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Showing papers on "Hadamard transform published in 2003"


Posted Content
TL;DR: The Hermite-Hadamard double inequality for convex functions has been studied extensively in the literature, see as discussed by the authors for a survey of the Hermite Hadamard inequalities.
Abstract: The Hermite-Hadamard double inequality is the first fundamental result for convex functions defined on a interval of real numbers with a natural geometrical interpretation and a loose number of applications for particular inequalities. In this monograph we present the basic facts related to Hermite- Hadamard inequalities for convex functions and a large number of results for special means which can naturally be deduced. Hermite-Hadamard type inequalities for other concepts of convexities are also given. The properties of a number of functions and functionals or sequences of functions which can be associated in order to refine the result are pointed out. Recent references that are available online are mentioned as well.

685 citations


Book
17 Oct 2003
TL;DR: It is shown here how orthogonal Latin squares can be transformed into BIBDs using Hadamard matrices, and how different sets and automorphisms can be modified for different levels of integration.
Abstract: Introduction to BIBDs.- Symmetric BIBDs.- Difference sets and automorphisms.- Hadamard matrices and designs.- Resolvable BIBDs.- Steiner triple systems.- Mutually orthogonal Latin squares.- Pairwise balanced designs.- t-designs.- Orthogonal arrays and codes.- Index.

498 citations



Journal ArticleDOI
TL;DR: New bounds on the TSC of binary signature sets are derived for any number of signatures K and any signature length L and for almost all K, L in {1,2,...,256}, and the design procedure is based on simple transformations of Hadamard matrices.
Abstract: The Welch lower bound (see Welch, R.L., IEEE Trans. Inform. Theory, vol.IT-20, p.397-9, 1974) on the total squared correlation (TSC) of signature sets is known to be tight for real-valued signatures and loose for binary signatures whose number is not a multiple of four. We derive new bounds on the TSC of binary signature sets for any number of signatures K and any signature length L. Then, for almost all K, L in {1,2,...,256}, we design optimum binary signature sets that achieve the new bounds. The design procedure is based on simple transformations of Hadamard matrices.

171 citations


Posted Content
TL;DR: In this article, Shi proved that Toffoli and Hadamard are universal for quantum computation and showed that one only needs to add the Hadamaard gate to make a 'classical' set of gates quantum universal.
Abstract: Recently Shi proved that Toffoli and Hadamard are universal for quantum computation This is perhaps the simplest universal set of gates that one can hope for, conceptually; It shows that one only needs to add the Hadamard gate to make a 'classical' set of gates quantum universal In this note we give a few lines proof of this fact relying on Kitaev's universal set of gates, and discuss the meaning of the result

169 citations


Journal ArticleDOI
TL;DR: In this paper, the notion of variational inequalities is extended to Hadamard manifolds and related to geodesic convex optimization problems, and a convexity property of the solution set of a variational inequality on a hadamard manifold is presented.
Abstract: The notion of variational inequalities is extended to Hadamard manifolds and related to geodesic convex optimization problems. Existence and uniqueness theorems for variational inequalities on Hadamard manifolds are proved. A convexity property of the solution set of a variational inequality on a Hadamard manifold is presented.

149 citations


Journal ArticleDOI
TL;DR: Direct frequency-domain excitation of NMR with an array of different radiofrequencies has been used to speed up two-dimensional NMR experiments by a large factor and is presented in the form of a high-resolution contour diagram similar to the familiar two- dimensional spectra obtained by Fourier transform methods.

127 citations


Journal ArticleDOI
TL;DR: This work examines feature-specific imaging using Wavelet, Karhunen-Loeve, Hadamard, and independent-component features, quantifying feature fidelity in Gaussian-, shot-, and quantization-noise environments, and demonstrates that within a high- noise environment it is possible to improve image fidelity via direct feature measurement.
Abstract: We analyze the performance of feature-specific imaging systems. We study incoherent optical systems that directly measure linear projects of the optical irradiance distribution. Direct feature measurement exploits the multiplex advantage, and for small numbers of projections can provide higher feature-fidelity than those systems that postprocess a conventional image. We examine feature-specific imaging using Wavelet, Karhunen-Loeve (KL), Hadamard, and independent-component features, quantifying feature fidelity in Gaussian-, shot-, and quantization-noise environments. An example of feature-specific imaging based on KL projections is analyzed and demonstrates that within a high-noise environment it is possible to improve image fidelity via direct feature measurement. A candidate optical system is presented and a preliminary implementational study is undertaken.

