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Topic: Hadamard transform

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	Hadamard transform coefficient predictor - US Patent 6009211 (Site not responding. Last check: 2007-10-08)
		For the prediction of the transform coefficient y(4), y(2) is multiplied by 1/4 in the multiplier 16, and for the prediction of the transform coefficient y(6), y(2) is multiplied by 1/2 in the multiplier 17.
		For the prediction of the transform coefficients y(1,3) and y(3,1), y(1,1) is multiplied by 1/2 in the multiplier 31 and then output, and for the prediction of the transform coefficients y(1,7), y(3,3) and y(7,1), y(1,1) is multiplied by 1/4 in the multiplier 32 and then output.
		For the prediction of the transform coefficients y(1,6) and y(3,2), y(1,2) is multiplied by 1/2 in the multiplier 36 and then output, and for the prediction of the transform coefficients y(1,4), y(3,6) and y(7,2), y(1,2) is multiplied by 1/4 in the multiplier 37 and then output.
	www.patentstorm.us /patents/6009211.html (3583 words)

	United States Patent Application: 0030228068
		Transformed image data is obtained from intermediate image data which in turn is obtained from processed image data transmitted from the encoder.
		Transformed image data 30 is obtained from the intermediate image data 44, intermediate image data 44 is obtained from processed image data 16 received from the encoder 12.
		Transformed image data 30 is obtained from intermediate image data 44, intermediate image data 44 being obtained from processed image data 16 transmitted from encoder 12.
	appft1.uspto.gov /netacgi/nph-Parser?Sect1=PTO2&Sect2=HITOFF&p=1&u=/netahtml/PTO/search-bool.html&r=4&f=G&l=50&co1=AND&d=PG01&s1=dhavala.IN.&OS=IN/dhavala&RS=IN/dhavala (3711 words)

	55:148 Dig. Image Proc. Chapter 11
		The discrete Fourier transform is analogous to the continuous one and may be efficiently computed using the fast Fourier transform algorithm.
		The properties of linearity, shift of position, modulation, convolution, multiplication, and correlation are analogous to the continuous case, with the difference of the discrete periodic nature of the image and its transform.
		The Hadamard transform is sometimes called a Walsh-Hadamard transform, since the base of the transformation consists of Walsh functions.
	www.icaen.uiowa.edu /~dip/LECTURE/LinTransforms.html (1462 words)

	Noise reduction system - Patent 4163258
		An orthogonal transform of the input signal is derived, this orthogonal transform having n transformed signal components.
		When the Hadamard transform matrix of a composite video signal is derived, the resultant n transformed signal components represent different respective portions of the frequency spectrum of the original video signal.
		In the embodiment being described, orthogonal transform matrix 20 is an Hadamard matrix adapted to perform the Hadamard transform represented mathematically by equation (6).
	www.freepatentsonline.com /4163258.html (6633 words)

	United States Patent Application: 0040034676
		To find the maximum value of the output of a fast Hadamard transform and its corresponding index, the N-1 stages of a conventional N stage fast Hadamard transform are computed while a find-maximum stage is inserted in place of the N.sup.th stage.
		Hadamard matrices and their transforms can be found in signal compression algorithms and encoding and decoding algorithms, for example.
		To aid in illustrating the principles of the present invention, the derivation of the transform is described in the context of the correlation of an input sequence consisting of a received signal to an H.sub.16 matrix.
	appft1.uspto.gov /netacgi/nph-Parser?Sect1=PTO1&Sect2=HITOFF&d=PG01&p=1&u=/netahtml/PTO/srchnum.html&r=1&f=G&l=50&s1="20040034676".PGNR.&OS=DN/20040034676&RS=DN/20040034676 (8500 words)

	Image processing method using a collapsed Walsh-Hadamard transform - Patent 4549212
		(As with the 4 by 4 Walsh-Hadamard transform, it is evident from FIG.
		In the third stage 50, the 4 by 4 "collapsed" Walsh-Hadamard transform operates on sixteen image signals assembled from nine image signals taken from fourth adjacent image signals of fourth adjacent rows of the twice-averaged image signals presented by one alignment of the incoming stream of signals.
		Each transform network 74a, 74b and 74c transforms the image signals by a set of linear combinations (characteristic of the 4 by 4 Walsh-Hadamard transform) into a corresponding set of coefficient signals representative of a smoothed light value and differences in light value between image elements.
	www.freepatentsonline.com /4549212.html (6665 words)

