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Explicit four-tap Daubechies filter and its high-pass partner

Definition

Set $h = \frac{1}{4 \sqrt{2}} (1 + \sqrt{3}, 3 + \sqrt{3}, 3 - \sqrt{3}, 1 - \sqrt{3}), g_{j} = (- 1)^{j} h_{3 - j} (0 \leq j \leq 3) .$ Both filters are zero outside the indices $0, 1, 2, 3$ . The high-pass filter is therefore $g = (h_{3}, - h_{2}, h_{1}, - h_{0})$ . The exact admissibility and two-moment properties of this pair are the statement of The explicit four-tap Daubechies pair satisfies the orthogonal filter and two-moment conditions ↗.

Used by

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Nothing. This result depends on no other item in the library.

Sources

Gilbert Strang and Kevin Amaratunga, Wavelets and Filter Banks, MIT OpenCourseWare 18.327, Handout 8 (standard reference, not scraped)
Jelena Kovačević, Vivek K. Goyal, and Martin Vetterli, Fourier and Wavelet Signal Processing (standard reference, not scraped)