Showing papers on "Harmonic wavelet transform published in 1993"
IBM1
TL;DR: An indexing method for time sequences for processing similarity queries using R * -trees to index the sequences and efficiently answer similarity queries and provides experimental results which show that the method is superior to search based on sequential scanning.
Abstract: We propose an indexing method for time sequences for processing similarity queries. We use the Discrete Fourier Transform (DFT) to map time sequences to the frequency domain, the crucial observation being that, for most sequences of practical interest, only the first few frequencies are strong. Another important observation is Parseval's theorem, which specifies that the Fourier transform preserves the Euclidean distance in the time or frequency domain. Having thus mapped sequences to a lower-dimensionality space by using only the first few Fourier coefficients, we use R * -trees to index the sequences and efficiently answer similarity queries. We provide experimental results which show that our method is superior to search based on sequential scanning. Our experiments show that a few coefficients (1–3) are adequate to provide good performance. The performance gain of our method increases with the number and length of sequences.
2,082 citations
TL;DR: A progressive texture classification algorithm which is not only computationally attractive but also has excellent performance is developed and is compared with that of several other methods.
Abstract: A multiresolution approach based on a modified wavelet transform called the tree-structured wavelet transform or wavelet packets is proposed. The development of this transform is motivated by the observation that a large class of natural textures can be modeled as quasi-periodic signals whose dominant frequencies are located in the middle frequency channels. With the transform, it is possible to zoom into any desired frequency channels for further decomposition. In contrast, the conventional pyramid-structured wavelet transform performs further decomposition in low-frequency channels. A progressive texture classification algorithm which is not only computationally attractive but also has excellent performance is developed. The performance of the present method is compared with that of several other methods. >
1,507 citations
Book•
01 Dec 1993
TL;DR: In this paper, the authors introduce the idea of joint probability distributions and average for linear systems and their response to random vibrational signals. But they do not discuss the relationship between these distributions and the average.
Abstract: 1. Introduction To Probability Distributions And Averages. 2. Joint Probability Distributions, Ensemble Averages. 3. Correlation. 4. Fourier Analysis. 5. Spectral Density. 6. Excitation - Response Relations For Linear Systems. 7. Transmission Of Random Vibration. 8. Statistics Of Narrow Band Processes. 9. Accuracy Of Measurements. 10. Digital Spectral Analysis I: Discrete Fourier Transforms. 11. Digital Spectral Analysis II: Windows And Smoothing. 12. The Fast Fourier Transform. 14. Application Notes. 15. Multi-Dimensional Spectral Analysis. 16. Response Of Continuous Linear Systems To Stationary Random Excitation. 17. Discrete Wavelet Analysis.
855 citations
TL;DR: In this paper, the linear transform kernel for fractional Fourier transform is derived and the spatial resolution and the space-bandwidth product for propagation in graded-index media are discussed.
Abstract: The linear transform kernel for fractional Fourier transforms is derived. The spatial resolution and the space–bandwidth product for propagation in graded-index media are discussed in direct relation to fractional Fourier transforms, and numerical examples are presented. It is shown how fractional Fourier transforms can be made the basis of generalized spatial filtering systems: Several filters are interleaved between several fractional transform stages, thereby increasing the number of degrees of freedom available in filter synthesis.
806 citations
TL;DR: This note is a very basic introduction to wavelets, starting with an orthogonal basis of piecewise constant functions, constructed by dilation and translation, and leading to dilation equations and their unusual solutions.
Abstract: This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The «wavelet transform» maps each f(x) to its coefficients with respect to this basis. The mathematics is simple and the transform is fast (faster than the Fast Fourier Transform, which we briefly explain), but approximation by piecewise constants is poor. To improve this first wavelet, we are led to dilation equations and their unusual solutions. Higher-order wavelets are constructed, and it is surprisingly quick to compute with them - always indirectly and recursively
339 citations
TL;DR: This work discusses the general properties of the CWT and applies it, both analytically and graphically, to a number of simple geometrical objects: a line, a square, an angle, etc.
276 citations
TL;DR: In this paper, a new harmonic wavelet is suggested, which is orthogonal to its own unit translations and octave dilations, and its frequency spectrum is confined exactly to an octave band so that it is compact in the frequency domain (rather than in the x domain).
