An important tool for the construction of tight wavelet frames on local fields of positive characteristic with the help of unitary extension principles was presented by Shah and Debnath [Tight wavelet frames on local fields, Analysis, 33 (2013), 293–307]. In this paper, we continue the study based on the extension principles and give an explicit construction of a class of tight framelet packets...

In this paper, we obtain symmetric C∞ real-valued tight wavelet frames in L2(R) with compact support and the spectral frame approximation order. Furthermore, we present a family of symmetric compactly supported C∞ orthonormal complex wavelets in L2(R). A complete analysis of nonstationary tight wavelet frames and orthonormal wavelet bases in L2(R) is given.

We present a design scheme to generate tight and semi-tight frames in the space of discrete-time periodic signals, which are originated from four-channel perfect reconstruction periodic filter banks. The filter banks are derived from interpolating and quasi-interpolating polynomial splines. Each filter bank comprises one linear phase low-pass filter (in most cases interpolating) and one high-pa...

Based on the method for constructing tight wavelet frames of [RS2], we show that one can construct, for any dilation matrix, and in any spatial dimension, tight wavelet frames generated by compactly supported functions with arbitrarily high smoothness. AMS (MOS) Subject Classifications: Primary 42C15, Secondary 42C30

Frames are an essential tool for many emerging applications such as data transmission. Their main advantage is the fact that frames can be designed to be redundant while still providing reconstruction formulas. This makes them robust against noise and losses while allowing freedom in design (see, for example, [5, 10]). Due to their numerical stability, tight frames and Parseval frames are of in...

Finite tight frames are used widely for many applications. An important problem is to construct finite frames with prescribed norm for each vector in the tight frame. In this paper we provide a fast and simple algorithm for such purpose. Our algorithm employs the Householder transformations. For a finite tight frame consisting m vectors in R or C only O(nm) operations are needed. In addition, w...

Oversampled filter banks can be used to enhance resilience to erasures in communication systems in much the same way that finite-dimensional frames have previously been applied. This paper extends previous finite dimensional treatments to frames and signals in l2(Z) with frame expansions that can be implemented efficiently with filter banks. It is shown that tight frames attain best performance...