atrous_dwt {fastWavelets}

A Trous Discrete Wavelet Transform

Description

This function calculates the wavelet and scaling coefficients of the a trous (AT) version of the Discrete Wavelet Transform (DWT).

Usage

atrous_dwt(X, wavelet, decomp_level)

Arguments

X

An (N x 1) matrix or a vector

wavelet

Scaling filter name (see Details below) (string)

decomp_level

Decomposition level (integer, 1 < decomp_level < N/2)

Details

The argument wavelet can take one of the following values:

c("haar", "d1", "sym1", "bior1.1", "rbio1.1", "d2", "sym2", "d3", "sym3", "d4", "d5", "d6", "d7", "d8", "d9", "d10", "d11", "sym4", "sym5", "sym6", "sym7", "sym8", "sym9", "sym10", "coif1", "coif2", "coif3", "coif4", "coif5", "bior1.3", "bior1.5", "bior2.2", "bior2.4", "bior2.6", "bior2.8", "bior3.1", "bior3.3", "bior3.5", "bior3.7", "bior3.9", "bior4.4", "bior5.5", "bior6.8", "rbio1.3", "rbio1.5", "rbio2.2", "rbio2.4", "rbio2.6", "rbio2.8", "rbio3.1", "rbio3.3", "rbio3.5", "rbio3.7", "rbio3.9", "rbio4.4", "rbio5.5", "rbio6.8", "la8", "la10", "la12", "la14", "la16", "la18", "la20", "bl14", "bl18", "bl20", "fk4", "fk6", "fk8", "fk14", "fk18", "fk22", "b3spline", "mb4.2", "mb8.2", "mb8.3", "mb8.4", "mb10.3", "mb12.3", "mb14.3", "mb16.3", "mb18.3", "mb24.3", "mb32.3", "beyl", "vaid", "han2.3", "han3.3", "han4.5", "han5.5")

Value

Wavelet and scaling coefficients (N x J+1) (wavelet coefficients in first J columns of returned matrix)

References

Benaouda, D., F. Murtagh, J. L. Starck, and O. Renaud (2006), Wavelet-based nonlinear multiscale decomposition model for electricity load forecasting, Neurocomputing, doi:10.1016/j.neucom.2006.04.005.

Maheswaran, R., and R. Khosa (2012), Comparative study of different wavelets for hydrologic forecasting, Comput. Geosci., doi:10.1016/j.cageo.2011.12.015.

Examples

N <- 1000 #  number of time series points
J <- 4 # decomposition level
wavelet <- 'coif1' # wavelet filter
X <- matrix(rnorm(N),N,1)
W <- atrous_dwt(X,wavelet,J)
Xr <- as.matrix(rowSums(W)) # reconstruct time series
mse_r <- mean( (X - Xr)^2) # confirm additive reconstruction
plot.ts(W) # plot wavelet and scaling coefficients