Showing papers on "Hadamard transform published in 1997"

Multi-Terminal Binary Decision Diagrams: An Efficient DataStructure for Matrix Representation

Abstract: In this paper, we discuss the use of binary decision diagrams to represent general matrices. We demonstrate that binary decision diagrams are an efficient representation for every special-case matrix in common use, notably sparse matrices. In particular, we demonstrate that for any matrix, the BDD representation can be no larger than the corresponding sparse-matrix representation. Further, the BDD representation is often smaller than any other conventional special-case representation: for the n×n Walsh matrix, for example, the BDD representation is of size O(log n). No other special-case representation in common use represents this matrix in space less than O(n²). We describe termwise, row, column, block, and diagonal selection over these matrices, standard an Strassen matrix multiplication, and LU factorization. We demonstrate that the complexity of each of these operations over the BDD representation is no greater than that over any standard representation. Further, we demonstrate that complete pivoting is no more difficult over these matrices than partial pivoting. Finally, we consider an example, the Walsh Spectrum of a Boolean function.

On the Asymptotic Geometry of Nonpositively Curved Manifolds

Abstract: In this paper we derive new asymptotic properties of all Hadamard manifolds admitting compact quotients. We study the growth function of the volume of geodesic spheres, generalizing the work of Margulis in the case of negative curvature. We show that the growth is of purely exponential type if and only if the Hadamard manifold is of rank 1. In general, there is a polynomial deviation from purely exponential behavior, depending in an unexpected way on the rank of the manifold. Furthermore, we obtain new results on the growth rate of closed geodesics on compact rank 1 spaces.

Spectral Transforms for Large Boolean Functions withApplications to Technology Mapping

Abstract: The Walsh transform has numerous applications in computer-aided design, but the usefulness of these techniques in practice has been limited by the size of the boolean functions that can be transformed. Currently available techniques limit the functions to less than 20 variables. In this paper, we show how to compute concise representations of the Walsh transform for functions with several hundred variables. We have applied our techniques to boolean technology mapping and, in certain cases, we obtained a speed up of as much as 50% for the matching phase.

A note on hadamard's inequality

Abstract: In this paper, we investigate a class of matrices, called F-matrices, which contains symmetric positive semidefinite matrices, totally nonnegative matrices, T-matrices and M-matrices. We establish some ineqalities that are improvement of Hadamard's inequality for F-matrices. We prove that det A = a 11… ann if and only if any diagonal line except the main diagonal line of A has at least a zero. And we characterize an F-matrix A satisfying det A = a11… ann by the pattern of zero of A. Our results generalize the known results on Hadamard's Inequality.

Existence of continuous families of complex hadamard matrices of certain prime dimensions and related results

Abstract: One proves the existence of continuous families of complex Hadamard matrices of certain prime dimensions, n = 7, 13, 19, 31, 79 This result implies the existence in the corresponding matrix algebras $M\sb{n}$(C) of uncountably many non isomorphic orthogonal pairs of maximal abelian $\sp\*$-subalgebras (MASA's) in the sense of SPopa A main point of interest of our result is that it might produce examples of one parameter families of nonisomorphic subfactors of same index n and same graph $A\sb{\infty}$ The numerical and symbolic computations that motivated this class of examples, as well as their formal construction are presented We are also exploring the possibility of extending this construction to all the primes of the form $n = 3\sp{2k} - 2, (k \ge 1)$ For any prime dimension n one proves that the standard complex Hadamard matrix (which corresponds to the matrix of the Fourier transform of vectors in C$\sp{n}$) is an isolated point among the normalized complex Hadamard matrices of the same dimension We also draw connections to the recent finiteness results of UHaagerup regarding circulant complex Hadamard matrices

Soft-in/soft-out Hadamard despreader for iterative decoding in the IS-95(A) system

Abstract: In the uplink of the CDMA IS-95(A) system decoding of a serial concatenated coding scheme has to be performed, where the inner code comprises M-ary orthogonal modulation with Hadamard (Walsh) spreading codes. For a coherent and a noncoherent RAKE-receiver structure we give the optimum symbol-by-symbol maximum a posteriori (MAP) decoding rules considering the a priori information about the systematic bits of the codewords if available. These algorithms are necessary for iterative decoding of the whole system. We present simulation results which demonstrate the gain of the modified receivers.

A new speech scrambling concept based on Hadamard matrices

Abstract: The principles of a new speech scrambling concept are presented, whereby the speech components are linearly combined in contrast to their conventional permutation. A computationally and cryptographically efficient solution based on Hadamard matrices is proposed and its advantages shown. The idea is general and easily applies to all existing speech scramblers providing for both lower residual intelligibility and greater cryptanalytic efforts, maintaining the bandwidth and the speech quality.

Method and apparatus for fast modulation in synchronous CDMA communications

Abstract: A system and method for modulating synchronous CDMA (S-CDMA) signals in antenna array wireless system. By taking advantage of the symmetric property of Walsh code words utilized in S-CDMA perform modulation of signals intended for a plurality of users. The system includes a Fast Hadamard Transform (FHT) Processor that realizes baseband operations including spreading and digital combining in one step. In addition to significant reduction in computations and storage over prior methods, the invention also provides substantial advantages in hardware implementation. While the exemplary embodiment is described in the context of antenna array CDMA systems, the disclosed techniques have general applications in CDMA systems with arbitrary symbol values.

