).

References

G. Fay, E. Moulines, F. Roueff, M. S. Taqqu (2009) Estimators of long-memory: Fourier versus wavelets. Journal of Econometrics, vol. 151, N. 2, pages 159-177.

S. Achard, I. Gannaz (2014) Multivariate wavelet Whittle estimation in long-range dependence. arXiv, http://arxiv.org/abs/1412.0391

See Also

scaling_filter

Examples

res_filter <- scaling_filter('Daubechies',8);
filter <- res_filter$h
u <- rnorm(2^10,0,1)
x <- vfracdiff(u,d=0.2)

	resw <- DWTexact(x,filter)
		xwav <- resw$dwt
		index <- resw$indmaxband
		Jmax <- resw$Jmax

## Wavelet scale 1
ws_1 <- xwav[1:index[1]]
## Wavelet scale 2
ws_2 <- xwav[(index[1]+1):index[2]]
## Wavelet scale 3
ws_3 <- xwav[(index[2]+1):index[3]]
### upto Jmax