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Topic: Z-transform

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In the News (Sat 19 Jan 19)

 Frequency transform: Definition and Links by Encyclopedian.com - All about Frequency transform
Frequency transforms are often used as part of the process of transform coding, but have many other uses, including scientific and engineering analysis.
The result of the transform are the coefficients of the components (basis functions), i.e.
The transform can be reversed (mostly perfectly or nearly perfectly) summing of the correctly weighted base functions.
www.encyclopedian.com /fr/Frequency-transform.html   (136 words)

 List of Fourier-related transforms - Wikipedia, the free encyclopedia
Such transformations map a function to a set of coefficients of basis functions, where the basis functions are sinusoidal and are therefore strongly localized in the frequency spectrum.
Discrete-time Fourier transform (DTFT), the Fourier transform of a discrete sequence or, equivalently, the continuous Fourier Transform of continuous-time function consisting of a sequence of impulses.
Discrete Fourier transform (DFT), the Fourier transform of a discrete periodic sequence (yielding discrete periodic frequencies).
en.wikipedia.org /wiki/List_of_Fourier-related_transforms   (333 words)

 Hadamard transform coefficient predictor - US Patent 6009211
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(1,6) 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.
For the prediction of the transform coefficients y(2,6) and y(6,2), y(2,2) is multiplied by 1/2 in the multiplier 46 and then output, and for the prediction of the transform coefficients y(2,4), y(4,2) and y(6,6), y(2,2) is multiplied by 1/4 in the multiplier 47 and then output.
www.patentstorm.us /patents/6009211.html   (3583 words)

 Transform coding - Wikipedia, the free encyclopedia
The basic process of digitizing an analog signal is a kind of transform coding that uses sampling in one or more domains as its transform.
The common JPEG image format is an example of a transform coding, one that examines small blocks of the image and "averages out" the color using a discrete cosine transform to form an images with far fewer colors in total.
Transform coding is a type of data compression for "natural" data like audio signals or photographic images.
www.wikipedia.org /wiki/Transform_coding   (418 words)

 Transform fault - Wikipedia, the free encyclopedia
The San Andreas fault of southern California is a large transform fault connecting the East Pacific Rise off the coast of California with a segment of the ridge in the Gulf of California.
Transform faults comprise one of the three types of plate boundaries in plate tectonics.
A transform fault is a geological fault that is a special case of strike-slip faulting which terminates abruptly, at both ends, at a major transverse geological feature.
www.wikipedia.org /wiki/Transform_fault   (200 words)

 Fractal compression - Wikipedia, the free encyclopedia
Fractal compression appeared to be a promising technology in the late 1980s, when in some circumstances it appeared to compress much better than JPEG, its main competitor at that time.
Fractal compression is a lossy compression method used to compress images using fractals.
Today fractal compression seems to be even less relevant, with wavelet compression outperforming it in most applications for those willing to accept the patent situation.
en.wikipedia.org /wiki/Fractal_compression   (391 words)

 Fourier transform: Facts and details from Encyclopedia Topic
The short-time fourier transform (stft), or short-term fourier transform, is a fourier-related transform used to determine the sinusoidal frequency and...
In mathematics, the mellin transform is an integral transform that may be regarded as the multiplicative version of the two-sided laplace transform....
In mathematics, the two-sided laplace transform or bilateral laplace...
www.absoluteastronomy.com /encyclopedia/f/fo/fourier_transform.htm   (3572 words)

 ipedia.com: Wavelet Article
All wavelet transforms may be considered to be forms of time-frequency representation and are, therefore, related to the subject of harmonic analysis.
Wavelet transforms are now being adopted for a vast number of different applications, often replacing the conventional Fourier transform in many applications.
Wavelet transforms are most broadly classified into the discrete wavelet transform (DWT) and the continuous wavelet transform (CWT).
www.ipedia.com /wavelet.html   (321 words)

 Ralph Hartley - Wikipedia, the free encyclopedia
He invented the Hartley oscillator, the Hartley transform, and contributed to the foundations of information theory.
Hartley was born in Spruce, Nevada and attended the University of Utah, receiving an A.B. degree in 1909.
A patent for the oscillator was filed on June 1, 1915 and awarded on October 26, 1920.
en.wikipedia.org /wiki/Ralph_Hartley   (321 words)

 Encyclopedia: Geologic fault
Faults can be categorized into three groups: normal faults, transform (or strike-slip) faults and reverse (or thrust) faults.
Faults In plate tectonics, a transform boundary fault (also known as transform fault boundary, transform plate boundary, transform plate margin or conservative plate boundary) is said to occur when continental plates slide and grind against each other.
Faults are the source of many earthquakes that are caused by slippage vertically or laterally along the fault.
www.nationmaster.com /encyclopedia/Geologic-fault   (1103 words)