Three-dimensional localized proton NMR spectroscopy using a hybrid of one-dimensional hadamard with two-dimensional chemical shift imaging

Abstract: Acquisition of three-dimensional image-guided localized proton spectroscopy ( 1 H-MRS) in the human brain is achieved on a standard clinical imager with a hybrid of chemical shift imaging (CSI) and transverse Hadamard spectroscopic imaging (HSI). 16×16×4 arrays of 3.5 and 1 ml voxels were obtained in 27 minutes. The spatially-selective HSI 90° pulses were incorporated naturally into a PRESS double spin-echo sequence to subdivide the VOI into 4 partitions along its short axis. Two-dimensional CSI is performed along the other long axes. Because the hybrid excites the spins in the entire VOI, a √N signal-to-noise-ratio (SNR) gain per given examination time is realized compared to sequentially interleaving N two-dimensional slices. A twofold gain in sensitivity is demonstrated in the brain for N=4.

Compression/decompression engine for enhanced memory storage in MPEG decoder

Abstract: A compression/decompression engine is disclosed for reducing memory requirements of a decode system by storing decoded video data in compressed form. The compression engine comprises parsing chrominance UV data into separate chrominance U data and chrominance V data, and transform logic implementing a Hadamard transformation of multiple bytes of decoded video data in parallel into frequency domain signals. Compression logic is coupled to the transform logic and performs, preferably, a 2:1 transformation of the frequency domain signals to produce compressed video signals for storage in memory. The transform logic and compression logic transform and compress multiple bytes of decoded video data in parallel within a single clock cycle of the decode system. Upon retrieval from memory, the compressed data is returned to original format by the decompression engine, which employs the same transform logic as used by the compression engine. Reassembly logic then returns the separate chrominance U data and chrominance V data to chrominance UV data for use by the associated motion compensation unit or for display.

Chemical Mapping in the Mid- and Near-IR Spectral Regions by Hadamard Transform/FT-IR Spectrometry

Abstract: A movable two-dimensional (2D) Hadamard encoding mask is obtained and combined with conventional FT-IR spectrometers for use in both the mid- and near-infrared spectral regions. Chemical maps and spectra of individual pixels of the maps can be obtained from heterogeneous samples by using this combination of a moveable 2D Hadamard encoding mask and an FT-IR spectrometer. We call the procedure Hadamard transform/FT-IR spectrometry. Spectra of usable signal-to-noise ratio and reliable chemical maps are obtained in reasonable data acquisition and processing time.

Fixed-Pipeline Two-Dimensional Hadamard Transform Algorithms

Abstract: In this correspondence, we first propose a new two-dimensional (2-D) Hadamard transform algorithm, which can be realized in fixed and identical pipeline stages. By introducing exchangeable permutations, the fixed-pipeline algorithm can be further extended to provide all 2-D lower-dimension transformations in intermediate pipeline stages. Finally, the parallel pipeline realization of the proposed algorithm is also suggested. For VLSI implementation, the proposed fixed-pipeline structure with the same computational complexity provides better modularity than the other famous algorithms. With lower dimension transformations, the proposed algorithm is suitable for applications in variable-block-size compression.

Non-Fourier encoding with multiple spin echoes.

Abstract: The advantages and limitations of multiple spin-echo sequences for non-Fourier encoding are investigated. Complications caused by improper encoding of alternate magnetization pathways due to imperfect refocusing pulses are analyzed. It is shown that mirror image ghosts result if the encoding RF pulse matrix is real-valued. These ghosts can be avoided as long as the rows of the RF pulse matrix are conjugate symmetric, which implies that spatial profiles are real valued. Non-Fourier encoding using bases derived from wavelet, Hadamard, and other real-valued orthogonal functions does not result in a mirror ghost artifact. A RARE sequence for non-Fourier encoding has been implemented on a clinical imaging system and successfully applied for brain imaging.

Hadamard transform application in speech scrambling

Abstract: Speech scrambling procedures may be considered as typical orthogonal transforms applications. This point of view was rarely applied since all the scramblers were based on the same orthogonal transform-simple permutation of speech components (time segments and/or frequency subbands). This approach is regarded as an insecure speech encryption method and a new speech scrambling concept was proposed, based on Hadamard transform of the speech components. Linear combination of the speech components based on Hadamard matrices instead of conventional permutation gives better cryptographic performance, maintaining all the good features of the scrambling concept. Scrambling procedures are investigated from two points of view: the transform matrix features as well as the transform kernel. This theoretical analysis gives a subtle view to scrambling procedures.

