Showing papers on "Harmonic wavelet transform published in 1989"
TL;DR: The author describes the mathematical properties of such decompositions and introduces the wavelet transform, which relates to the decomposition of an image into a wavelet orthonormal basis.
Abstract: The author reviews recent multichannel models developed in psychophysiology, computer vision, and image processing. In psychophysiology, multichannel models have been particularly successful in explaining some low-level processing in the visual cortex. The expansion of a function into several frequency channels provides a representation which is intermediate between a spatial and a Fourier representation. The author describes the mathematical properties of such decompositions and introduces the wavelet transform. He reviews the classical multiresolution pyramidal transforms developed in computer vision and shows how they relate to the decomposition of an image into a wavelet orthonormal basis. He discusses the properties of the zero crossings of multifrequency channels. Zero-crossing representations are particularly well adapted for pattern recognition in computer vision. >
2,109 citations
01 Jan 1989
TL;DR: One of the aims of wavelet transforms is to provide an easily interpretable visual representation of signals that is a prerequisite for applications such as selective modifications of signals or pattern recognition.
Abstract: One of the aims of wavelet transforms is to provide an easily interpretable visual representation of signals This is a prerequisite for applications such as selective modifications of signals or pattern recognition
356 citations
01 Jan 1989
TL;DR: It will be shown that the computation load grows with the scale factor of the analysis, which leads to a prohibitive computation time, so a more effective computation procedure is needed.
Abstract: The computation of the wavelet transform involves the computation of the convolution product of the signal to be analysed by the analysing wavelet. It will be shown that the computation load grows with the scale factor of the analysis. We are interested in musical sounds lasting a few seconds. Using a straightforward algorithm leads to a prohibitive computation time, so we need a more effective computation procedure.
261 citations
Book•
28 Dec 1989
TL;DR: In this paper, Fourier Transform Spectrometry (FT-Spectrometry) is used to derive the line shape derived from the motion of a Damped Mass on a Spring, which is then used for spectral line shape estimation.
Abstract: 1. Spectral Line Shape Derived from the Motion of a Damped Mass on a Spring. 2. Fourier Transforms for Analog (Continuous) Waveforms. 3. Fourier Transforms of Digital (Discrete) Waveforms. 4. Fourier Transform Spectrometry: Common Features. 5. Noise. 6. Non-FT Methods for Proceeding from Time- to Frequency-Domain. 7. Fourier Transform Ion Cyclotron Resonance Mass Spectrometry. 8. FT/NMR. 9. FT/Interferometry. 10. Epilog: Fourier Transforms in Other Types of Spectroscopy. References. Problems (at the end of each chapter). Solutions to problems. Appendices. Index.
223 citations
TL;DR: In this article, the authors compared five real-valued orthogonal transforms in terms of learning characteristics and computational complexity, and showed that the effect of an ideal transform is to convert equal error contours that are initially hyperellipses in the parameter space into hyperspheres.
Abstract: It has been previously shown that a real-time decomposition of the incoming signal into a set of partially uncorrelated components via an orthogonal transform, and a subsequent adaptation on these individual components, leads to faster convergence rates. Here, transform domain processing is characterized by the effect of the transform on the shape of the mean-square error surface. It is shown that the effect of an ideal transform is to convert equal error contours that are initially hyperellipses in the parameter space into hyperspheres. Five specific real-valued orthogonal transforms are compared in terms of learning characteristics and computational complexity. Since the Karhunen-Loeve transform (KLT) is the ideal transform for this application, and since the KLT is defined in terms of the statistics of the input signal, it is certain that no fixed-parameter transform can deliver optimal learning characteristics for all input signals. However, the simulations suggest that transforms can be found which give much improved performance in a given situation. >
165 citations
TL;DR: Although in theory the Fourier transform method is valid only for small rejections, in practice it can be modified for the synthesis of high rejection filters with minimum transmittances as low as 10(-4).
