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Topic: Discrete Hartley transform

	The Discrete Hartley Transform - FFTW 3.1.2
		The discrete Hartley transform (DHT) is an invertible linear transform closely related to the DFT.
		The DHT was originally proposed as a more efficient alternative to the DFT for real data, but it was subsequently shown that a specialized DFT (such as FFTW's r2hc or r2c transforms) could be just as fast.
		However, we have heard rumors that the DHT might be the most appropriate transform in its own right for certain applications, and we would be very interested to hear from anyone who finds it useful.
	www.fftw.org /fftw3_doc/The-Discrete-Hartley-Transform.html (371 words)

	Discrete Hartley transform
		A discrete Hartley transform (DHT) is a frequency transform of discrete, periodic data similar to the discrete Fourier transform (DFT), with analogous applications in signal processing etcetera.
		Just as the DFT is the discrete analogue of the continuous Fourier transform, the DHT is the discrete analogue of the continuous Hartley transform, introduced by R. Hartley in 1942.
		Because there are fast algorithms for the DHT analogous to the Fast Fourier Transform (FFT), the DHT was originally proposed by R. Bracewell in 1983 as a more efficient computational tool in the common case where the data are purely real.
	www.ebroadcast.com.au /lookup/encyclopedia/di/Discrete_Hartley_transform.html (939 words)

	Fast Fourier transform - Encyclopedia, History, Geography and Biography
		This article describes the algorithms, of which there are many; see discrete Fourier transform for properties and applications of the transform.
		It was once believed that real-input DFTs could be more efficiently computed by means of the Discrete Hartley transform (DHT), but it was subsequently argued that a specialized real-input DFT algorithm (FFT) can typically be found that requires fewer operations than the corresponding DHT algorithm (FHT) for the same number of inputs.
		Yet another variation is to perform matrix transpositions in between transforming subsequent dimensions, so that the transforms operate on contiguous data; this is especially important for out-of-core and distributed memory situations where accessing non-contiguous data is extremely time-consuming.
	www.arikah.net /encyclopedia/FFT (2310 words)

	Frequency transform
		A frequency transform is the mapping of functions of a function space[?] on the coefficients of basis functions, where the basis functions must have a locality in the frequency spectrum.
		The result of the transform are the coefficients of the components (basis functions), i.e.
		Frequency transforms are often used as part of the process of transform coding, but have many other uses, including scientific and engineering analysis.
	www.ebroadcast.com.au /lookup/encyclopedia/fr/Frequency_transform.html (105 words)

	FFTW 3.0.1 (Site not responding. Last check: 2007-11-06)
		The discrete Hartley transform (DHT) is an invertible linear transform closely related to the DFT.
		The DHT was originally proposed as a more efficient alternative to the DFT for real data, but it was subsequently shown that a specialized DFT (such as FFTW's r2hc or r2c transforms) could be just as fast.
		However, we have heard rumors that the DHT might be the most appropriate transform in its own right for certain applications, and we would be very interested to hear from anyone who finds it useful.
	www.uic.edu /depts/accc/hardware/argo/fftw/The-Discrete-Hartley-Transform.html (474 words)

	1d Discrete Hartley Transforms (DHTs) - FFTW 3.1.2 (Site not responding. Last check: 2007-11-06)
		The discrete Hartley transform (DHT) of a 1d real array X of size n computes a real array Y of the same size, where:
		FFTW computes an unnormalized transform, in that there is no coefficient in front of the summation in the DHT.
		In other words, applying the transform twice (the DHT is its own inverse) will multiply the input by n.
	www.fftw.org /doc/1d-Discrete-Hartley-Transforms-_0028DHTs_0029.html (83 words)

	Discrete Cosine Transform (Site not responding. Last check: 2007-11-06)
		Modified discrete cosine transform - The modified discrete cosine transform (MDCT) is a Fourier-related transform based on the type-IV discrete cosine transform (DCT-IV), with the additional property of being lapped: it is designed to be performed on consecutive blocks of a larger dataset,
		Discrete cosine transform - The discrete cosine transform (DCT) is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers.
		Discrete Hartley transform - A discrete Hartley transform (DHT) is a Fourier-related transform of discrete, periodic data similar to the discrete Fourier transform (DFT), with analogous applications in signal processing and related fields.
	so98.iasoft.org /discretecosinetransform.html (919 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		The routines to perform real-data transforms are almost the same as those for complex transforms: you allocate arrays of `double' and/or `fftw_complex' (preferably using `fftw_malloc'), create an `fftw_plan', execute it as many times as you want with `fftw_execute(plan)', and clean up with `fftw_destroy_plan(plan)' (and `fftw_free').
		Half of these column transforms, however, are of imaginary parts, and should therefore be multiplied by i and combined with the r2hc transforms of the real columns to produce the 2d DFT amplitudes; FFTW's r2r transform does _not_ perform this combination for you.
		Note that the boundary conditions of the transform output array are given by the input boundary conditions of the inverse transform.
	www.math.temple.edu /doc/packages/fftw3/fftw3.info-1 (5887 words)