120 citations


Reference EntryDOI
15 Apr 2003
TL;DR: In this article, the authors give an up-to-date review of complementary sequences, first defined by Marcel Golay, and discuss correlation and spectral properties of the sequences as well as describing applications.
Abstract: This chapter gives an up-to-date review of Complementary Sequences, first defined by Marcel Golay. The survey discusses correlation and spectral properties of the sequences aswell as describing applications. It also presents fundamental constructions for Complementary Sequences and Complementary Sets. Connections with orthogonal and Hadamard matrices are also elaborated. Keywords: Golay complementary sequences; complementary sets; Rudin-Shapiro; aperiodic autocorrelation; flat polynomials; peak-to-mean envelope power ratio; PMEPR; PAPR merit factor; orthogonal matrices; Hadamard matrices

114 citations


Journal ArticleDOI
TL;DR: Deterministic sequences of perturbations for two-timescale SPSA algorithms are considered: complete lexicographical cycles and much shorter sequences based on normalized Hadamard matrices.
Abstract: Simultaneous perturbation stochastic approximation (SPSA) algorithms have been found to be very effective for high-dimensional simulation optimization problems. The main idea is to estimate the gradient using simulation output performance measures at only two settings of the N-dimensional parameter vector being optimized rather than at the N + 1 or 2N settings required by the usual one-sided or symmetric difference estimates, respectively. The two settings of the parameter vector are obtained by simultaneously changing the parameter vector in each component direction using random perturbations. In this article, in order to enhance the convergence of these algorithms, we consider deterministic sequences of perturbations for two-timescale SPSA algorithms. Two constructions for the perturbation sequences are considered: complete lexicographical cycles and much shorter sequences based on normalized Hadamard matrices. Recently, one-simulation versions of SPSA have been proposed, and we also investigate these algorithms using deterministic sequences. Rigorous convergence analyses for all proposed algorithms are presented in detail. Extensive numerical experiments on a network of M/G/1 queues with feedback indicate that the deterministic sequence SPSA algorithms perform significantly better than the corresponding randomized algorithms.

100 citations


Journal ArticleDOI
TL;DR: It is shown that the BEP performance of the commonly used Hadamard transform is asymptotically bad, and alternative orthogonal transforms with better asymPTotic performance are proposed.
Abstract: Multicarrier spread spectrum transmission methods based on orthogonal frequency division multiplexing employ a linear transform to spread energy of transmitted symbols over statistically independent Rayleigh fading subcarriers, in order to enable a diversity gain at the receiver. We jointly treat the mapping from bits into transmit symbols and the spreading transform as a code in Euclidean space. We describe criteria to identify good and bad spreading transforms, in terms of the asymptotic bit-error probability (BEP) at high signal-to-noise ratio. Upper and lower bounds on the BEP are derived. It is shown that the BEP performance of the commonly used Hadamard transform is asymptotically bad. Alternative orthogonal transforms with better asymptotic performance are proposed. Simulation results are given for the example of 2-phase-shift keying, block length 8.

Journal ArticleDOI
TL;DR: Three-dimensional TOCSY-HSQC experiments on strychnine at 700 MHz bear out the ideas, indicating that the measurement time can be reduced by as much as three orders of magnitude in favorable cases.

Journal ArticleDOI
Tae Young Lee1
TL;DR: An algorithm and its implementation to recompress video frame data, which is to be stored into external memory, are proposed, thereby enabling reduction of memory requirements and bandwidth and reducing the total compression/decompression latency cycles.
Abstract: An algorithm and its implementation to recompress video frame data, which is to be stored into external memory, are proposed, thereby enabling reduction of memory requirements and bandwidth. To support random access capability, frames are organized as 1/spl times/8-pixel arrays, which are then compressed into 32-bit segments. The compression ratio is fixed at 50%. For both compression efficiency and low complexity, modified Hadamard transform and Golomb-Rice (GR) coding are utilized. Objective and subjective video quality assessments are performed. Efficient hardware designs including GR encoding/decoding and packing/unpacking are also proposed to reduce the total compression/decompression latency cycles. The proposed hardware designs are suitable for the integration with MPEG-2 decoders thanks to fast operation and simple interface logic.