 Niels Abel
In 2002, the Abel Prize was established in his honour.
Abel's first notable work was a proof of the impossibility of solving the quintic equation by radicals (see Abel-Ruffini theorem.) This investigation was first published in 1824 in abstruse and difficult form, and afterwards (1826) more elaborately in the first volume of Crelle's Journal.
In 1826 Abel moved to Paris, and during a ten month stay he met the leading mathematicians of France; but he was poorly appreciated, as his work was scarcely known, and his modesty restrained him from proclaiming his researchings.
www.algebra.com /algebra/about/history/Niels_Abel.wikipedia   (601 words)

 Plate tectonics - Wikipedia, the free encyclopedia
The massive amounts of energy that are released are the cause of earthquakes, a common phenomenon along transform boundaries.
Such volcanoes are characterized by alternating periods of quiet and episodic eruptions that start with explosive gas expulsion with fine particles of glassy volcanic ash and spongy cinders, followed by a rebuilding phase with hot magma.
Divergent boundaries are typified in the oceanic lithosphere by the rifts of the oceanic ridge system, including the Mid-Atlantic Ridge, and in the continental lithosphere by rift valleys such as the famous East African Great Rift Valley.
en.wikipedia.org /wiki/Plate_tectonics   (4245 words)

 Discrete Wavelet Transform for Audio Compression
Wavelet coefficients in the lower frequency bands are encoded using 2 schemes, 8-bit log PCM and the 3 level Max-Lloyd quantizer.
The wavelet transform is performed on the residual using edge-prediction and noise modeling.
This portion consists of transients and noise, and is represented using a wavelet transform.
is.rice.edu /~welsh/elec431/wavelets.html   (984 words)

 Bilinear operator - Wikipedia, the free encyclopedia
In mathematics, a bilinear operator is a generalized "multiplication" which satisfies the distributive law.
The set L(V,W;X)of all bilinear maps is a linear subspace of the space (viz vector space, module) of all maps from V×W into X.
In general, for a vector space V over a field F, a bilinear form on V is the same as a bilinear operator V × V → F.
en.wikipedia.org /wiki/Bilinear_operator   (634 words)

 Transform Coding
The lapped orthogonal transforms are a special case in which the coefficients' influence is confined to a few adjacent blocks, with a tapering-off influence toward the edges.
A portion of a sine wave coded with a Fourier transform has all the energy concentrated at the same frequency coefficients regardless of the phase of the sinusoid (although the energy will be apportioned differently between the sine and cosine components).
Transform coding is used to convert spatial image pixel values to transform coefficient values.
www.bretl.com /mpeghtml/xfrmcode.HTM   (567 words)

 PlanetMath: Hough transform
The Hough transform is a general technique for identifying the locations and orientations of certain types of features in a digital image.
This is version 9 of Hough transform, born on 2002-04-28, modified 2005-09-04.
For this reason the Hough transform is more typically used for simpler curves, such as straight lines and parabolas.
planetmath.org /encyclopedia/HoughTransform.html   (870 words)

One drawback of using the Hartley transform is that it is difficult to extend to higher dimensions because it is not a separable transform.
Possibly his greatest contribution was the creation of a new transform: The Hartley Transform which has many practical applications.
It is likely that Hartley was aware of the earlier work of Nyquist and that he assumed implicitly, as Nyquist did explicitly, that all symbol sequences were of the same length or size.
www.geocities.com /neveyaakov/electro_science/hartley.html   (870 words)

 Perspective (graphical) - Wikipedia, the free encyclopedia
In the former case it is generally referred to as artistic, spatial foreshortening; in the latter case it is referred to as perspective projection or if calculated using matrix multiplication (usually by a computer) as a perspective transform.
Perspective images generated by computers (for example, in three-dimensional computer games) use some method of perspective transform.
Natural perspective projection is the name given by Leonardo to the projection that produces the image beheld by the human eye.
en.wikipedia.org /wiki/Perspective_(graphical)   (870 words)

 3D projection - Wikipedia, the free encyclopedia
To complete the transform in the most general way possible, another matrix called the scaling matrix is used to scale the model along the axes.
One can, for example, pop the world transform off a stack of transforms and multiply a new world transform on, without having to do anything with the camera transform and perspective transform.
The four matrices are multiplied together, and the result is the world transform matrix: a matrix that, if a point's coordinates were multiplied by it, would result in the point's coordinates being expressed in the "world" reference frame.
en.wikipedia.org /wiki/3D_projection   (870 words)

 PlanetMath: Cayley's parameterization of orthogonal matrices
In conclusion, it might be worth pointing out that the Cayley transform generalizes to the case of infinite dimensions, if one replaces matrices with operators on a Hilbert space.
In particular, this allows one to parameterize pseudo-orthogonal matrices such as Lorentz transformations using a Cayley parameterization.
This is version 12 of Cayley's parameterization of orthogonal matrices, born on 2004-11-27, modified 2005-02-19.
planetmath.org /encyclopedia/CayleyTransform.html   (870 words)

