Symmetric tight wavelet frames with rational coefficients

• Published in: Applied and computational harmonic analysis Vol. 31; no. 2; pp. 249 - 263
• Main Authors: Mo, Qun, Li, Song
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01-09-2011
• Subjects: Algorithms; Construction; Fejér–Riesz Lemma; Filter banks; Filter design; Fourier analysis; Frames; Harmonic analysis; Rational coefficients; Symmetry; Tight wavelet frames; Wavelet; Tight wavelet frames; Rational coefficients; Filter design; Fejér–Riesz Lemma; Symmetry
• ISSN: 1063-5203; 1096-603X
• DOI: 10.1016/j.acha.2011.01.002

In this paper we present a necessary and sufficient condition to construct a symmetric framelet system
a
(
z
)
,
b
1
(
z
)
and
b
2
(
z
)
having rational coefficients. Once a low-pass filter
a
(
z
)
is given and such a necessary and sufficient condition is satisfied, a step-by-step algorithm will be used to construct a symmetric framelet filter bank with two high-pass filters
b
1
(
z
)
and
b
2
(
z
)
which is of interest in applications such as signal de-noising and image de-blurring, etc. Two new examples will be given to illustrate our results and the algorithm.