Journal ArticleDOI
TL;DR: A new technique is proposed for multichannel excitation and detection of NMR signals in the frequency domain, an alternative to the widely used pulse-excited Fourier transform method, which offers the same sensitivity advantage as conventional Fouriertransform spectroscopy.

Journal ArticleDOI
TL;DR: In this paper, the authors investigate (ω 1,ω 2 ) -convex functions and obtain characterization theorems and Hadamard-type inequalities for them, and show that these inequalities are equivalent to the same properties for (ω 2,ω 3 ) functions.
Abstract: In this paper we investigate (ω1,ω2) -convex functions and obtain characterization theorems and Hadamard-type inequalities for them. Mathematics subject classification (2000): 26A51, 26B25.

Journal ArticleDOI
TL;DR: This paper studies the open cases of the Welch lower bound on the total-squared-correlation (TSC) of binary signature sets whose length L is not a multiple of 4.
Abstract: The Welch lower bound on the total-squared-correlation (TSC) of binary signature sets is loose for binary signature sets whose length L is not a multiple of 4 Recently Karystinos and Pados l6,7r developed new bounds that are better than the Welch bound in those cases, and showed how to achieve the bounds with modified Hadamard matrices except in a couple of cases In this paper, we study the open cases

Journal ArticleDOI
TL;DR: This review covers the basic principles of Hadamard transform time-of-flight mass spectrometry and illustrates the source of the high-duty cycle and the increase in SNR.
Abstract: Hadamard transform time-of-flight mass spectrometry (HT-TOF MS) is a type of mass analysis that was developed to couple continuous ion sources to the inherently pulsed nature of time-of-flight measurements. Unlike conventional TOF MS, the Hadamard transform method offers a duty cycle of 50 %, with the possibility of extending it to 100 %. Because it is a multiplexing technique, the attainable signal-to-noise ratio (SNR) is also significantly higher than that of conventional TOF MS. This review covers the basic principles behind HT TOF MS. We illustrate, through examples, the source of the high-duty cycle and the increase in SNR. These features translate to a mass spectral storage rate that is the fastest among similar instruments, which enables its use as a detector for high-speed separations.

Patent
05 Dec 2003
TL;DR: In this article, the authors proposed an image processing apparatus for carrying out image compression/decoding with a simple arithmetic operation, making the processing system compact, and obtaining a compression efficiency and image quality after decoding equivalent to those by the JPEG.
Abstract: PROBLEM TO BE SOLVED: To provide an image processing apparatus for carrying out image compression/decoding with a simple arithmetic operation, making the processing system compact, and obtaining a compression efficiency and image quality after decoding equivalent to those by the JPEG. SOLUTION: The image processing apparatus includes: a DC image generating section 3 for averaging pixel values to obtain a DC value in a pixel block comprising 4×4 pixels; a first stage Hadamard encoding section 5 that divides the pixel block into sub pixel blocks each comprising 2×2 pixels, obtains the average pixel value of each of the sub pixel blocks, performs an arithmetic operation for predicting an AC component to obtain a DC pixel value of the sub pixel blocks on the basis of the DC values of the pixel block of the processing object and other pixel blocks adjacent to the processing object pixel block, carries out a composite arithmetic operation of the difference between the average pixel value and the DC pixel value, applies Hadamard transform to each pixel of the difference and outputs a first Hadamard coefficient; and a second stage Hadamard encoding section 7 that performs a composite arithmetic operation of an arithmetic operation to predict an AC component for obtaining the DC value of each pixel from the average pixel value and an arithmetic operation to obtain the difference between the DC value and the pixel block for each pixel and obtains the Hadamard coefficient of the difference. COPYRIGHT: (C)2005,JPO&NCIPI