	2D discrete hartley transform
		Transform is not intrinsically any more efficient to compute than the
		Discrete Fourier Transform, are there applications in which the former
		One attractive aspect (of the DHT) is it is self inverting.
	www.dsprelated.com /showmessage/13742/1.php (3494 words)

	[No title]
		Most of the processing in DSP is linear, built around the use of filters and transforms, which effectively are linear mappings on discrete vector spaces.
		Many different transforms are used in DSP including the discrete Fourier transform (DFT), various discrete cosine and sine transforms, and the discrete Hartley transform.
		Finally, by understanding the connection between the algebraic structure of a transform and its DSP properties, it is possible to derive new transforms.
	www.math.cmu.edu /users/nw0z/abstracts/Peuschel.html (372 words)

	Fast Fourier Transform : FFT (Site not responding. Last check: 2007-11-06)
		It is of great importance to a wide variety of applications, from digital signal processing to solving partial differential equations to algorithms for quickly multiplying large integers.
		It was once believed that real-input DFTs could be more efficiently computed by means of the Discrete Hartley transform (DHT), but this was subsequently disproved: a specialized real-input DFT algorithm (FFT) can typically be found that requires fewer operations than the corresponding DHT algorithm (FHT) for the same number of inputs.
		The Rio Salado, a tributary of the Gila, is a the old ruins now seen there, must have had formerly a large that the reaching their destination on the Pacific, the country recollected that the most productive fields in California, before of cultivation from that of the natives of the.
	www.termsdefined.net /ff/fft.html (2550 words)

	Soliman1 - Abstract
		The discrete Hartley transform (DHT) is a real-valued transform and is closely related to the familiar Fourier transform (FT).
		In this paper, the convolution property of the DHT is used in the identification and measurement process.
		Because the Hartley transform is a real transform, it is more computationally efficient than the Fourier and Laplace transforms.
	webcenter.ru /~eeaa/ejta/eng/abstracts2005eng/soliman1eng.shtml (428 words)

	Automatic Generation of Transform Algorithms
		The approach extends the well known concept of discrete Fourier transforms over finite groups and became feasible through two advances: A method to decompose monomial representations of solvable groups by structural recursion and a method to compute certain symmetries of matrices by combinatorial search.
		The methods have been implemented in the library AREP and used to generate fast algorithms for a class of transforms including the discrete Fourier, cosine, sine, and Hartley transform, automatically.
		We have successfully demonstrated the method by computing automatically efficient transforms in several important cases: for the DFT, we obtain the Cooley/Tukey FFT; for a class of transforms including the DCT, type 2, the number of arithmetic operations for our fast transforms is the same as for the best known algorithms.
	www.ece.cmu.edu /~smart/papers/autgen.html (615 words)

	Research Areas
		In our work on architectures for the Discrete Wavelet Transform, we showed that while the traditional Mallat's algorithm mapped well to a SIMD array of processors and processors with large on-chip memory, new on-line algorithms have to be developed for single chip implementations with limited memory.
		We chose to represent the object by straight-line approximations of the boundary using the Hough transform and estimated the motion parameters from shifts in the theta-p space.
		The DWT accelerator implements the transform using a lifting-based scheme.
	enws155.eas.asu.edu:8001 /research.html (2333 words)

	E71 Final 2000
		The Inverse Discrete Hartely Transform is the same except for a division by N (eq 3.167),
		You showed, as part of the first exam, that the DHT (and IDHT) can be more efficient for certain operations than the DFT (and IDFT) because all multiplications are with real numbers instead of complex numbers (recall that a complex multiplication generally uses four real multiplications).
		Since the DHT is so closely linked to the DFT it seems reasonable to to try to develop a Fast Hartley Transform, or FHT.
	www.swarthmore.edu /NatSci/echeeve1/Class/e71/FinalExam/Final.html (892 words)

	The Discrete Hartley Transform for the HP-41
		Jean-Marc Baillard and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.
		-The Discrete Hartley Transform is closely related to the Discrete Fourier Transform,
		-Thus, applying the DHT twice yields the original vector multiplied by n.
	www.hpmuseum.org /software/41/41dhartl.htm (1297 words)

	Discrete Hartley Transform (Site not responding. Last check: 2007-11-06)
		The discrete Hartley transform, DHT, is given by the matrix
		The following structured, sparse matrix factorization represents a fast algorithm for a DHT, size 8, and has been automatically generated (even in the presented Latex format) using the package AREP.
		Note that this algorithm requires 2 multiplications and 22 additions and is thus among the best ones known.
	www.ece.cmu.edu /~smart/examples/algogen/dht.html (76 words)

