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: In this paper, the existence, uniqueness and Hyers-Ulam stability of an implicit coupled system of impulsive fractional differential equations having Hadamard type fractional derivative was studied.
Abstract: We present some results on the existence, uniqueness and Hyers–Ulam stability to the solution of an implicit coupled system of impulsive fractional differential equations having Hadamard type fractional derivative. Using a fixed point theorem of Kransnoselskii’s type, the existence and uniqueness results are obtained. Along these lines, different kinds of Hyers–Ulam stability are discussed. An example is given to illustrate the main theorems.
34 citations
TL;DR: In this paper, a non-recursive transform equation for the Fourier transform of a discrete Walsh function with a rectangular pulse was developed, which is a function of the bits of the Gray code number for the order of the Walsh function.
Abstract: Convolution of a discrete Walsh function with a rectangular pulse simplifies the derivation of an expression for the Fourier transform of a Walsh function. The nonrecursive transform equation that is developed is a function of the bits of the Gray code number for the order of the Walsh function.
33 citations
TL;DR: In this article, the Hermite-Hadamard type inequalities for fractional integrals were established for the first time, depending on a parameter of the integrals' complexity.
Abstract: In this paper, we have established Hermite-Hadamard type inequalities for
fractional integrals depending on a parameter.
33 citations
TL;DR: The proposed transform outperforms the well-known Walsh?Hadamard transform and the current state-of-the-art 16-point approximation and is experimentally validated using hardware implementations that are physically realized and verified on a maximum clock rate of 342?MHz.
Abstract: The discrete cosine transform (DCT) is the key step in many image and video coding standards. The eight-point DCT is an important special case, possessing several low-complexity approximations widely investigated. However, the 16-point DCT transform has energy compaction advantages. In this sense, this paper presents a new 16-point DCT approximation with null multiplicative complexity. The proposed transform matrix is orthogonal and contains only zeros and ones. The proposed transform outperforms the well-known Walsh?Hadamard transform and the current state-of-the-art 16-point approximation. A fast algorithm for the proposed transform is also introduced. This fast algorithm is experimentally validated using hardware implementations that are physically realized and verified on a 40?nm CMOS Xilinx Virtex-6 XC6VLX240T FPGA chip for a maximum clock rate of 342?MHz. Rapid prototypes on FPGA for a 8-bit input word size show significant improvement in compressed image quality by up to 1?2?dB at the cost of only eight adders compared to the state-of-art 16-point DCT approximation algorithm in the literature (Bouguezel et al 2010 Proc. 53rd IEEE Int. Midwest Symp. on Circuits and Systems).
33 citations
33 citations