Abstract: Although in theory the Fourier transform method is valid only for small rejections, in practice it can be modified for the synthesis of high rejection filters with minimum transmittances as low as 10−4. Two new spectral functions are proposed for use in the Fourier transforms. An empirical procedure which is much faster than refinement is described for optimization of the spectral performance. The method and optimization are illustrated numerically for several different spectral shapes.
67 citations
CNET1
TL;DR: The authors propose a transform coding algorithm for bit rate reduction of high-quality sound that provides for long-term stationarity in the transform coder while keeping fixed blocklength.
Abstract: The authors propose a transform coding algorithm for bit rate reduction of high-quality sound. The algorithm provides for long-term stationarity in the transform coder while keeping fixed blocklength. Side information is drastically reduced, and predictive coding of DFT (discrete Fourier transform) coefficients is used to remove the interblock redundancy. Perceptual properties are incorporated in the bit-allocation procedure to achieve spectral noise shaping. The complete algorithm is described, and results of coding at 96 kb/s for a monophonic 15-kHz audio signal are discussed. >
33 citations
01 Jan 1989
TL;DR: The wavelet transform is presented as a mathematical microscope which is well suited for studying the local scaling properties of fractal measures and is applied to probability measures on self-similar Cantor sets, to the 2∞ cycle of period-doubling and to the golden-mean trajectories on two-tori at the onset of chaos.
Abstract: We present the wavelet transform as a mathematical microscope which is well suited for studying the local scaling properties of fractal measures. We apply this technique, recently introduced in signal analysis, to probability measures on self-similar Cantor sets, to the 2∞ cycle of period-doubling and to the golden-mean trajectories on two-tori at the onset of chaos. We emphasize the wide range of application of the wavelet transform which turns out to be a natural tool for characterizing the structural properties of fractal objects arising in a variety of physical situations.
30 citations
Dissertation•
01 Jan 1989
TL;DR: The multiresolution Fourier transform (MFT) has the potential to provide a basis for the solution of general image analysis problems and is shown to be invertible and amenable to efficient computation via familiar signal processing techniques.
Abstract: The extraction of meaningful features from an image forms an important area of image
analysis. It enables the task of understanding visual information to be implemented in a
coherent and well defined manner. However, although many of the traditional approaches to
feature extraction have proved to be successful in specific areas, recent work has suggested
that they do not provide sufficient generality when dealing with complex analysis problems
such as those presented by natural images.
This thesis considers the problem of deriving an image description which could form the basis
of a more general approach to feature extraction. It is argued that an essential property of such
a description is that it should have locality in both the spatial domain and in some
classification space over a range of scales. Using the 2-d Fourier domain as a classification
space, a number of image transforms that might provide the required description are investigated.
These include combined representations such as a 2-d version of the short-time Fourier
transform (STFT), and multiscale or pyramid representations such as the wavelet transform.
However, it is shown that these are limited in their ability to provide sufficient locality in both
domains and as such do not fulfill the requirement for generality.
To overcome this limitation, an alternative approach is proposed in the form of the multiresolution
Fourier transform (MFT). This has a hierarchical structure in which the outermost levels
are the image and its discrete Fourier transform (DFT), whilst the intermediate levels are
combined representations in space and spatial frequency. These levels are defined to be
optimal in terms of locality and their resolution is such that within the transform as a whole
there is a uniform variation in resolution between the spatial domain and the spatial frequency
domain. This ensures that locality is provided in both domains over a range of scales. The
MFT is also invertible and amenable to efficient computation via familiar signal processing
techniques. Examples and experiments illustrating its properties are presented.
The problem of extracting local image features such as lines and edges is then considered. A
multiresolution image model based on these features is defined and it is shown that the MET
provides an effective tool for estimating its parameters.. The model is also suitable for
representing curves and a curve extraction algorithm is described. The results presented for
synthetic and natural images compare favourably with existing methods. Furthermore, when
coupled with the previous work in this area, they demonstrate that the MFT has the potential
to provide a basis for the solution of general image analysis problems.
