Daubechies wavelet and scaling filters

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Description

Ingrid Daubechies, a noted pioneer in wavelet theory, has established a number of wavelet filter types, each with different mathematical properties. This function calculates the wavelet and scaling coefficients for a given filter type. The wavelet coefficients, h(k) for k=0,...,L-1 where L is the filter length, are related to the scaling coefficients through the quadrature mirror filter (QMF) relation

h(k)=(-1)^(k-L) g(L-1-k)

Usage

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wavDaubechies(wavelet="s8", normalized=TRUE)

Arguments

normalized

a logical value. If TRUE, the filters are normalized by dividing each filter coefficient by the sqrt(2) (useful for maximum overlap wavelet transforms). If FALSE, no normalization is used. Default: TRUE.

wavelet

a character string denoting the filter type. Supported types include:

EXTREMAL PHASE (daublet):

"haar", "d2", "d4", "d6", "d8", "d10", "d12", "d14", "d16", "d18", "d20"

LEAST ASYMMETRIC (symmlet):

"s2","s4", "s6", "s8", "s10", "s12", "s14", "s16", "s18", "s20"

BEST LOCALIZED:

"l2","l4", "l6", "l14", "l18", "l20"

COIFLET:

"c6", "c12", "c18", "c24", "c30"

Default: "s8".

Details

Only relevant for Daubechies filter types. Inconsistent ordering of the coefficients in Daubechies' book was recognized and corrected by Percival (see references). The "correct" order is given here.

Value

an object of class wavDaubechies.

S3 METHODS

plot

plot Daubechies filters.

Usage: plot(x, type="time")

x

A wavDaubechies object.

type

A character string denoting the type of plot to produce. Choices are "time", "gain", and "phase" for an impulse response, squared gain, and phase plot, respectively. Default: "time".

print

print Daubechies filters.

Usage: print(x, verbose=TRUE)

x

A wavDaubechies object.

verbose

A logical value. If TRUE, the filter coefficients are also printed. Default: TRUE.

References

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

I. Daubechies, Orthonormal Bases of Compactly Supported Wavelets, Communications on Pure and, Applied Mathematics, 41, 909–96.

See Also

wavGain, wavDWT, wavMODWT, wavMODWPT.

Examples

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## obtain Daubechies least asymmetric 8-tap filter 
## set 
filters <- wavDaubechies("s8", normalize=TRUE)

## plot the impulse responses 
plot(filters, type="time")

## plot the gain function 
plot(filters, type="gain")

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