Showing papers on "Hadamard transform published in 1974"

Hybrid Coding of Pictorial Data

Abstract: Two hybrid coding systems utilizing a cascade of a unitary transformation and differential pulse code modulators (DPCM) systems are proposed. Both systems encode the transformed data by a bank of DPCM systems. The first system uses a one-dimensional transform of the data where the second one employs two-dimensional transformations. Theoretical results for Markov data and experimental results for a typical picture are presented for Hadamard, Fourier, cosine, slant, and the KarhunenLoeve transformations. The visual effects of channel error and also the impact of noisy channel on the performance of the hybrid system, measured in terms of the signal-to-noise ratio of the encoder, is examined and the performance of this system is compared to the performances of the two-dimensional DPCM and the standard two-dimensional transform encoders.

Experimental Investigation of Automatic Signature Verification

Abstract: This paper describes an approach to the problem of signature verificzation that treats the signature as a two-dimensional image and uses the Hadamard transform of that image as a means of data reduction and feature selection. This approach does not depend on the language or alphabet used and is general enough to have applications in such areas as cloud pattern surveys, aerial reconnaisance, and human-face recognition.

Seismic data compression methods

Abstract: This paper discusses two ways of compressing seismic data prior to long‐distance transmission for display. A Walsh transform technique and an analogous time‐domain method eliminate redundant seismic information allowing data sets to be compressed with little visual degradation. The basic approach consists of using an average 3-bit code to describe data in such a way as to minimize information loss; the method also uses the Walsh transform to achieve further compaction through sequency bandlimiting. A second technique is entirely a time‐domain operation and does not use transforms. The Walsh method, however, produces larger compression ratios than the time technique before serious image degradation occurs. Both schemes have six basic parts: bandlimiting, quantization, encoding, decoding, interpolation, and band‐pass filtering; they differ only in band limiting and interpolation. Band limiting sequencies in the Walsh domain is very similar to, but not the same as, alias filtering and resampling in time. Red...

Comparative Study of a Discrete Linear Basis for Image Data Compression

Abstract: Transform image data compression consists of dividing the image into a number of nonoverlapping subimage regions and quantizing and coding the transform of the data from each subimage. Karhunen-Loeve, Hadamard, and Fourier transforms are most commonly used in transform image compression. This paper presents a new discrete linear transform for image compression which we use in conjunction with differential pulse-code modulation on spatially adjacent transformed subimage samples. For a set of thirty-three 64 × 64 images of eleven different categories, we compare the performancea of the discrete linear transform compression technique with the Karhunen-Loeve and Hadamard transform techniques. Our measure of performance is the mean-squared error between the original image and the reconstructed image. We multiply the mean-squared error with a factor indicating the degree to which the error is spatially correlated. We find that for low compression rates, the Karhunen-Loeve outperforms both the Hadamard and the discrete linear basis method. However, for high compression rates, the performance of the discrete transform method is very close to that of the Karhunen-Loeve transform. The discrete linear transform method performs much better than the Hadamard transform method for all compression rates.

Theoretical Comparison of Singly Multiplexed Hadamard Transform Spectrometers and Scanning Spectrometers

Abstract: We present a general mathematical framework within which the relative performance of singly multiplexed Hadamard transform spectrometers (HTS) and conventional scanning spectrometers (SS) may be compared. The theoretical multiplex advantage (Fellgett advantage) is calculated for spectrometers operating in two spectral regions. For the low energy region, i.e., infrared, the determined multiplex advantage F is (N/2)1/2 (N is the number of slots), in accordance with predictions given by Fellgett. For the high spectral energy region, i.e., uv-vis, F=(x/2x¯)1/2, where x is the intensity of the spectal element sought and x¯ is the average intensity produced across the whole spectrum. Our predictions are verified by computer simulation of various characteristic spectra. Based on these results, we arrive at some conclusions concerning the practical application of HTS systems.

Two Asymmetric Hadamard Transform Spectrometers

Abstract: We develop the theory of operation for dispersive spectrometers that modulate radiation at both the entrance and exit apertures by means of Hadamard codes. Specifically, we examine the operation of instruments illuminated by a beam of radiation known to be homogeneous. In this case, all spatial information obtained in the operation of the instrument can be effectively suppressed at no loss of spectral performance and at a considerable reduction in the number of measurements that need to be made. A particularly interesting instrument which mocks a monochromator is described. The spectrum is directly obtained from the data by simply subtracting a constant intensity value from all readings. This instrument bears a resemblance to the Girard grill spectrometer. We describe the construction and operation of an instrument that has been tested in both modes of operation and show some of the spectra obtained.

Walsh-Transform Analysis of Discrete Dyadic-Invariant Systems

Abstract: This short paper shows how the sampled output of a dyadic-invariant linear system with a given sequency-domain transfer function, in response to a sampled input, can be determined by 1) a term-wise multiplication of the sampled transfer function and the discrete Walsh transform of the sampled input function, followed by an inverse Walsh transform, or 2) a discrete dyadic convolution of the sampled impulse response and the sampled input directly in the time domain. Functions in both time and sequency domains are represented by column matrices, and discrete Walsh transformation is effected simply by the multiplication with a Walsh matrix. An example is included to illustrate both procedures. The validity of the solutions is further verified by showing that the governing dyadic differential equation of the system is satisfied.

