Topic
Hadamard transform
About: Hadamard transform is a research topic. Over the lifetime, 7262 publications have been published within this topic receiving 94328 citations.
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TL;DR: A variant of Hadamard (HDM) ratio test is devised to exploit the NC property of the primary signals for spectrum sensing, which is named the NC-HDM algorithm, and it is shown that it is superior to the state-of-the-art algorithms in detection accuracy and/or robustness.
Abstract: Although noncircular (NC) signals are frequently encountered in wireless communications, their statistical property has not yet been utilized in state-of-the-art methods for spectrum sensing. In this paper, a variant of Hadamard (HDM) ratio test is devised to exploit the NC property of the primary signals for spectrum sensing, which is named the NC-HDM algorithm. As the NC-HDM approach is able to exploit full statistical property of the NC signals and handle deviations from independent and identically distributed (IID) noise, it is superior to the state-of-the-art algorithms in detection accuracy and/or robustness. Moreover, performance analysis is conducted for the NC-HDM approach, including the invariant property, false-alarm probability and detection probability. That is, employing the moment-matching Box's Chi-square approximation, the false-alarm probability can be determined. Since the exact moments of the NC-HDM test statistic under the signal-absence hypothesis can be determined and all moments have been matched, the derived false-alarm probability is very accurate, leading to simple and precise computation of the theoretical decision threshold. On the other hand, as the first two exact moments of the NC-HDM test statistic under the signal-presence hypothesis can be precisely calculated, the detection probability based on moment-matching Beta approximation is quite accurate. Numerical results are included to demonstrate the superiority of the NC-HDM approach and validate our theoretical calculations.
35 citations
15 May 2014
TL;DR: In this article, the Tikhonov regularization was combined with the theory of reproducing kernels to give natural generalized solutions of Hadamard and tensor products equations for matrices.
Abstract: We shall give natural generalized solutions of Hadamard and tensor products equations for matrices by the concept of the Tikhonov regularization combined with the theory of reproducing kernels.
35 citations
TL;DR: A Unified fast algorithm for computation of the introduced tree-structured Haar transforms is presented, which requires 2(N − 1) additions and 3N −2 multiplications.
Abstract: The Haar transform is generalized to the case of an arbitrary time and scale splitting. To any binary tree we associate an orthogonal system of Haar-type functions – tree-structured Haar (TSH) functions. Unified fast algorithm for computation of the introduced tree-structured Haar transforms is presented. It requires 2(N − 1) additions and 3N −2 multiplications, where N is transform order or, equivalently, the number of leaves of the binary tree.
35 citations
TL;DR: In this article, the Hermite-Hadamard type inequalities for generalized convex functions were established for Tcheby-chev systems, based on moment spaces induced by Tchebyschev systems.
Abstract: Applying some fundamental results concerning moment spaces induced by Tcheby-chev systems, we establish Hermite–Hadamard type inequalities for generalized convex functions.
35 citations
TL;DR: In this article, an integral identity and some Hermite-Hadamard-Fejer type integral inequalities for p-convex functions in fractional integral forms are obtained.
Abstract: In this paper, firstly, Hermite–Hadamard–Fejer type inequalities for p-convex functions in fractional integral forms are built. Secondly, an integral identity and some Hermite–Hadamard–Fejer type integral inequalities for p-convex functions in fractional integral forms are obtained. Finally, some Hermite–Hadamard and Hermite–Hadamard–Fejer inequalities for convex, harmonically convex and p-convex functions are given. Many results presented here for p-convex functions provide extensions of others given in earlier works for convex, harmonically convex and p-convex functions.
34 citations