Proceedings ArticleDOI
25 May 2003
TL;DR: A robust and efficient digital image watermarking algorithm using the fast Hadamard transform (FHT) is proposed for the copyright protection of digital images that can embed or hide an entire image or pattern as a watermark directly into the original image.
Abstract: In this paper, a robust and efficient digital image watermarking algorithm using the fast Hadamard transform (FHT) is proposed for the copyright protection of digital images. This algorithm can embed or hide an entire image or pattern as a watermark such as a company's logo or trademark directly into the original image. The performance of the proposed algorithm is evaluated using Stirmark 3.1 that consists of 90 different types of image attacks. Results show that this algorithm is very robust and can survive most of the Stirmark attacks. These attacks were tested on a number of test images of size 512/spl times/512/spl times/8 bits, embedded with a watermark image of size 64/spl times/64/spl times/8 bits. The simplicity of the fast Hadamard transform also offers a significant advantage in shorter processing time and ease of hardware implementation than other orthogonal transforms, such as the discrete cosine transform and wavelet transform.

Journal ArticleDOI
TL;DR: In this article, Hadamard and Liouville type properties for nonnegative viscosity supersolutions of fully nonlinear uniformly elliptic partial differential inequalities in the whole space were proved.
Abstract: In this paper we prove some Hadamard and Liouville type properties for nonnegative viscosity supersolutions of fully nonlinear uniformly elliptic partial differential inequalities in the whole space.

Journal ArticleDOI
TL;DR: The application of a Hadamard transform technique to microchip electrophoresis is described and the S/N ratio of the signal in the electropherogram can be improved by a factor of 5 in comparison with that obtained by a conventional single-injection method.
Abstract: The application of a Hadamard transform technique to microchip electrophoresis is described. The sample is electrokinetically injected into a separation channel and is then detected by diode laser-induced fluorometry. The sample and buffer solutions are introduced into the channel by controlling the high voltages applied to the solutions, according to a code determined by a Hadamard matrix. The S/N ratio of the signal in the electropherogram can be improved by a factor of 5 in comparison with that obtained by a conventional single-injection method, although an 8-fold improvement is theoretically predicted when a 255-order matrix is used.

Book ChapterDOI
01 Jan 2003
TL;DR: In this paper, the authors discuss algorithms for the construction of Hadamard matrices and give algorithms for constructing orthogonal designs, short amicable and amicable sets for use in the Kharaghani array.
Abstract: We discuss algorithms for the construction of Hadamard matrices. We include discussion of construction using Williamson matrices, Legendre pairs and the discret Fourier transform and the two circulants construction.Next we move to algorithms to determine the equivalence of Hadamard matrices using the profile and projections of Hadamard matrices. A summary is then given which considers inequivalence of Hadamard matrices of orders up to 44.The final two sections give algorithms for constructing orthogonal designs, short amicable and amicable sets for use in the Kharaghani array.

Journal ArticleDOI
TL;DR: It is shown that some UCHT sequences provide better autocorrelation properties than orthogonal Walsh-Hadamard sequences under simulation of systems in the presence of multiple access interference and additive white Gaussian noise.
Abstract: The use of orthogonal spreading codes has attracted much attention due to their ability to suppress interference from other users, compared with the nonorthogonal sequences in the synchronous case. In this paper, new sets of orthogonal sequences derived from the unified complex Hadamard transforms (UCHTs) are investigated. Various correlation properties of the sequences are mathematically derived and analyzed. It is shown that some UCHT sequences provide better autocorrelation properties than orthogonal Walsh-Hadamard sequences. Performance comparisons between UCHT sequences, Gold, small set of Kasami, and m-sequences show that some UCHT sequences outperform these well-known spreading sequences under simulation of systems in the presence of multiple access interference and additive white Gaussian noise.

Journal ArticleDOI
A. Boariu1, D.M. Ionescu1
TL;DR: Conditions that link the matrix formulation of the receive equation to the matrix formulations of a multiuser detection scheme are discussed and a class of rate one block STCs with a controlled number of interference terms per detected symbol is presented.
Abstract: Complex, rate one, orthogonal block space-time codes (STCs) exist only for two transmit antennas and were proposed by Alamouti (1998). Designing rate-one block STCs for more than two transmit antennas implies giving up orthogonality. For more than two transmit antennas a class of rate one block STCs with a controlled number of interference terms per detected symbol is presented. Conditions that link the matrix formulation of the receive equation to the matrix formulation of a multiuser detection scheme are discussed. The block STCs design problem is closely related to the class of linear real Hadamard codes.