28 citations
TL;DR: A new fast algorithm for computing the two-dimensional discrete Hartley transform that requires the lowest number of multiplications compared with other related algorithms is presented.
Abstract: A new fast algorithm for computing the two-dimensional discrete Hartley transform is presented. This algorithm requires the lowest number of multiplications compared with other related algorithms.
18 citations
TL;DR: It is shown that the number of data points the arithmetic Fourier transform (AFT) needs for an N-point Fouriertransform is proportional to N/sup 2/.
Abstract: It is shown that the number of data points the arithmetic Fourier transform (AFT) needs for an N-point Fourier transform is proportional to N/sup 2/. Thus, for example, while a standard fast Fourier transform algorithm requires 1024 samples to yield 1024 spectral components, AFT would take more than 300000 samples to do the same job. >
23 May 1989
TL;DR: A method of extracting formant information from the short-time Fourier transform phase spectrum of speech by developing algorithms to reduce the effects of wrapping.
Abstract: A method of extracting formant information from the short-time Fourier transform phase spectrum of speech is proposed. Fourier transform phase has not been used for formant extraction because it appears to be noisy and difficult to interpret. The effects of wrapping of phase (due to zeros close to the unit circle and the linear phase component) make it difficult to derive useful information. The authors develop algorithms to reduce the effects of wrapping. >
31 Mar 1989
TL;DR: In this article, the authors compared the performance of the fringe tracking, the heterodyne, the phase step or phase shift, and the Fourier transform method without additional carrier frequency.
Abstract: The methods used for automatic evaluation of interference patterns are presented and compared. These are the fringe tracking, the heterodyne, the phase step or phase shift, and the Fourier transform methods, especially the Fourier transform method without additional carrier frequency. The special advantages of the individual methods are described. Experimental results of holographic interferometric deformation measurement at a thick-walled pressure vessel by phase stepping, Fourier transform evaluation of an object not covering the whole frame, and Fourier transform evaluation of a speckle interferogram are presented.
TL;DR: The Hartley transform achieves better coding performance than the Fourier transform, but is inferior to the cosine transform.
Abstract: The data compression performance of the Hartley transform on a Markov-1 signal is theoretically compared to that of the Fourier transform. Covariance distribution and residue correlation measurements have been computed for the Hartley, Fourier, and cosine transforms. The Hartley transform achieves better coding performance than the Fourier transform, but is inferior to the cosine transform. >
TL;DR: The authors investigated the implementation aspects of the fast Hartley transform (FHT) in both software and hardware and describe the modifications required to convert existing fast Fourier transform programs to execute FHTs, showing the ease with which these modifications can be implemented.
Abstract: The authors investigated the implementation aspects of the fast Hartley transform (FHT) in both software and hardware. They describe the modifications required to convert existing fast Fourier transform (FFT) programs to execute FHTs, showing the ease with which these modifications can be implemented. They compare execution time and memory storage requirements of both transforms and present power spectrum calculation and convolution as illustrative examples to compare the performances of the two transform techniques. They also give a comparative survey of the performances of various microprocessors and digital signal processors in FFT and FHT computation. >
TL;DR: The fast Hartley transform provides the same information as the fast Fourier transform (FFT) but with greater speed and efficiency when the input data are real.
Abstract: The fast Hartley transform provides the same information as the fast Fourier transform (FFT) but with greater speed and efficiency when the input data are real. An algorithm for taking the Hartley transform of a long sequence on a multiprocessor machine by simultaneously transforming short subsequences does not require complex arithmetic and is faster than analogous techniques which use the Fourier transform.
23 May 1989
TL;DR: The authors describe the implementation of real and complex FFT (fast Fourier transform) algorithms on the Motorola DSP96002, a general-purpose, dual-bus IEEE standard floating-point digital signal processor that provides the basis for efficient implementation of FFTs and other fast transforms.
