Showing papers on "S transform published in 1992"

Linear and quadratic time-frequency signal representations

Abstract: A tutorial review of both linear and quadratic representations is given. The linear representations discussed are the short-time Fourier transform and the wavelet transform. The discussion of quadratic representations concentrates on the Wigner distribution, the ambiguity function, smoothed versions of the Wigner distribution, and various classes of quadratic time-frequency representations. Examples of the application of these representations to typical problems encountered in time-varying signal processing are provided. >

A resolution comparison of several time-frequency representations

Abstract: Two signal components are considered resolved in a time-frequency representation when two distinct peaks can be observed. The time-frequency resolution limit of two Gaussian components, alike except for their time and frequency centers, is determined for the Wigner distribution, the pseudo-Wigner distribution, the smoother Wigner distribution, the squared magnitude of the short-time Fourier transform, and the Choi-Williams distribution. The relative performance of the various distributions depends on the signal. The pseudo-Wigner distribution is best for signals of this class with only one frequency component at any one time, the Choi-Williams distribution is most attractive for signals in which all components have constant frequency content, and the matched filter short-time Fourier transform is best for signal components with significant frequency modulation. A relationship between the short-time Fourier transform and the cross-Wigner distribution is used to argue that, with a properly chosen window, the short-time Fourier transform of the cross-Wigner distribution must provide better signal component separation that the Wigner distribution. >

Wavelet transform as a bank of the matched filters.

Abstract: The wavelet transform is a powerful tool for the analysis of short transient signals. We detail the advantages of the wavelet transform over the Fourier transform and the windowed Fourier transform and consider the wavelet as a bank of the VanderLugt matched filters. This methodology is particularly useful in those cases in which the shape of the mother wavelet is approximately known a priori. A two-dimensional optical correlator with a bank of the wavelet filters is implemented to yield the time-frequency joint representation of the wavelet transform of one-dimensional signals.

Optical wavelet transform

Abstract: The wavelet transform is implemented using an optical multichannel correlator with a bank of wavelet transform filters. This approach provides a shift-invariant wavelet transform with continuous translation and discrete dilation parameters. The wavelet transform filters can be in many cases simply optical transmittance masks. Experimental results show detection of the frequency transition of the input signal by the optical wavelet transform.

Transform image enhancement

Abstract: Blockwise transform image enhancement techniques are discussed. Previously, transform image enhancement has usually been based on the discrete Fourier transform (DFT) applied to the whole image. Two major drawbacks with the DFT are high complexity of implementation involving complex multiplications and additions, with intermediate results being complex numbers, and the creation of severe block effects if image enhancement is done blockwise. In addition, the quality of enhancement is not very satisfactory. It is shown that the best transforms for transform image coding, namely, the scrambled real discrete Fourier transform, the discrete cosine transform, and the discrete cosine-III transform, are also the best for image enhancement. Three techniques of enhancement discussed in detail are alpha-rooting, modified unsharp masking, and filtering motivated by the human visual system response (HVS). With proper modifications, it is observed that unsharp masking and HVS-motivated filtering without nonlinearities are basically equivalent. Block effects are completely removed by using an overlap-save technique in addition to the best transform.

A Comparison of the Existence of "Cross Terms" in the Wigner Distribution and the Squared Magnitude of the Wavelet Transform and the Short Time

Abstract: The wavelet transform (WT), a time-scale repre- sentation, is linear by definition. However, the nonlinear en- ergy distribution of this transform is often used to represent the signal; it contains ''cross terms" which could cause prob- lems while analyzing multicomponent signals. In this paper, we show that the cross terms that exist in the energy distribution of the WT are comparable with those found in the Wigner dis- tribution (WD), a quadratic time-frequency representation, and the energy distribution of the short time Fourier transform (STFT), of closely spaced signals. The cross terms of the WT and the STFT energy distributions occur at the intersection of their respective WT and STFT spaces, while for the WD they occur midtime and midfrequency. The parameters of the cross terms are a function of the difference in center frequencies and center times of the perpended signals. The amplitude of these cross terms can be as large as twice the product of the magni- tudes of the transforms of the two signals in question in all three cases. In this paper, we consider the significance of the effect of the cross terms on the analysis of a multicomponent signal in each of these three representations. We also compare the advantages and disadvantages of all of these methods in appli- cations to signal processing.

