Finite equal norm Parseval wavelet frames over prime fields

Abstract

Abstract. In the framework of wave packet analysis, finite wavelet systems are particular classes of finite wave packet systems. In this paper, using a scaling matrix on a permuted version of the discrete Fourier transform (DFT) of system generator, we derive a locally-scaled version of the DFT of system genarator and obtain a finite equal-norm Parseval wavelet frame over prime fields. We also give a characterization of all multiplicative subgroups of the cyclic multiplicative group, for which the associated wavelet systems form frames. Finally, we present some concrete examples as applications of our results.

More on Inequalities for Weaving Frames in Hilbert Spaces

“…The appearance of frames can be tracked back to the early 1950s when they were used in the work on nonharmonic Fourier series owing to Duffin and Schaeffer [1]. We refer to [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] for more information on general frame theory. It should be pointed out that frames have played an important role such as in signal processing [17,18], sigma-delta quantization [19], quantum information [20], coding theory [21], and sampling theory [22], due to their nice properties.…”