Abstract: The authors describe the implementation of real and complex FFT (fast Fourier transform) algorithms on the Motorola DSP96002. The DSP96002 is a general-purpose, dual-bus IEEE standard floating-point digital signal processor (DSP). At a 74-ns instruction cycle, the DSP96002 implements a 1024-point real FFT in 0.905 ms and a 1024-point complex FFT in 1.55 ms. This performance is achieved by calculating up to three floating-point results in a single instruction cycle, or 40.5 MFLOPS peak. A radix-2 FFT butterfly is executed every four cycles, an average of 33.75 IEEE MFLOPS. The instruction set and architecture of the DSP96002 provide the basis for efficient implementation of FFTs and other fast transforms, such as the discrete Walsh-Hadamard transform, discrete cosine transform, and discrete Hartley transform. >
TL;DR: An algorithm is introduced for computing the multidimensional finite Fourier transform and offers a substantial reduction in the computational complexity.
Abstract: An algorithm is introduced for computing the multidimensional finite Fourier transform. The algorithm can be applied to data samples of any size. In most cases, it offers a substantial reduction in the computational complexity. >
01 Jan 1989
TL;DR: A fast algorithm for computing the Hankel transform of order one is derived by slightly modifying the algorithm developed by E.W. Hansen (1985), which enjoys computational advantages using a rapid Abel transform with shift-variant recursive filter and a fast Fourier transform.
Abstract: A fast algorithm for computing the Hankel transform of order one is derived by slightly modifying the algorithm developed by E.W. Hansen (1985). Since the algorithm uses the formal equivalency between a Hankel transform and an Abel transform followed by a Fourier transform, it enjoys computational advantages using a rapid Abel transform with shift-variant recursive filter and a fast Fourier transform. Good agreement between actual and computer transforms was obtained in the simulation with a known transform pair. >
TL;DR: In this paper, the authors illustrate how morphological operators can be expressed in terms of Fourier optics using the properties of the Fourier transform hologram and demonstrate basic operations which are usually involved in morphological filtering.
23 May 1989
TL;DR: It is demonstrated that invalid assumptions on the bandwidth of the input signal will cause aliasing errors to occur in the AFT spectrum that are different from the aliase errors that occur inThe DFT.
Abstract: The computational complexity and the effects of quantization and sampling instant errors in the arithmetic Fourier transform (AFT) and the summation by parts discrete Fourier transform (SBP-DFT) algorithms are examined. The relative efficiency of the AFT and SBP-DFT algorithms is demonstrated by comparing the number of multiplications, additions, memory storage locations, and input signal samples as well as the latency time and level of parallelism of these two methods with that of more conventional single-output DFT and multiple-output fast Fourier transform (FFT) routines. The error response of the kth Fourier bin of these algorithms is analyzed as a function of increasing levels of input signal sampling errors in the AFT and coefficient quantization errors in the SBP-DFT. It is demonstrated that invalid assumptions on the bandwidth of the input signal will cause aliasing errors to occur in the AFT spectrum that are different from the aliasing errors that occur in the DFT. >
14 Nov 1989
TL;DR: In this article, the modulus squared of the wavelet transform is defined as the estimate of a bilinear joint time-frequency distribution characterized by a product kernel, and expressed in terms of any bilinearly joint timefrequency distribution.
Abstract: We define the modulus squared of the wavelet transform to be the wavelet estimate, and express it in terms of any bilinear joint time-frequency distribution characterized by a product kernel.
23 May 1989
TL;DR: A method is presented for computing the discrete Fourier transform (DFT) of data compressed using vector quantization (VQ), suitable for both one-dimensional and multidimensional DFTs or, in general, any linear process.
