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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24 Oct 2005
TL;DR: The authors developed a programmable Walsh function generator for 64 outputs by both field programmable gate arrays and lookup table cascades to estimate the amount of hardware and performance.
Abstract: This paper presents an algorithm to generate Walsh functions in four different orderings: Hadamard, Harmuth, Paley and strict sequency. By the analysis of the properties and mutual relations among these four orderings, the authors found a unified approach to generate any of the orderings from the primary set of Rademacher functions. By using these properties, the authors developed a programmable Walsh function generator for 64 outputs by both field programmable gate arrays and lookup table cascades to estimate the amount of hardware and performance. Such a programmable Walsh function generator can be used in VLSI testing, CDMA, pattern recognition, as well as image and signal processing.
36 citations
TL;DR: The concept of energy packing efficiency of the Walsh-Hadamard transform is extended to other discrete orthogonal transforms and it is shown that the EPE is invariant for the generalized transforms as long as the ordering is the same.
Abstract: The concept of energy packing efficiency (EPE) of the Walsh-Hadamard transform (WHT) first proposed by Kitajima [1], is extended to other discrete orthogonal transforms. The concept as a criterion for evaluating the transforms is discussed. It is shown that the EPE is invariant for the generalized transforms as long as the ordering is the same.
36 citations
TL;DR: A block based lossless image compression algorithm using Hadamard transform and Huffman encoding which is a simple algorithm with less complexity that yields better results in terms of compression ratio when compared with existing lossless compression algorithms such as JPEG 2000.
36 citations
TL;DR: A synthesis method of optical Hadamard transformer using multimode interference (MMI) couplers is proposed and it is shown that sum and difference units of input signals can be synthesized.
Abstract: We propose a synthesis method of optical Hadamard transformer using multimode interference (MMI) couplers. By using the signal transfer matrix of 2 x 2, 4 x 4, and 8 x 8 MMI couplers, we show that sum and difference units of input signals can be synthesized. An interchange unit of two signals can also be synthesized. One synthesis method of Hadamard transformers is a combination of only 2 x 2 units, and the other is a combination of N x N(N > or = 4) units as well as 2 x 2 units. The design examples of operation units are shown, and the size and the output power of Hadamard transformers are estimated.
36 citations
TL;DR: The four smallest cases among these 17 cases are examined and the conjecture that all cyclic Hadamard difference sets have parameter v which falls into one of the three types of v is confirmed for all v ≤ 3435.
Abstract: Balanced binary sequences with ideal autocorrelation are equivalent to (v, k, λ)-cyclic Hadamard difference sets with v = 4n − 1, k = 2n − 1, λ = n − 1 for some positive integer n. Every known cyclic Hadamard difference set has one of the following three types of v : (1) v = 4n − 1 is a prime. (2) v is a product of twin primes. (3) v = 2n − 1 for n = 2, 3, …. It is conjectured that all cyclic Hadamard difference sets have parameter v which falls into one of the three types. The conjecture has been previously confirmed for n < 10000 except for 17 cases not fully investigated. In this paper, four smallest cases among these 17 cases are examined and the conjecture is confirmed for all v ≤ 3435. In addition, all the inequivalent cyclic Hadamard difference sets with v = 2n − 1 for n ≤ 10 are listed and classified according to known construction methods.
36 citations