Abstract: A new harmonic wavelet is suggested. Unlike wavelets generated by discrete dilation equations, whose shape cannot be expressed in functional form, harmonic wavelets have the simple structure w(x) = {exp(i4$\pi $x)-exp(i2$\pi $x)}/i2$\pi $x. This function w(x) is concentrated locally around x = 0, and is orthogonal to its own unit translations and octave dilations. Its frequency spectrum is confined exactly to an octave band so that it is compact in the frequency domain (rather than in the x domain). An efficient implementation of a discrete transform using this wavelet is based on the fast Fourier transform (FFT). Fourier coefficients are processed in octave bands to generate wavelet coefficients by an orthogonal transformation which is implemented by the FFT. The same process works backwards for the inverse transform.
275 citations
TL;DR: The application of 3D orthogonal wavelet transforms to real volume data is discussed and examples of the wavelet transform and the reconstruction of 1D functions are presented.
Abstract: The application of 3D orthogonal wavelet transforms to real volume data is discussed. Examples of the wavelet transform and the reconstruction of 1D functions are presented. The application of the 3D wavelet transform to real volume data generated from a series of 115 slices of magnetic resonance (MR) images is described. >
206 citations
TL;DR: The wavelet transform of random processes with wide-sense stationary increments is shown to be a wide- sense stationary process whose correlation function and spectral distribution are determined.
Abstract: The wavelet transform of random processes with wide-sense stationary increments is shown to be a wide-sense stationary process whose correlation function and spectral distribution are determined. The second-order properties of the coefficients in the wavelet orthonormal series expansion of such processes is obtained. Applications to the spectral analysis and to the synthesis of fractional Brownian motion are given. >
133 citations
01 Sep 1993
TL;DR: In this article, the wavelet transform is generalized to produce a library of orthonormal bases of modulated wavelet packets, where each basis comes with a fast transform, and hence give rise to the notion of a "best basis" for a signal subject to a given cost function.
Abstract: . The wavelet transform is generalized to produce a library of orthonormal bases of modulated wavelet packets, where each basis comes with a fast transform. These bases are similar to adaptive windowed Fourier transforms, and hence give rise to the notion of a “best basis” for a signal subject to a given cost function. This paper discusses some early results in acoustic signal compression using a simple counting cost function.
106 citations
TL;DR: The pitch-synchronous wavelet transform is particularly suitable to the analysis, rate-reduction coding and synthesis of speech signals and it may serve as a preprocessing block in automatic speech recognition systems.
Abstract: A new wavelet representation is explored. The transform is based on a pitch-synchronous vector representation and it adapts to the oscillatory or aperiodic characteristics of signals. Pseudo-periodic signals are represented in terms of an asymptotically periodic trend and aperiodic fluctuations at several scales. The transform reverts to the ordinary wavelet transform over totally aperiodic signal segments. The pitch-synchronous wavelet transform is particularly suitable to the analysis, rate-reduction coding and synthesis of speech signals and it may serve as a preprocessing block in automatic speech recognition systems. Feature extraction such as separation of voice from noise in voiced consonants is easily performed by means of partial wavelet expansions. A stochastic model of aperiodic fluctuations is proposed. >
TL;DR: In this paper, the wavelet analysis technique is applied to analyze the frequency-domain electromagnetic backscattered signal from finite-size targets, which consists of both small-scale natural resonances and large-scale scattering center information.
Abstract: The wavelet analysis technique is applied to analyze the frequency-domain electromagnetic backscattered signal from finite-size targets. Since the frequency-domain radar echo consists of both small-scale natural resonances and large-scale scattering center information, the multiresolution property of the wavelet transform is well suited for analyzing such multiscale signals. Wavelet analysis examples of backscattered data from an open-ended waveguide cavity and a plasma cylinder are presented. Compared with the conventional short-time Fourier transform, the wavelet transform provides a more efficient representation of both the early-time scattering center data and the late-time resonances. The different scattering mechanisms are clearly resolved in the time-frequency representation. >
TL;DR: The fast wavelet transform is applied to the integral-equation solution of two-dimensional electromagnetic scattering problems and the total computational complexity is found to be reduced without sacrificing much accuracy.