 Transform boundary - Wikipedia, the free encyclopedia
Most transform boundaries are found on the ocean floor, where they often offset active spreading ridges to form a zigzag plate boundary.
In plate tectonics, a transform boundary (also known as transform fault boundary, transform plate boundary, transform plate margin or conservative plate boundary) is said to occur when tectonic plates slide and grind against each other along a transform fault.
The relative motion of such plates is horizontal in either sinistral or dextral direction.
en.wikipedia.org /wiki/Transform_boundary   (136 words)

 Method for transmitting fractal transform data to support different compressor/decompressor designs - Patent 5867603
The fractal transform process may be described as the determination of mapping function parameters which may be iteratively applied to a random data buffer to generate an attractor which represents a data set or a portion of a data set.
Likewise, the fractal transform parameters in the fractal transform data segment include a translation factor q which is preferably multiplied by 16,384 and divided by the greatest possible value for the intensity value in the color space before storage.
Mathematically, the original data set F may be expressed as a set of fractal transforms, F.sub.x, F.sub.y, and F.sub.v.
www.freepatentsonline.com /5867603.html   (8124 words)

The Two-Dimensional FT The two-dimensional Fourier transform (2-DFT)
The second set of Fourier transforms is performed in the t" dimension to yield an f' by f" set of data.
Recall from Chapter 2 that the Fourier transform is a mathematical technique for converting time domain data to frequency domain data, and vice versa.
www.cis.rit.edu /htbooks/nmr/chap-5/chap-5.htm   (1199 words)

 PlanetMath: Fourier transform
This is version 11 of Fourier transform, born on 2002-04-07, modified 2005-03-04.
The Fourier transform has some important properties, that can be used when solving differential equations.
So when looking a transform up in a table you should find out how it is defined in that table.
planetmath.org /encyclopedia/FourierTransform.html   (192 words)

 Apparatus for compression-coding image data and method of the same based on quantification and frequency transform coefficient amplitude reduction - Patent 5754696
The quantification of the transform coefficients is performed by dividing the transform coefficients by a corresponding quantification value which is previously stored in a quantification table 350.
The quantification of the transform coefficients is performed by dividing each transform coefficient by a corresponding quantification value, which is, for example, shown in FIG.
Accordingly, as the specified degree of the quantification coefficient data increases, namely, as the frequency becomes higher, an increase in the quantification error which is generated by the level conversion of the quantification coefficient data having a small amplitude becomes larger.
www.freepatentsonline.com /5754696.html   (6388 words)

 Plate Tectonics
This boundary is one of the longer transform margins in the world, and it is unusual in that it occurs on continental crust.
Transform margins are in the middle, generating moderate to strong earthquakes depending on what kind of crust they occur in.
Most transform margins occur between segments of divergent margins, and thus are found in oceanic crust.
geology.csusb.edu /DIVGRANT/ptect/ptect4.htm   (706 words)

 Transform boundary - Wikipedia, the free encyclopedia
Most transform boundaries are found on the ocean floor, where they often offset active spreading ridges to form a zigzag plate boundary.
In plate tectonics, a transform boundary (also known as transform fault boundary, transform plate boundary, transform plate margin or conservative plate boundary) is said to occur when tectonic plates slide and grind against each other along a transform fault.
The relative motion of such plates is horizontal in either sinistral or dextral direction.
www.wikipedia.org /wiki/Transform_boundary   (101 words)

 A Brief History of Stirling, Scotland
Stirling castle was originally built in wood but in the late 13th century it was rebuilt in stone.
That was partly because the king moved to England and Stirling castle gradually ceased to be a royal residence and became a barracks.
Stirling castle fell to the English in 1304 but the Scots recaptured it in 1314 after the battle of Bannockburn.
www.localhistories.org /stirling.html   (101 words)

 Radon transform package
A Radon transform is an array of size radii * angles * angles, where the radial size (NCOL) is the same as the edge of the image, and the number of angles (NTHETA) covers the range 0 - 2*PI.
Because half of this angular range is redundant, a smaller transform is calculated with the number of angles covering 0 - PI equal to the image edge size (NTHETA/2 = NCOL).The POCS filter imposes consistency on a Radon transform and can be used to fill in missing points.
There are three actions defined to do the forward and backward transformations, and the POCS filtering.
www.niams.nih.gov /rcn/labbranch/lsbr/software/bsoft/radon/Radon.html   (101 words)

 WWRC 89-30 : Uncertainty on Travel Time in Kinematic Wave Channel Routing
As the one last reminder, although the Mellin transform is powerful for uncertainty analysis under the conditions stated previously, it possesses one drawback which should be pointed out: under some certain combinations of distribution and functional form, the resulting transform may not be analytic for all s's, especially when quotients are involved.
From this convolutional property of the Mellin transform and its relationship between statistical moments, one can immediately see the advantage of the Mellin transform as the tool in obtaining the moments of a random variable which is related to other random variables in a multiplicative fashion.
The Mellin transform is especially attractive and simple to use when the dependent random variable is related to a number of independent random variables in multiplicative manner.
library.wrds.uwyo.edu /wrp/89-30/89-30.html   (3361 words)

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