A comparison of the existence of 'cross terms' in the Wigner distribution and the squared magnitude of the wavelet transform and the short-time Fourier transform

Abstract: It is shown that cross terms comparable to those found in the Wigner distribution (WD) exist for the energy distributions of the wavelet transform (WT) and the short-time Fourier transform (STFT). The geometry of the cross terms is described by deriving mathematical expressions for the energy distributions of the STFT and the WT of a multicomponent signal. From those mathematical expressions it is inferred that the STFT and the WT cross terms: (1) occur at the intersection of the respective transforms of the two signals under consideration, whereas the WD cross terms occur at mid-time-frequency of the two signals; (2) are oscillatory in nature, as are the WD cross terms, and are modulated by a cosine whose argument is a function of the difference in center times and center frequencies of the signals under consideration; and (3) can have a maximum amplitude as large as twice the product of the magnitude of the transforms of the two signals in question, like WD cross terms. It is shown that the presence of these cross terms could lead to problems in analyzing a multicomponent signal. The consequences of this effect with respect to speech applications are discussed. >

Wavelets and their Applications

Abstract: Contributions discuss signal analysis discrete-time signal processing, wavelets for Quincunx pyramid, transform maxima and multiscale edges, among other topics; numerical analysis; other applications the optical wave transform, continuous wavelet transform, quantum mechanics; and theoretical develop

A formal definition of the Hough transform: Properties and relationships

Abstract: Shape, in both 2D and 3D, provides a primary cue for object recognition and the Hough transform (P.V.C. Hough, U.S. Patent 3,069,654, 1962) is a heuristic procedure that has received considerable attention as a shape-analysis technique. The literature that covers application of the Hough transform is vast; however, there have been few analyses of its behavior. We believe that one of the reasons for this is the lack of a formal mathematical definition. This paper presents a formal definition of the Hough transform that encompasses a wide variety of algorithms that have been suggested in the literature. It is shown that the Hough transform can be represented as the integral of a function that represents the data points with respect to a kernel function that is definedimplicitly through the selection of a shape parameterization and a parameter-space quantization. The kernel function has dual interpretations as a template in the feature space and as a point-spread function in the parameter space. A novel and powerful result that defines the relationship between parameterspace quantization and template shapes is provided. A number of interesting implications of the formal definition are discussed. It is shown that the Radon transform is an incomplete formalism for the Hough transform. We also illustrate that the Hough transform has the general form of a generalized maximum-likelihood estimator, although the kernel functions used in estimators tend to be smoother. These observations suggest novel ways of implementing Hough-like algorithms, and the formal definition forms the basis of work for optimizing aspects of Hough transform performance (see J. Princen et. al.,Proc. IEEE 3rd Internat. Conf. Comput. Vis., 1990, pp. 427–435).

On local linear transform and Gabor filter representation of texture

Abstract: Presents a comparative study of two approaches to texture representation under the computational framework of multichannel spatial filtering. The two approaches compared are the Gabor multichannel receptive field model and local linear transform techniques. In the local linear transform approach, it is shown that the orthogonal masks derived from the discrete cosine transform (DCT) have some interesting features which resemble Gabor filters. Although the texture representation concepts of orthogonal DCT basis masks and Gabor filters are fundamentally different, it is demonstrated that the representational structure of both approaches is inherently identical. This allows one to devise an experiment to compare the two approaches in terms of their computational efficiency and the representation potential of the extracted texture features. The performance of the approaches is assessed by means of their segmentation result accuracy on a set of images composed of Brodatz textures. >

On the use of the Hilbert transform for processing measured CW data

Abstract: The Hilbert transform is a commonly used technique for relating the real and imaginary parts of a causal spectral response. It is found in both continuous and discrete forms and is widely used in circuit analysis, digital signal processing, image reconstruction and remote sensing. One useful application in the area of high-power microwave (HPM) technology is in correcting measured continuous wave (CW) transfer function data, so as to insure causality in reconstructed transient responses. Another application of the Hilbert transform is in the area of complex spectral estimation using magnitude-only data. Here, the applications of the transform to several specific spectral filtering and phase reconstruction problems are illustrated. >

Performance analysis of transient detectors based on a class of linear data transforms

