A characterization of nonhomogeneous dual and weak dual wavelet superframes for Walsh‐reducing subspace of L2(ℝ+,ℂL)$$ {L}^2\left({\mathbb{R}}_{+},{\mathbb{C}}^L\right) $$

Abstract

The concept of superframe was first introduced by Balan in the context of signal multiplexing and by Han and Larson from the perspective of pure mathematics. Since then, the theory of super wavelet (Gabor) frames has been well developed. In recent years, due to enjoying the same fast algorithm as affine wavelet frames and having more freedom to design wavelet masks, nonhomogeneous wavelet frames have attracted much attention of many mathematicians. This paper addresses (weak) nonhomogeneous dual wavelet superframes in the setting of Walsh‐reducing subspaces of . We present a characterization of nonhomogeneous (weak) dual wavelet superframe pairs in a Walsh‐reducing subspace of . Some examples are also provided.