	Mladen Victor Wickerhauser's book "Mathematics for Multimedia" - 8 February 2006
		fft.c: factored discrete Fourier transform, or FFT, and its inverse iFFT.
		fht.c: factored discrete Hartley transform, or FHT, and its inverse iFHT.
		pdwt.c: mallat's periodic discrete wavelet transform to specified depth, implemented by periodic filter convolution.
	www.math.wustl.edu /~victor/mfmm (1068 words)

	FFTW3 - Fast Fourier Transforms - FORTRAN77 Calling Examples (Site not responding. Last check: 2007-11-06)
		FFTW3 is a library of C routines which can compute the Fourier transform very efficiently.
		FFTW3 can also compute the discrete Hartley transform of real data.
		The length of the data is not required to be a power of 2.
	www.csit.fsu.edu /~burkardt/f77_src/fftw3/fftw3.html (200 words)

	[No title]
		Just as a pair of sunglasses reduces the glare of white light, permitting only the softer green light to pass, so the DFT may be used to modify a signal to achieve a desired effect.
		Among the applications of the DFT are digital signal processing, oil and gas exploration, medical imaging, aircraft and spacecraft guidance, and the solution of differential equations of physics and engineering.
		Introduction; The Laplace Transform; The z- Transform; The Chebyshev Transform; Orthogonal Polynomial Transforms; The Discrete Hartley Transform (DHT); Problems; Chapter 9: Quadrature and the DFT.
	www.ec-securehost.com /SIAM/ot45.html (627 words)

	:: Conference Papers ::
		P.K. Meher, T. Srikanthan, J.Gupta, and H.K. Agarwal: ‘Low-Complexity Unified-Adaptive Compression of Biomedical Images Using Integer Hartley Transform’, 1st International Bioengineering Conference 2004, pp.125 - 128, September 2004.
		P.K. Meher, T. Srikanthan, J. Gupta, and H.K. Agarwal, "Controlled-Accuracy-Lossy Compression Using Integer Hartley Transform", Proceedings of The IEEE International Symposium on Consumer Electronics (ISCE-2003), December 2003.
		P.K. Meher and T. Srikanthan: 'A Scalable Multiplier-less Fully-Pipelined Architecture for VLSI Implementation of the Discrete Hartley Transform', The 2003 IEEE International Symposium on Signals, Circuits and Systems' (SCS-2003), Iasi, Romania, pp.
	www.chipes.ntu.edu.sg /contents/library/ConferencePapers.htm (4537 words)

	Miao - DSP and Statistical Classification (Site not responding. Last check: 2007-11-06)
		As you order, each item will be listed in Your Shopping Cart in the upper left corner.
		This is the first book to introduce and integrate the topics of digital signal processing (DSP) and statistical classification together, and the only volume to introduce state-of-the-art transforms, including DFT, FFT, DCT, DST, DHT, DHLT, DFHT, DTWT, DWT, DHAT, PCT, CCT, CDT, and ODT together for DSP and digital communication applications.
		You get step-by-step guidance in discrete-time random processes; discrete-time domain signal processing and frequency domain signal analysis; discrete-time transforms; digital filter design and adaptive filtering; multirate digital signal processing; and statistical signal classification.
	www.scitechpub.com /miao.htm (432 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		I. Guo, C. Liu, and C. Jen, "New systolic arrays for prime length discrete cosine transform," Proc.
		I. Guo, C. Liu, and C. Jen,"A memory-based systolic array chip for the 1-D discrete cosine transform," Proc.
		I. Guo, C. Liu, and C. Jen,"A novel VLSI array design for the discrete Hartley transform using cyclic convolution," Proc.
	soc1.cs.ccu.edu.tw /~jiguo/JIGUO_publication_list.htm (2385 words)

	ISCAS 2000 Paper information (Site not responding. Last check: 2007-11-06)
		Abstract: Polynomial algorithms for Multidimensional Discrete Hartley Transform (MD-DHT) are proposed.
		Based on the multidimensional Polynomial Transform, the MD-DHT is converted into a series of one-dimensional type-II discrete W transforms (DWT).
		The number of multiplications for computing an r-dimensional DHT is only 1/r times that needed by the row-column method.
	iscas.epfl.ch /program/paper.asp?id=145 (124 words)

	FFTW3 - Fast Fourier Transforms - C Calling Examples (Site not responding. Last check: 2007-11-06)
		FFTW3 - Fast Fourier Transforms - C Calling Examples
		This directory contains examples of the use of the FFTW3 library by a C calling program.
		You can go up one level to the C source codes.
	www.csit.fsu.edu /~burkardt/c_src/fftw3/fftw3.html (197 words)

	Concept Index - FFTW 3.0.1
		discrete cosine transform: Real even/odd DFTs (cosine/sine transforms)
		discrete Fourier transform: The 1d Discrete Fourier Transform (DFT)
		discrete Hartley transform: 1d Discrete Hartley Transforms (DHTs)
	www.physics.louisville.edu /help/fftw/Concept-Index.html (75 words)

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