Abstract: The problem of detecting short-duration nonstationary signals, which are commonly referred to as transients, is addressed. Transients are characterized by a signal model containing some unknown parameters, and by a 'model mismatch' representing the difference between the model and the actual signal. Both linear and nonlinear signal models are considered. The transients are assumed to undergo a noninvertible linear transformation prior to the application of the detection algorithm. Examples of such transforms include the short-time Fourier transform, the Gabor transform, and the wavelet transform. Closed-form expressions are derived for the worst-case detection performance for all possible mismatch signals of a given energy. These expressions make it possible to evaluate and compare the performance of various transient detection algorithms, for both single-channel and multichannel data. Numerical examples comparing the performance of detectors based on the wavelet transform and the short-time Fourier transform are presented. >

Applications of Gabor and wavelet expansions to the Radon transform

Abstract: We investigate the relationship between the Radon transform and certain phase space localization functions, namely the continuous Gabor and wavelet transforms. We derive inversion formulas for the Radon transform based on the Gabor and wavelet transform. Some of these formulas give a direct reconstruction of f or of Δ1/2f from the Radon transform data. Others show how the Gabor and wavelet transforms of f or Δ1/2f can be recovered directly from the Radon transform data. We suggest ways in which these formulas can lead to efficient reconstruction algorithms and can be applied to noise reduction in reconstructed images.

Optical N4 implementation of a two-dimensional wavelet transform

Abstract: A two-dimensional wavelet transform is implemented by a bank of wavelet transform filters in the Fourier domain. An optical N 4 multichannel correlator architecture is proposed to perform parallel optical 2-D wavelet transforms. A holographic recording scheme is proposed to implement such a wavelet transform filter array. The optical experimental results are presented using the computer-generated transmittance masks as the wavelet transform filters.

A wavelet transform approach to texture analysis

Abstract: Traditional texture analysis algorithms focus too much on the local coupling between image pixels. Time/frequency analytical tools such as the Gabor and wavelet transforms can efficiently characterize the coupling of different scales in textures, and help to overcome this difficulty. However, the conventional wavelet transform, which has a finer resolution in the lower frequency channels, does not work properly for textured images, since textures are quasi-periodic signals whose dominant frequencies are located in the middle frequency regions. In the present research, a tree-structured wavelet transform is proposed. An adaptive procedure is developed to zoom into any frequency channels with significant information so that the decomposition can be further performed. The application of the new transform to texture classification is demonstrated. >

Performance of the short-time Fourier Transform and Wavelet Transform to phonocardiogram signal analysis

Abstract: In this paper the shortages of using the Nan&ml Fourier Transform to analyze the Phonocardiogram (KG) signals is first pointed out and the need for time-varyingdigitat signal processing techniquesto conectly analyzeKG signals is discussed.‘I%vo timefrequency analysis techniques am presented in this pape~ namely, the Spectrogram and the Wavelet Transform. Furthermore, a comparisonstudy between these two techniques has shown the ~lution diffenmces between them. The Wavelet Transform is shown to be capable to detect the two components, aortic valve component A2 and pulmonary valve compment P2, of the second sound S2 of a normal PCG signal which am not detectable neitherusing the standardFourier‘fkansfonnmr the Spectrogram.In addition to thz the Wavelet ‘fYansfomtenables Physicians to obtain qualitative and quantitative measurements of time-fiwpency characteristicsof phonocadiogram (KG) signals.

New number theoretic transform

Abstract: A new number theoretic transform is introduced. This transform is defined modulo the Mersenne primes, has long transform length which is a power of two, a fast algorithm, and the inverse transform has within a factor of (1/N) the same form as the forward transform. Thus, it is well suited for the calculation of error free convolutions and correlations.

Evidence for a generalized Laguerre transform of temporal events by the visual system

Abstract: It is generally assumed that the early visual processing is constituted by a set of filters operating in parallel. In this respect the visual system performs a transform, generating a code of the characteristics of the input signal. Recently, it has been suggested that the coding of the spatial characteristics by the visual system can be described by a Hermite transform (Martens, 1990a, b). It was also suggested that a three-dimensional Hermite transform can be used to code spatiotemporal events. In contrast to this latter suggestion, we argue that the coding of temporal events takes the form of a generalized Laguerre transform. We review psychophysical evidence supporting this hypothesis.

