We propose a design procedure for the real, equal-norm, lapped tight frame transforms (LTFTs). These transforms have been recently proposed as both a redundant counterpart to lapped orthogonal transforms and an infinite-dimensional counterpart to harmonic tight frames. In addition, LTFTs can be efficiently implemented with filter banks. The procedure consists of two steps. First, we construct n...

We introduce a new discrete fractional Fourier transform (DFrFT) based on only the DFT matrix and its powers. Eigenvectors of the DFT matrix are obtained in a simple-yetelegant and straightforward manner. We show that this DFrFT definition based on the eigentransforms of the DFT matrix mimics the properties of continuous fractional Fourier transform (FrFT) by approximating the samples of the co...

A fundamental result of free probability theory due to Voiculescu and subsequently refined by many authors states that conjugation by independent Haar-distributed random unitary matrices delivers asymptotic freeness. In this paper we exhibit many other systems of random unitary matrices that, when used for conjugation, lead to freeness. We do so by first proving a general result asserting “asym...

background: a balanced nutrition schedule provides the essential substances for proper oral health. objectives: the aim of this study was to investigate the association between dental caries and body mass index in 6-11 year-old children in zahedan. materials and methods: in this cross-sectional study 1213 children (670 girls, 543 boys) were included. body mass index (bmi) and clinical examinati...

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A DFT algorithm, the Extended Subband DFT (ESB−−DFT), is presented, which aims to overcome the problem of low accuracy the Subband DFT (SB−−DFT) algorithm suffers from, when applied in its approximate mode for signals with full spectrum. The proposed ESB−DFT is based upon the analysis of the input signal using a Filter Bank (FB) and the computation of its DFT from the lower length DFTs that cor...