	Fourier transform infrared Hadamard tomography of sooting flames (Site not responding. Last check: 2007-10-08)
		The Hadamard technique leads to a major simplification in the tomographic apparatus in that the scanning apparatus that would normally be required is eliminated, and focusing of the infrared light is much easier.
		The Hadamard encoding mask replaces the spectrometer exit slit with an aperture that is either reflective (or opaque) or transmissive to chosen spectral elements; the spectral elements allowed to impinge upon the detector are determined by the Hadamard encodement.
		The Hadamard encodement matrix is cyclic, such that a moving Hadamard encoding mask is made with 2N-1 slots for N spectral elements and translated across the N-wide opening to give the proper N different slot combinations.
	www.tvu.com /HadamardFTIRweb.htm (5118 words)

	Coefficient extrapolator for the Haar, Walsh, and Hadamard domains - United States Patent 4,261,043
		In particular, this invention relates to the extrapolation in the transform domain of higher order transform coefficients, which otherwise are not present in the output of the compression system, from the lower order transform coefficients that are output by the compression system.
		The rate at which transform coefficients are passed on to the transmitter 5 normally is limited to a predetermined rate, either by the rate at which transform coefficients are output by the transformer 3 or by the operation of compressor 4 which usually selects only the lower order coefficeints for transmission.
		This invention which is the extrapolator 7, operates on the output of receiver 6 in the transform domain to obtain approximations to the higher order coefficients, that have not been received by reciever 6, by means of extrapolation from the lower order coefficients which have been received by receiver 6.
	xrint.com /patents/us/4261043 (2837 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		2, the Hadamard matrix is multiplied by the (transpose of v to obtain the values of the Hadamard transformed sequences, w.
		After undergoing the Hadamard transform, the number of times the possible values of the Hadamard-transform entries in w are counted in an array of accumulators to obtain an average number of times that each possible value in the vector, w, appears over a time period.
		transform calculation falls into one of said predetermined range of values in the respective said accumulator over a predetermined time period; and, (e) comparing the output of said exponential-frequency calculation (Z) to a predetermined acceptance range.
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=03/88034.031023&ELEMENT_SET=DECL (3928 words)

	Hadamard transform - TheBestLinks.com - Hadamard gate, France, Fourier transform, Mathematician, ... (Site not responding. Last check: 2007-10-08)
		Hadamard gate, Hadamard transform, France, Fourier transform, Mathematician...
		The Hadamard transform (Hadamard transformation, also known as Walsh-Hadamard transformation) is an example of a generalized class of Fourier transforms.
		The Hadamard matrix can also be regarded as the Fourier transform on the two-element additive group of Z/(2).
	www.thebestlinks.com /Hadamard_gate.html (232 words)

	[No title]
		Furthermore, the Hadamard transform H is real, symmetric, and orthogonal; thus, the forward and inverse Hadamard transforms are identical.
		The 8 x 8 Hadamard transform matrix is defined as 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 1 1 -1 -1 -1 -1 1 1 H = [ 1 1 -1 -1 1 1 -1 -1 ].
		To verify that the statistics of the Hadamard transform coefficients that we collected in the open loop (without quantization) process are close to the statistics of the closed loop (with quantization), we collected the statistics of the Hadamard transform coefficients, again using the designed quantizers.
	www.research.ibm.com /journal/rd/434/lam.txt (4109 words)

	[No title]
		The origins of the Hadamard matrix go back at least to 1867 when, in a most interestingly titled article (Ref 2), J Sylvester published his construction of what later became known as the Hadamard matrix.
		Hadamard published his work in 1893, and later work in the same area came from Rademacher (1922) and Walsh (1923).
		This result is the "2-point Hadamard transform" of the vector x, and it's exactly the same as a 2-point discrete Fourier transform (DFT).
	archive.chipcenter.com /dsp/DSP000517F1.html (2459 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		A method of producing a second binary codeword from a first binary codeword destined for decoding using a Hadamard transform, the method comprising selecting soft decisions from the first codeword into one or more groups, and combining the soft decisions within each group to produce a number of resultant soft decisions forming the second codeword.
		A method according to claim 7, wherein said Hadamard transform is of a lower order than the Hadamard transform applicable to the first codeword.
		Apparatus according to claim 15, wherein the Hadamard transform applicable to the second codeword is of lower order than the Hadamard transform applicable to the first codeword.
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=02/51014.020627&ELEMENT_SET=DECL (1627 words)