Frequency tracking for communication signals using m-ary orthogonal walsh modulation

Abstract: A frequency tracking loop for a communication system using orthogonal Walsh modulation is provided. The frequency tracking loop includes a correlator (120) such as a fast Hadamard transformation device, and a discriminator (130). The correlator (120) produces a correlation vector (122) representing the result of correlating the input signal with each of a set of Walsh functions, with corresponding index values. The discriminator (130) produces a frequency error signal (e) based on the correlator (120) output with the highest energy level and other correlator outputs whose indices are related to the index of highest energy correlator output by powers of two. The frequency error signal (e) is generated by producing a cross product between the highest energy output and one or more of the other related correlator outputs. In further aspects, a filter (140) can be used to further shape the resulting error signal (e) and form a frequency offset estimate signal (f).

Transform domain techniques for efficient extraction of substrate parasitics

Abstract: A semi-analytical technique for computation of the frequency-behavior of silicon substrates is demonstrated. The technique uses a boundary element approach, that utilizes the complex substrate Green Function and the two-dimensional Fast Fourier Transform. The resultant dense system matrix is sparsified by application of orthogonal transform operators on the matrix representing the system. Three transform operators are evaluated for this purpose- the Discrete Cosine Transform (DCT), the Discrete Wavelet Transform (DWT) and the Discrete Hadamard Transform (DHT). The application of any one of these operators provides a rigorous sparsification technique, which significantly reduces the computation time. The Green Function is computed in the two layers at the top of the substrate. This is done so that contacts in the oxide layer can be included in the substrate model, along with contacts in the silicon substrate. Hence, substrate loss terms in metal interconnect lines and in line-to-line interaction models, can be evaluated using this technique. Extraction of a simple circuit-simulator compatible model from frequency-domain data is discussed.

Hadamard 1D 1H TOCSY and its application to oligosaccharides

Abstract: Replacement of a series of N consecutive one‐site selective excitation NMR experiments by N simultaneous N‐site excitations with phases of component pulses varied according to the N×N Hadamard matrix offers a sensitivity improvement of the order of √N (for N=2, 4, 8, ...) [R. Freeman, Spin Choreography, pp. 177–183. Spektrum, Oxford (1996)]. Here this principle was extended to one‐dimensional (1D) 1H TOCSY experiments, in the absence and presence of heteronuclear decoupling. The 1D 1H Hadamard TOCSY technique was applied to selected oligosaccharides, representing a class of biomolecules for which multiple 1D TOCSY experiments are the mainstay in 1H NMR spectral assignment and structural characterization. © 1997 John Wiley & Sons, Ltd.

Magnetic resonance apparatus

Abstract: A magnetic resonance apparatus acquires a magnetic resonance signal matrix as follows. While a gradient field is applied to an object to be examined, a plurality of selective inversion pulses having different frequencies as high-frequency fields are sequentially applied to the object. Thereafter, a non-selective excitation pulse as a high-frequency field is applied to the object without application of a gradient field. In addition, a magnetic resonance signal generated upon application of the non-selective excitation pulse is acquired. Such a series of sequences are repeated a plurality of times, while the frequencies of the selective inversion pulses are sequentially selected to cause a magnetization vector of a nuclear spin of an area corresponding to either of "-1" and "1" an Hadamard matrix to be inverted by each selective inversion pulse. Chemical shift information is obtained by transforming a magnetic resonance signal matrix thus acquired in an aligning direction of the magnetic resonance signal matrix by an inverse Hadamard transform, and transforming the transformed matrix in a time base direction by an inverse Fourier transform.

Properties and applications of unified complex Hadamard transforms

Abstract: A family of Unified Complex Hadamard Transforms derived from Walsh functions is defined. Newly developed direct matrix operator is introduced which is able to generate different types of Complex Hadamard matrices. Higher dimension matrices of the transforms may also be generated recursively by means of Kronecker product from basic matrices. Sparse matrix factorization or matrix partitioning of the Complex Hadamard matrices leads to the fast algorithms with complexity Nlog/sub 2/N. One of the shown fast algorithms may be implemented as in-place architecture which reduces memory requirements and allows on simple implementation in software or in hardware. Finally, different properties of the new transforms are shown and the performance of the transforms for Wiener filtering is evaluated and compared with the known discrete orthogonal transforms.

Classifications and graph-based representations of switching functions using a novel complex spectral technique

Abstract: In this paper, a novel spectral technique based on the transform constructed from a Complex Hadamard matrix is introduced. The technique finds potential applications in various synthesis and optimization processes of logic circuits. Classification of switching function is shown here as one of the possible applications. The technique uses the Complex Hadamard matrix as the spectral transform, manipulates the complex spectral coefficients of the functions and classifies them into the NPN-equivalent and linearly separable functions. The method has proven to be a more efficient classification scheme than the existing classification method using the standard spectral technique based on the Walsh Transform. For efficient manipulation of switching functions, some new decision diagrams to represent Complex Hadamard matrices and their spectra of integervalued functions are proposed. With the intrinsic properties of the new transform in handling complex numbers, the presented decision diagrams lead to a more effici...

Equalization and coding for extended MC-CDMA over time and frequency selective channels

Abstract: In this work Multi Carrier Code Division Multiple Access (MCCDMA) — based on Orthogonal Frequency Division Multiplex (OFDM) combined with Hadamard spreading sequences — is extended by an additional spreading in time direction. Introducing the Kronecker Product the two transformations in time and frequency direction can be merged, resulting in one larger transformation.