Abstract: The fast wavelet transform is applied to the integral-equation solution of two-dimensional electromagnetic scattering problems. In the wavelet transform domain, the moment-method impedance matrix becomes sparse, and sparse matrix algorithms can be utilized to solve the resulting matrix equation. Using the fast wavelet transform in conjunction with the conjugate gradient method, we present the time performance for the solution of a dihedral corner reflector. The total computational complexity is found to be reduced without sacrificing much accuracy. The reason for the sparsity of the wavelet domain representation is discussed and additional areas of research are pinpointed. © 1993 John Wiley & sons, Inc.
TL;DR: In this paper, an optimal and dynamic multiresolutional distributed filtering algorithm for dynamic multisensor/data fusion is derived, where the wavelet transform is utilized as a bridge linking signals at different resolution levels.
Abstract: An algorithm for optimal and dynamic multiresolutional distributed filtering is derived. The wavelet transform is utilized as a bridge linking signals at different resolution levels. The algorithm can be employed for dynamic multisensor/data fusion. >
01 Jan 1993
TL;DR: In this paper, the authors used the theory of the continuous wavelet transform to derive inversion formulas for the Radon transform on L 1 \L 2 (R d) in even dimensions, and gave explicit a priori estimates on the error in the L 2 and L 1 norms.
Abstract: We use the theory of the continuous wavelet transform to derive inversion formulas for the Radon transform on L 1 \L 2 (R d). These inversion formulas turn out to be local in even dimensions in the following sense. In order to recover a function f from its Radon transform in a ball of radius R > 0 about a point x to within error , we can nd () > 0 such that this can be accomplished by knowing the projections of f only on lines passing through a ball of radius R + () about x. We give explicit a priori estimates on the error in the L 2 and L 1 norms.
TL;DR: In this paper, the authors obtained irregular sampling theorems for the wavelet transform and the short-time Fourier transform, yielding irregular weighted frames for wavelets and Gabor functions with explicit estimates for the frame bounds.
Abstract: We obtain irregular sampling theorems for the wavelet transform and the short-time Fourier transform. These sampling theorems yield irregular weighted frames for wavelets and Gabor functions with explicit estimates for the frame bounds.
01 Sep 1993
TL;DR: In this paper, wavelet and short-time Fourier analysis is introduced in the context of frequency decompositions, and using this fact, filter bank theory is used to construct multiplicity M wavelet frames and tight frames.
Abstract: . Wavelet and short-time Fourier analysis is introduced in the context of frequency decompositions. Wavelet type frequency decompositions are associated with filter banks, and using this fact, filter bank theory is used to construct multiplicity M wavelet frames and tight frames.
01 Jan 1993
TL;DR: Alternative matrix- and vector-filter implementations of alternative truncated, circulant, and extended versions of the wavelet transform yield identical results and enhance, respectively, didactic conceptualization and computational efficiency.
Abstract: The algorithms split for the wavelet transform and merge for the inverse wavelet transform are presented for finite-duration discrete-time signals of arbitrary length not restricted to a power of 2. Alternative matrix- and vector-filter implementations of alternative truncated, circulant, and extended versions are discussed. Matrix- and vector-filter implementations yield identical results and enhance, respectively, didactic conceptualization and computational efficiency. Truncated, circulant, and extended versions produce the signal-end effects of, respectively, errors, periodization, and redundancy in the transform coefficients. The use of any one of these three versions avoids the signal-end effects associated with the other two versions. Additional alternatives which eliminate all signal-end effects (albeit at the cost of increased algorithmic complexity) are discussed briefly.
Journal Article•
TL;DR: In this article, a concrete parameter space for the compactly supported wavelet systems of Daubechies is constructed, which is a closed convex set in R (N−2)/2, which can be explicitly described in the Fourier transform domain.
Abstract: In this paper a concrete parameter space for the compactly supported wavelet systems of Daubechies is constructed. For wavelet systems with N (generic) nonvanishing coefficients the parameter space is a closed convex set in R (N−2)/2 , which can be explicitly described in the Fourier transform domain. The moment-free wavelet systems are subsets obtained by the intersection of the parameter space and an affine subspace of R (N−2)/2
TL;DR: The authors propose a new method for signal modification in auditory peripheral representation: an auditory wavelet Transform and algorithms for reconstructing a signal from a modified wavelet transform.