	Compression
		Transform of a 1D discrete input signal (a column vector x of N components) is the computation of y=A
		Transform of an N×M image X is transform of each column followed by transform of each row.
		Drawback of KL: the transform matrix is data-dependent, that is, for each new signal X, the transform matrix A is different and depends on the statistical properties of X. KL is a costly ideal for decorrelation/energy compaction/minimization of MSE
	www.seas.gwu.edu /~ayoussef/cs225/transforms.html (932 words)

	Robert M. Hammaker (Site not responding. Last check: 2007-10-08)
		Another spectroscopic transform technique is Hadamard transform spectrometry where the choice of transparent or opaque for the elements of a mask provides an encoding of spectral information that may be decoded into a conventional spectrum by Hadamard mathematics.
		We have developed a Hadamard transform spectrometer for operation in the visible and near-infrared spectral regions using a stationary mask with electro-optical control of the transmission properties of the mask elements.
		In our present development are (1) a photoacoustic Hadamard transform spectrometer for depth profiling in the visible spectral region by optical modulation and phase sensitive detection and (2) a stationary two-dimensional Hadamard encoding mask for spatial mapping of a surface such as a thin layer chromatography (TLC) plate, initially without spectral resolution.
	www.ksu.edu /chem/personnel/faculty/grad/rmh/hammaker.html (563 words)

	Transform2DForward() -- Forward 2D Cosine/Walsh/Hadamard Transform
		Normally in the transform result, zero frequency is in the upper-left corner of the image.
		The algorithm is based on a series of 1D transforms on the rows and the columns of the image.
		Perform 2D inverse Cosine transform on a 0,0,256,256 window of frequency image in channel 8 of "irvine.pix".
	www.pcigeomatics.com /cgi-bin/pcihlp/Transform2DForward() (598 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		The second method is the application of the Hadamard transform to a log-magnitude frequency spectrum.
		After the application of the Fourier transform the Hadamard transform is applied to detect a pitch period or to get a smoothed spectrum.
		This method shows some positive aspects of the Hadamard transform for the analysis of a speech wave with regard to the reduction of processing time required for smoothing, but at the cost of precision.
	www-db.stanford.edu /TR/CS-TR-72-307.html (130 words)

	Memory reduction for HDTV decoders
		Another important property of the Hadamard transform is its good energy compaction for highly correlated images, which is an essential requirement for signal compression.
		The Hadamard transform ac coefficients are nearly identically distributed after normalization and resemble a Laplacian density function as defined by
		In this case, the eight Hadamard transform coefficients must be compressed into 16 bits in total.
	www.research.ibm.com /journal/rd/434/lam.html (3855 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		This is an implementation of a Hadamard Transform if the form of a 4x4 matrix multiplication.
		The vector to transform are stored in a MMX register with 16 bits per component, having 4 components.
		This has the added benefit of being much more generally useful, because all the intermediate operations are done on 32-bit values, with a single saturated pack operation at the end to get back to 16-bit results.
	www.df.lth.se /~john_e/gems/gem0044.html (128 words)

	Math::WalshTransform README and POD (Site not responding. Last check: 2007-10-08)
		Also included are routines for converting a Hadamard to a Walsh transform and vice versa, for calculating the Logical Convolution of two lists, or the Logical Autocorrelation of a list, and for calculating the Walsh Power Spectrum - in short, almost everything you ever wanted to do with a Hadamard Transform.
		Intelligible speech can be reconstructed by transforming blocks of, say, 64 samples, deleting all but the several largest transform components, and inverse-transforming; in other words, these transforms extract from a time-series the most significant things that are going on.
		The Hadamard matrix is a square array of plus and minus ones, whose rows and columns are orthogonal to each other.
	www.pjb.com.au /comp/walshtransform.html (1360 words)

	Walsh-Hadamard Transforms: A Literature Survey
		But the transformation process itself is just arithmetic, and has an easily-comprehended structure which could be widely understood.
		Transformed data can be easier to manipulate for differential or integral equation solution, and some parts of digital circuit synthesis.
		The study of Walsh transforms provides an excellent introduction to this, because their simplicity enables calculations to be made by hand.
	www.ciphersbyritter.com /RES/WALHAD.HTM (2825 words)

