Daubechies wavelet and scaling filters
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
a logical value. If
a character string denoting the filter type. Supported types include:
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.
an object of class
plot Daubechies filters.
Usage: plot(x, type="time")
A character string denoting the type of plot to produce. Choices are
"phase"for an impulse response, squared gain, and phase plot, respectively. Default:
print Daubechies filters.
Usage: print(x, verbose=TRUE)
A logical value. If
TRUE, the filter coefficients are also printed. Default:
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.
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