Abstract: A method is presented for computing the discrete Fourier transform (DFT) of data compressed using vector quantization (VQ). The VQ compressed data are not reconstructed before use; instead, a codebook that has been processed with the DFT (discrete Fourier transform) algorithm is used for VQ reconstruction. An overlap-and-add technique is used to combine the processed reconstruction codebook vectors to give the DFT directly. The technique is suitable for both one-dimensional and multidimensional DFTs or, in general, any linear process. The technique is called the computation compression technique (CCT). The CCT implementation yields exactly the same result as if the compressed data had been reconstructed and the DFT performed on the data directly. CCT convolution on a 68020/6881-based computer is described. Speedups of two orders of magnitude are obtained. >
18 Jul 1989
TL;DR: In this paper, a fast discrete Radon transform method for enhancement of lines in noisy images is described, based on the Fourier slice theorem, with variable length slices to utilise all of the frequency domain data.
Abstract: A new fast discrete Radon transform method for enhancement of lines in noisy images is described. It is based on the Fourier slice theorem, with variable length slices to utilise all of the frequency domain data. It is shown that this new method achieves a significant increase in computational speed compared with an existing technique.
TL;DR: When the optical Hartley transform of a real, 2-D input object is constructed by the addition of two Fourier transforms with the correct relative amplitude, phase, and orientation the resulting field then encodes all the information normally associated with Fourier amplitude and phase.
Abstract: When the optical Hartley transform of a real, 2-D input object is constructed by the addition of two Fourier transforms with the correct relative amplitude, phase, and orientation the resulting field then encodes, in the form of amplitude only, all the information normally associated with Fourier amplitude and phase. If the transformer fails to correctly realize the desired relationship between the two Fourier transforms, the field at the transform plane no longer represents a true Hartley transform. Nevertheless knowledge of the nature of the error along with measurements in the transform plane enables the Hartley transform to be precisely recovered.
23 May 1989
TL;DR: A parallel adder configuration that is much faster than the usual serial adder is proposed and a scheme for fast reordering of the input data that increases the reordering speed without increasing the memory size is also proposed.
Abstract: A fast implementation of recursive DFTs (discrete Fourier transforms) is presented. It only needs (N-1)/2 real multiplications to compute all N frequency components. A factor R/sub T/ is introduced. If the ratio T/sub m//T/sub a/ of the multiplier and adder periods is greater than R/sub T/, this scheme is faster than the FFT (fast Fourier transform). The error and signal-to-noise ratio are studied. A parallel adder configuration that is much faster than the usual serial adder is proposed. A scheme for fast reordering of the input data that increases the reordering speed without increasing the memory size is also proposed. >
17 May 1989
TL;DR: From results of numerical experiments on a simple test signal, it is observed that the performance of the algorithm is affected minimally by roundoff errors of the optical system.
Abstract: Anjan Ghosh, Susan D. Allen and Palacharla PaparaoDepartment of Electrical and Computer EngineeringUniversity of IowaIowa City, IA 52242.ABSTRACTThe Arithmetic Fourier Transform is a number -theoretic method for calculating Fourier coefficients of continu-ous time signals. In this paper, we present an efficient realization of the arithmetic Fourier transform algorithmon an optical parallel processor consisting of fiber optic tapped delay lines. The performance of the algorithm inpresence of optical errors and noise is analyzed. From results of numerical experiments on a simple test signal weobserve that the performance of the algorithm is affected minimally by roundoff errors of the optical system.
11 Oct 1989
TL;DR: In this paper, the Fourier Transform Method (FTM) of fringe pattern analysis is proposed to achieve automatic, high-accuracy analysis of a fringe pattern and new possibilities of on-line analysis ensuing from the recent advances in microcomputer technology are discussed.
Abstract: The Fourier Transform Method (FTM) of fringe pattern analysis is one of the most important phase measuring techniques. Its chief advantage is that it requires only one interferogram which is crucial for industrial inspection. The goal of a fully automated phase retrieving technique, however, remains still elusive. Several refinements in 2-D FTM are proposed to achieve fully automatic, high-accuracy analysis of a fringe pattern. The new possibilities of on-line analysis ensuing from the recent advances in microcomputer technology are discussed.