	A Lossless Version of the Hadamard Transform - Philips, Denecker (ResearchIndex)
		Abstract: This paper presents a lossless blocktransform coder based on the Hadamard transform that achieves a compression ratio as good as that of the current lossless JPEG-standard and about 10 to 20% lower than the currently best state-ofthe -art technique Calic.
		The main advantage of the proposed technique is that it produces an embedded data stream which may be truncated to achieve lossy compression.
		Philips and K. Denecker, "A lossless version of the Hadamard transform," in Proceedings of the PRORISC IEEE Benelux Workshop on Circuits, Systems and Signal Processing, Nov. 1997, Elsewhere in this volume.
	citeseer.ist.psu.edu /36351.html (437 words)

	SIGNALS IN SEQUENCES: Spectral analysis (Site not responding. Last check: 2007-10-08)
		(a) A Hadamard conjugation - a conjugation (in mathematics) is the successive application of three functions, the third being the inverse of the first.
		A Hadamard transform is a single multiplication of a vector by a Hadamard matrix.
		Transformation of observed patterns (s) to distances (d) depends on the model being used (for example the LogDet transformation is used for the general model) and only a single Hadamard transform is applied to these inferred distances.
	www.massey.ac.nz /~imbs/Research/MolEvol/Farside/DNA/0061.html (238 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Here's some code to do a walsh hadamard transform on long ints in-place (you need to divide by n to get transform) the order is bit-reversed at output, IIRC.
		The inverse transform is the same as the forward transform** (expects bit-reversed input).
		Statistics 6, 1184-1238 (1978) But somewhere in literature is Walsh transform used for this transform without reordering.
	cs.felk.cvut.cz /~vlkm3/HAD.C (148 words)

	Prof (Site not responding. Last check: 2007-10-08)
		Bellamy, J. Paukstelis and R. Hammaker, "Multi-Dimensional Hadamard Transform Spectrometry," Fourteenth International Conference on Raman Spectroscopy, proceedings of the Fourteenth International Conference on Raman Spectroscopy, Hong Kong, August 22-26, 1994, Edited by N. Yu and X. Li, John Wiley and Sons, Chichester, pp.
		Paukstelis, R. Hammaker, and W. Fateley, "Hadamard Transform Raman Imagery," Fourteenth International Conference on Raman Spectroscopy, proceedings of the Fourteenth International Conference on Raman Spectroscopy, Hong Kong, August 22-26, 1994, Edited by N. Yu and X. Li, John Wiley and Sons, Chichester, pp.
		Hammaker, and W. Fateley, "Hadamard Transform Raman Imagery," Fifteenth International Conference on Raman Spectroscopy, proceedings of the Fifteenth International Conference on Raman Spectroscopy, Pittsburgh, Pennsylvania, USA, August 11-16, 1996, Edited by S. Asher and P. Stein, John Wiley and Sons, Chichester, pp.
	www.ksu.edu /chem/personnel/faculty/grad/rmh/hammaker_pub.html (1264 words)

	Measuring Boolean Function Nonlinearity by Walsh Transform
		MEASURING NONLINEARITY BY WALSH TRANSFORM Terry Ritter ritter@io.com Ritter Software Engineering http://www.io.com/~ritter/ 1998-01-12 Abstract Nonlinearity is the number of bits which must change in the truth table of a Boolean function to reach the closest affine function.
		The Walsh-Hadamard Transform A Hadamard matrix H is an n x n matrix with all entries +1 or -1, such that all rows are orthogonal and all columns are orthogonal (see, for example, [HED78]).
		It is common to consider a Boolean function as consisting of the real values {0,1}, but it is also common to use the transformation x (5) x' = -1 where x is {0,1}.
	www.ciphersbyritter.com /ARTS/MEASNONL.HTM (1687 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		I did this for a transform data compression study a while back.
		Here's some code to do a walsh hadamard transform on long ints in-place (you need to divide by n to get transform) the order is bit-reversed at output, IIRC.
		The inverse transform is the same as the forward transform (expects bit-reversed input).
	www.musicdsp.org /showone.php?id=18 (360 words)

	Algorithms for first-order RM codes
		The operation of computing the correlation can be performed efficiently by means of the Hadamard transform.
		We simply find the coordinate in the transform with the largest value and determine the codeword from it.
		Fast algorithms exist for the Hadamard transform, making the decoding operation fairly efficient.
	www.engineering.usu.edu /classes/ece/7670/lecture9/node2.html (174 words)

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