Journal ArticleDOI
TL;DR: In this paper, the authors construct d-dimensional substitution sequences for which the continuous part of the spectrum is generated by measures equal to Lebesgue measure, and show that random application of these substitution sequences produces sequences with a lebesgue component in their spectrum.
Abstract: We construct d-dimensional substitution sequences for which the continuous part of the spectrum is generated by measures equal to Lebesgue measure. A special case is the Rudin–Shapiro substitution sequence. The construction uses Hadamard matrices in an essential way, so the dimension and size of a substitution is restricted by the size of the Hadamard matrix defining it. Each such substitution automatically has a dual substitution, which is defined by the same Hadamard matrix, and which retains a Lebesgue spectral component. We also see that random application of our substitutions produces sequences with a Lebesgue component in their spectrum. Finally, we see that any d-dimensional substitution with d > 1 can be ‘unraveled’ into lower-dimensional substitutions which still have Lebesgue spectral components.

Journal ArticleDOI
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.

Proceedings ArticleDOI
08 Apr 2003
TL;DR: In this paper, a hyperspectral Hadamard transform imaging spectrometer is presented, which is based on a flat field spectrometers and a spatial light modulator.
Abstract: A hyperspectral Hadamard transform imager is presented. It is based on a flat field spectrometer and a spatial light modulator. Compared to a typical dispersive pushbroom imaging spectrometer, the signal-to-noise-ratio can be increased by 1 ... 2 orders of magnitude for typical dimensions of the hyperspectral data cube. Applicable spatial light modulators include individually addressable MEMS based light modulators such as micro mirrors or newly developed micro shutters as well as mechanical slit positioning systems which are characterized by a fixed, movable pattern. In contrast to the individually addressable devices, the number of operational modes of the slit positioning system is constrained by the mask design, but high pixel numbers and high optical quality can be achieved by a mature and relatively simple micro machining technology. A detailed analysis of the relative performance of hyperspectral Hadamard transform, Fourier transform and hypothetical optimal imaging spectrometers with particular respect to the dimensions of the hyperspectral data cube and the composition of the detector noise reveals a considerable signal-to-noise advantage of the Hadamard transform imaging spectrometer over the Fourier transform imaging spectrometer for domination of read noise and a large number of spectral bands. In case the noise is dominated by dark current noise, the Hadamard transform imaging spectrometer can achieve 50% of the maximum possible sensitivity which is given by the hypothetical optimal imaging spectrometer. In contrast to the Fourier transform imaging spectrometer, the Hadamard transform imaging spectrometer is also suitable for use with short wavelengths.

Journal ArticleDOI
TL;DR: In this article, new properties of functionals associated to the Hermite-Hadamard integral inequality for convex functions are given, and properties of some function functions associated with the integral inequality are discussed.
Abstract: New properties of some functionals associated to the Hermite-Hadamard integral inequality for convex functions are given.

Proceedings ArticleDOI
06 Jul 2003
TL;DR: Intra prediction, Hadamard transform and motion estimation algorithms are reviewed and modified to a hardware friendly configuration and the rate distortion penalties of these modifications are simulated and shown in this paper.
Abstract: H.264 [Committee Draft of Joint Video Specification, July 2002] is initiated by ITU-T as H.26L and will become a joint standard of ITU-T and MPEG. The coding complexity of H.264 is much higher than MPEG-4 simple profile and advance simple profile algorithms. In order to achieve real-time encoding, hardware implementation is required. The original test model of H.264 (JM) [Joint Video Team, August 2002] is designed to achieve high coding performance. Some algorithms of the test model require lots of operations with little coding efficiency improvement. And some algorithms create data dependencies that prevent parallel hardware accelerations. This paper presents analysis of H.264 video coding algorithm in a hardware-oriented viewpoint. Intra prediction, Hadamard transform and motion estimation algorithms are reviewed and modified to a hardware friendly configuration. The rate distortion penalties of these modifications are simulated and shown in this paper.

Journal ArticleDOI
TL;DR: By isolating and exaggerating individual skewing effects in simulating the HT-TOFMS process, the nature of errors that arise from various defects are determined and it is found that the most damaging defects are mismatched voltages between the wire sets and the acceleration voltage of the instrument.