Filters

Functions to compute Daubechies scaling and wavelet filter coefficients.

The returned coefficients correspond to the compactly supported Daubechies wavelets indexed by the number of vanishing moments $p$, returning $2p$ taps.

Conventions: Boost indexes filters by vanishing moments (as in PyWavelets and Mathematica), normalizes coefficients to unit \(\ell_2\) norm, and uses the convolutional ordering shown in Daubechies (1988). Other libraries may index by number of taps, use a \(\sqrt{2}\) scaling, or reverse coefficient order.

Usage

daubechies_scaling_filter(order)

daubechies_wavelet_filter(order)

Arguments

order

An integer specifying the number of vanishing moments (1 to 19).

Value

A numeric vector of size 2*order containing the filter coefficients.

See also

Boost Documentation for more details on the mathematical background.

Examples

# Daubechies Scaling Filter of order 4
daubechies_scaling_filter(4)
#> [1]  0.23037781  0.71484657  0.63088077 -0.02798377 -0.18703481  0.03084138
#> [7]  0.03288301 -0.01059740
# Daubechies Wavelet Filter of order 4
daubechies_wavelet_filter(4)
#> [1] -0.01059740 -0.03288301  0.03084138  0.18703481 -0.02798377 -0.63088077
#> [7]  0.71484657 -0.23037781