Difference sets of the Hadamard type and quasi-cyclic codes

Abstract: For every twin prime and prime power p where p ≡ 3(4) we define a (2 p + 2, p + 1) binary code by a generator matrix of the form G = [ I, S p , where S p is given in terms of the incidence matrix of a difference set of the Hadamard type. For p ≡ 3(8) these codes are shown to be self-dual with weights divisible by four. For p = 7, 15, 23, 27, 31 and 35 the codes obtained are probably new and it is not known if they are related to cyclic codes. For p = 7, 15, 19 and 23 we present their weight distributions.

Williamson matrices of even order

Abstract: Recent advances in the construction of Hadamard matrices have depended on the existence of Baumert-Hall arrays and Williamson-type matrices. These latter are four (1,-1) matrices A,B,C,D, of order m, which pairwise satisfy (i) MNT = NMT, M,N e {A,B,C,D}, and (ii) AAT+BBT+CCT+DDT = 4mIm, where I is the identity matrix. Currently Williamson matrices are known to exist for all orders less than 100 except: 35,39,47,53,59,65,67,70,71,73,76,77,83,89,94. This paper gives two constructions for Williamson matrices of even order, 2n. This is most significant when no Williamson matrices of order n are known. In particular we give matrices for the new orders 2.39,2.203,2.303,2.333,2.689,2.915, 2.1603.

A class of generalized continuous orthogonal transforms

Abstract: This paper presents a class of generalized continuous transforms for the orthogonal decomposition of signals. Base functions for the continuous transform range from Walsh functions of order two to stair-like functions which resemble approximations to sinusoids and which are distinct from the generalized Walsh functions. Standard desirable properties which are shown to hold for the generalized continuous transform operator include orthogonality of the base functions, linearity of the transform operator, inverse transformability, and admissibility to fast transform representation. The transform class is governed by a definition of time translation in terms of signed-bit dyadic time shift. Mathematical properties leading to this definition are discussed and the impact of the definition is assessed. Properties of the continuous class of generalized transforms make feasible analysis which could be extremely tedious using matrix representations of the operations actually mechanized in a sampled-data system. Analysis techniques are illustrated with a target detection system which is conceptually designed using the generalized continuous transform and implemented using fast transform algorithms to perform correlation operations. Since the correlation operations are valid for inputs which include signals represented in terms of Walsh functions, the example illustrates one instance in which the binary Fourier representation (BIFORE) transform can be used for practical pattern recognition.

Sequency Domain Design of Frequency Filters

Abstract: Each discrete transform has its advantages over other transforms. Fourier domain filters are easier to design than Walsh domain filters. But Walsh transforms can be computed much faster than Fourier transforms. This paper considers the problem of designing a Walsh domain filter, given a Fourier domain filter. Same procedure can be applied to other transforms. Given a Slant filter its equivalent Fourier filter or Walsh ifiter can be found.

Binary Sequences and Redundancy

Abstract: The computational-complexity approach and entropy using nominal frequencies lead to different measures to characterize patterns in finite binary sequences. These have been compared to a measure obtained on taking integral transforms of the sequences. The transforms considered in this paper are the Walsh and the discrete Legendre. Pattern characterization through integral transforms turns out to be intuitively satisfying. In particular, Walsh transform characterization appears natural for binary sequences as does the use of discrete Legendre transforms for more general (nonbinary) sequences.

The Hadamard three-circles theorems for partial differential equations

Abstract: 1. The famous Hadamard three-circles theorem of the complex function theory has been generalized to solutions of elliptic and parabolic equations. For references as well as for some interesting applications we refer to [3]. The purpose of this note is to show that (a) three circles (spheres)theorems lead naturally to a sharpened version of the boundary point maximum principle (see [1], [2]), and (b) to prove a Hadamard type theorem for a quasilinear equation.

Two-Dimensional Encoding Masks for Hadamard Spectrometric Imager

Abstract: Techniques to improve upon the design of two-dimensional encoding masks for multiplex Hadamard spectrometric imagers are described. The technique to generate masks based on completely orthonormal codes is described. In some cases, self-supporting masks result which were not previously known. Transmission through the encoding masks (but not necessarily the signal-to-noise ratio) can also be increased.

How bad is Hadamard determinantal bound

Abstract: Thp Hadamard bound for t he determinant of an\" by n ma trix is a good o ne in that equal it y may be a tta ined in a ri ch c lass of cases. Howe ver , th e bound gene rally g ives up a good d e al , a nd we a nswe r th e titl e ques tion \" on the average.\" Ass uming the e ntries of A = I (J ;j ) are uniform ly di s tribut ed ove r som e interval symmetric about the origin , the expec ted va lue of the ratio of (de t A)\" 10 t.h e square of the \"t Hadamard bound is fo und tu be ---.: . The expecta tions of the square of the Hadama rd bound and of n1l n ! (de t A )\" a re a lso computed individua ll y. a nd the ir ra t.io t urns out a lso to be . n il

A note on Hadamard arrays

Abstract: Let V = mk + 1 be a prime power; we show for m even it is not possible to partition the Galois field GF(v) to give four (0, 1, −1) matrices X1, X2, X3, X4 satisfying:(i) Xi * Xj = 0, i ≠ j, i, j = 1, 2, 3, 4;(ii) is a (1, −1) matrix;(iii) Thus this method of partitioning the Galois field GF(V), into four matrices satisfying the above conditions, cannot be used to find Baumert-Hall Hadamard arrays BH[4V] for v = 9, 11, 17, 23, 27, 29, ….

Permutation Properties of Discrete Walsh Transform Pair

Abstract: Certain permutations of the sequence of signal samples before discrete Walsh transformation are equivalent to permuting the sequence of transform coefficients or to changing the sign of some transform coefficients. These imply certain invariance properties of the Walsh transformation. Some applications of permutation properties are discussed.