New square wave transform for digital signal processing

Abstract: A novel transform for spectral decomposition that uses regular square waves as the basis functions is presented. The digital transform requires order N operations. The transform possesses unusually symmetry properties which may prove useful in many applications. In particular, it can act as a generalized frequency filter that only depends on the periodicity of the data. >

Computing pseudo-Wigner distribution by the fast Hartley transform

Abstract: The use of the fast Hartley transform (FHT) to evaluate the Wigner distribution entirely in the real domain is proposed, and the computational complexity is reduced from three complex FFTs to three real FHTs. >

Gabor wavelet transform and application to problems in early vision

Abstract: Some of the work on the use of Gabor wavelets, a nonorthogonal family of functions, in the analysis of image data is reviewed. Applications to low-level vision problems such as boundary detection, feature detection and localization, and shape recognition are illustrated. A brief introduction to the Gabor wavelet transformation is included. >

Texture classification with tree-structured wavelet transform

Abstract: Proposes a multiresolution approach based on a tree-structured wavelet transform for texture classification. The development of tree-structured wavelet transform is motivated by the observation that textures are quasi-periodic signals whose dominant frequencies are located in the middle frequency channels. With the transform, one is able to zoom into desired frequency channels and performs further decomposition. In contrast, the conventional wavelet transform only decomposes subsignals in low frequency channels. A progressive texture classification algorithm which is not only computationally attractive but also has excellent performance is developed. >

Image invariant via the Radon Transform

Abstract: Proposes an alternative approach based on a new image invariant computed from the Radon Transform. The authors recall the definition of the Radon Transform which is a basic operator in the field of image reconstruction from projections. The Radon Transform associates to a 2D image the set of its integral on straight lines. It can be parametered by two variables (space and angle), and can be represented as a new 2D image. They then derive its properties relatively to translation and rotation. More precisely both operations are traduced by a translation on the Radon Transform image. These properties are illustrated by numerical examples. They propose a spectral image invariant computed from the Radon Transform. The relation between this quantity and the 2D Fourier Transform of the image is given. They then discuss the advantages and drawbacks of the computation of the image invariant by each of the two methods. At last some results computed on simulated digital images are presented.

Surface Interpolation Using Wavelets

Abstract: Extremely efficient surface interpolation can be obtained by use of a wavelet transform. This can be accomplished using biologicallyplausible filters, requires only O(n) computer operations, and often only a single iteration is required.

A general solution of biorthogonal analysis window functions for orthogonal-like discrete Gabor transform

Abstract: An algorithm for computing the analysis window function gamma (i) for the discrete Gabor transform (DGT) corresponding to an arbitrary synthesis window function h(i) and sampling pattern is presented. Numerical simulations indicate that the algorithm successfully addresses problems that could not be solved previously due to rank deficiency or numerical instability. >

Genetic search of a generalized Hough transform space

Abstract: We use a Generalized Hough transform (GHT) to detect and track instances of a class of sonar signals. This class consists of a four-dimensional set of curves and hence requires a four- dimensional transform space for the GHT. Many of the signals we need to detect are very weak. Such signals yield peaks in the transform space which are both very narrow and not too far above the random background variations. Finding such peaks is difficult. Exhaustive search over a predetermined discretization of the transform space will yield a nearly optimal point for a sufficiently fine discretization. However, even with an intelligently chosen discretization, exhaustive search requires searching over (and hence evaluating) many points in the transform space. We have therefore developed a genetic algorithm to more efficiently search the transform space. Designing the genetic algorithm to work properly has required experimentation with a number of its parameters. The most important of these are (1) the representation, (2) the population size, and (3) the number of runs.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Computational algorithms for discrete wavelet transform using fixed-size filter matrices

Abstract: This paper describes matrix based algorithms for computing wavelet transform representations with application to multiresolution analysis. Structure of the algorithm presented is well suited for programming purpose and also for the implementation on VLSI processors. By using overlap-add or overlap-save techniques, constant matrix size can be used to accommodate arbitrary data lengths. Performance of the algorithm described in this paper is illustrated by decomposing an image into details and smoothed components.

An algorithm for computing the inverse Z transform

Abstract: The authors determine an infinite impulse response of a causal system via a sampling algorithm applied to the transform on the unit circle. >

Computational accuracy and stability issues for the finite, discrete Gabor transform

Abstract: A Gabor expansion may use highly nonorthogonal basis functions and consequently inherit accuracy and stability problems due to near singularity when computed digitally Two methods to discretize the Gabor transform are studied from the viewpoint of controlling numerical properties: a Zak-transform-based method and a matrix method Theoretical issues relating to the singular behavior of each are cited, and stabilization techniques are proposed The validity of each technique is demonstrated by results of numerical experiments It is concluded that stability and accuracy can usually be achieved in a digitally implemented Gabor transform by proper choice of algorithm and stabilization mechanism >