Abstract: The authors propose a new method for signal modification in auditory peripheral representation: an auditory wavelet transform and algorithms for reconstructing a signal from a modified wavelet transform. They present the characteristics of signal analysis, synthesis, and reconstruction and also the data reduction criteria for signal modification. >
TL;DR: A new class of block transforms is presented, constructed from subband decomposition filter banks corresponding to regular wavelets, which are compared to the discrete cosine transform (DCT).
Abstract: A new class of block transforms is presented. These transforms are constructed from subband decomposition filter banks corresponding to regular wavelets. New transforms are compared to the discrete cosine transform (DCT). Image coding schemes that use the block wavelet transform (BWT) are developed. BWT's can be implemented by fast (O(N log N)) algorithms. >
TL;DR: A class of multiscale stochastic processes which are modeled using dynamic representations evolving in scale based on the wavelet transform can be well-approximated, leading to new, highly parallel and scale-recursive estimation algorithms for multi-scale data fusion.
27 Apr 1993
TL;DR: It is shown that the minimum mean squared error improves significantly with the use of the self-orthogonalizing wavelet transform least mean square (WLMS), and an exponentially weighted convergence factor is proposed to introduce scale-based variation to the weight update equation.
Abstract: The use of the wavelet transform in transform domain adaptive filtering (WTAF) is analyzed for performance as measured by learning curves. It is shown that the minimum mean squared error improves significantly with the use of the self-orthogonalizing wavelet transform least mean square (WLMS). An exponentially weighted convergence factor is proposed to introduce scale-based variation to the weight update equation. Simulations for learning curves are obtained by using a conventional smooth signal with sinusoidal components as well as a nonsmooth signal recorded in an electrically noisy environment. The latter signal consists of periodic as well as randomly occurring signals from multiple sources. >
TL;DR: A separable fast discrete Fourier transform (DFT) algorithm for hexagonally sampled data that directly computes output points on a rectangular lattice is reported.
Abstract: Hexagonal sampling is the most efficient sampling pattern for a two-dimensional circularly bandlimited function. A separable fast discrete Fourier transform (DFT) algorithm for hexagonally sampled data that directly computes output points on a rectangular lattice is reported. No interpolation is required. The algorithm has computational complexity comparable to that of standard two-dimensional fast Fourier transforms. >
23 May 1993
TL;DR: Simulations show that the proposed technique for redundancy removal of quantized coefficents of a wavelet transform performs better than classical methods, while maintaining an efficient implementation complexity.
Abstract: A novel technique for redundancy removal of quantized coefficents of a wavelet transform is discussed. This technique rests on the coding of the address of nonzero coefficients using blocks in both lossy and lossless approach. Simulations show that the proposed technique performs better than classical methods, while maintaining an efficient implementation complexity. >
28 Mar 1993
TL;DR: The theory and implementation in subthreshold analog CMOS technology of a circuit which performs continuous wavelet decompositions of a one-dimensional (e.g., audio) input are described.
Abstract: The theory and implementation in subthreshold analog CMOS technology of a circuit which performs continuous wavelet decompositions of a one-dimensional (e.g., audio) input are described. The analog wavelet outputs are the output of a logarithmically scaled bank of bandpass filters; each band is sampled at a rate proportional to the Nyquist rate of the highest frequency content of that band. The result is a matrix of discrete points describing the input signal as a function of both frequency and time. The filter function of each band is Gaussian shaped in order to best resolve the uncertainty relation between time and frequency at each sampled point. >
01 Nov 1993
TL;DR: In this paper, the authors considered the problem of finding the optimal P X P paraunitary transform that minimizes the approximation error when a signal is reconstructed from a reduced number of components Q < P.
Abstract: Most orthogonal signal decompositions, including block transforms, wavelet transforms, wavelet packets, and perfect reconstruction filterbanks in general, can be represented by a paraunitary system matrix. This paper considers the general problem of finding the optimal P X P paraunitary transform that minimizes the approximation error when a signal is reconstructed from a reduced number of components Q < P. This constitutes a direct extension of the Karhunen-Loeve transform which provides the optimal solution for block transforms (unitary system matrix). General solutions are presented for the optimal representation of arbitrary wide sense stationary processes. This work also investigates a variety of suboptimal schemes using FIR filterbanks. In particular, it is shown that low-order Daubechies wavelets and wavelet packets (D2 and D3) are near optimal for the representation of Markov-1 processes.