Showing papers on "Time–frequency analysis 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. >

Asymptotic wavelet and Gabor analysis: extraction of instantaneous frequencies

Abstract: The behavior of the continuous wavelet and Gabor coefficients in the asymptotic limit using stationary phase approximations are investigated. In particular, it is shown how, under some additional assumptions, these coefficients allow the extraction of some characteristics of the analyzed signal, such as frequency and amplitude modulation laws. Applications to spectral line estimations and matched filtering are briefly discussed. >

Alias-free generalized discrete-time time-frequency distributions

Abstract: A definition of generalized discrete-time time-frequency distribution that utilizes all of the outer product terms from a data sequence, so that one can avoid aliasing, is introduced. The new approach provides (1) proper implementation of the discrete-time spectrogram, (2) correct evaluation of the instantaneous frequency of the underlying continuous-time signal, and (3) correct frequency marginal. The formulation provides a unified framework for implementing members of Cohen's class, which was formulated in the continuous-time domain. Some requirements for the discrete-time kernel in the new approach are discussed in association with desirable distribution properties. Some experimental results are provided to illustrate the features of the proposed method. >

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.

Device for the coherent demodulation of time-frequency interlaced digital data, with estimation of the frequency response of the transmission channel and threshold, and corresponding transmitter

Abstract: A coherent demodulation device, for the demodulation of a digital signal of the type constituted by digital elements distributed in the time-frequency space and transmitted in the form of symbols constituted by a multiplex of N orthogonal carrier frequencies modulated by a set of the digital elements and broadcast simultaneously, the digital signal comprising reference elements, having a value and a position, in the time-frequency space, that are known to the demodulation device, comprising means for the estimation, by Fourier transform, of the frequency response of the transmission channel at any instant, carrying out the transformation of the received samples, corresponding to reference elements, from the frequency domain to the temporal domain, the multiplication in the temporal domain of the transformed samples by a rectangular temporal window (f n) and the reverse transformation, after the multiplication, of the obtained samples from the temporal domain into the frequency domain, the estimation means comprising means for the thresholding of the samples in the temporal domain, providing for the systematic elimination of the samples below a certain threshold.

Adaptive time-frequency decomposition with matching pursuits

Abstract: An adaptive time-frequency decomposition is introduced. It represents signals as a linear expansion of local time-frequency waveforms, selected in order to match the signal structures. The decomposition is performed with an algorithm, called matching pursuit, whose convergence is guaranteed. A new definition of signal energy density in the time-frequency plane is derived by summing the Wigner distribution of each local time-frequency waveform. This energy density does not have any interference terms, unlike Wigner and Cohen class distributions. Numerical examples are described. >

A combined Wigner-Ville and Hough transform for cross-terms suppression and optimal detection and parameter estimation

Abstract: An attempt is made to show that the combined use of the Wigner-Ville distribution (WVD) and the Hough transform (HT) provides an important tool for mapping the signals onto a parameter space where the detection and parameter estimation problems can be made easier, since the important features of the signal are emphasized. This mapping can be used in the detection and parameter estimation of unknown signals embedded in noise. It is shown that this mapping comes directly from the application of the matched filter theory. In particular, the method can be applied to multicomponent signals, since it reduces considerably the effect of the cross terms, produced by the WVD, on the signal parameters estimate. >

Wavelet packet based transient signal classification

Abstract: Nonstationary signals are not well suited for detection and classification by traditional Fourier methods. An alternate means of analysis needs to be used so that valuable time-frequency information is not lost. The wavelet packet transform is one such time-frequency analysis tool. The authors summarize efforts which examine the feasibility of applying the wavelet packet transform to automatic transient signal classification through the development of a classification algorithm for biologically generated underwater acoustic signals in ocean noise. The formulation of a wavelet-packet based feature set specific to the classification of snapping shrimp and whale clicks is given. >

Some unique properties and applications of perfect squares minimum phase CAZAC sequences

Abstract: Properties described include the Constant Amplitude (CA) and Zero AutoCorrelation (ZAC) features, the ideal unfiltered and filtered Fourier transforms, the complex time domain, phase trajectory and perfect (unfiltered as well as filtered) periodic autocorrelation function properties. Additional characteristics presented are the remarkable resemblance between the CAZAC sequences and CWFM chirp signals, as well as the relationship between their instantaneous frequency and Fourier transform representations. Examples of the generation of typical PS-MP CAZAC sequences are given. It is demonstrated that these sequences are periodically, self-invertible and therefore constitute the optimum sequences for maximum-likelihood channel estimation. The paper includes simulation results with reference to potential applications. >

Radon transformation of time-frequency distributions for analysis of multicomponent signals

Abstract: The Radon transform of a time-frequency distribution produces local areas of signal concentration that facilitate interpretation of multicomponent signals. The Radon transform can be efficiently implemented with dechirping in the time domains; however, only half of the possible projections through the time-frequency plane can be realized because of aliasing. It is shown that the frequency dual to dechirping exists, so that all of the time-frequency plane projections can be calculated efficiently. Some Radon transforms of Wigner distributions are demonstrated. >

Analysis of transient signals using higher-order time-frequency distributions

Abstract: A general class of higher-order time-frequency representations, including Wigner higher-order spectra (WHOS), has been defined and studied recently as an extension of bilinear time-frequency distributions in terms of instantaneous higher-order moments of the signal. The analysis of mono- and multicomponent signals is considered using higher-order based time-frequency distributions. A computationally feasible implementation of the Wigner bispectrum and trispectrum (WHOS in the third and fourth order domain) is proposed considering one slice of the multifrequency space. The problem of cross-terms cancellation is addressed, and reduced interference distributions are defined as an extension of the Choi-Williams distribution. >

Arbitrary orthogonal tilings of the time-frequency plane

Abstract: Expansions which give arbitrarily orthonormal tilings of the time-frequency plane are considered. These differ from the short-time Fourier transform, wavelet transform, and wavelet packets tilings in that they change over time. It is shown how orthonormal tilings can be achieved using time-varying orthogonal tree structures, which preserve orthogonality, even across transitions. One method is based on lapped orthogonal transforms, which makes it possible to change the number of channels in the transform. A second method is based on the construction of boundary filters and gives arbitrary tilings. An algorithm is presented which for a given signal decides on the best binary segmentation and which tree split to use for each segment. It is optimal in a rate-distortion sense. The results of experiments on test signals are presented. >

Whistler analysis in the time‐frequency plane using chirplets

Abstract: This paper shows the benefits of using chirplet analysis of multipath magnetospheric whistlers. Higher resolution can be achieved than with the customary dynamic spectra (Gabor diagram), in which the cells characterizing resolution in time and frequency are the same over the whole diagram. Here we not only allow the aspect ratio of a resolution cell to vary within the one diagram but also introduce oblique cells corresponding to a new kind of elementary signal not discovered by Gabor. Chirplet analysis is also applicable to arbitrary signals and is most striking where certain kinds of finely detailed structure are present. We also describe a user interactive system that allows regions of interest to be selected in the time-frequency plane and enhanced by selecting chirplets appropriate to the local structure.

Computation of affine time-frequency distributions using the fast Mellin transform

Abstract: The theoretical approach to broadband time-frequency problems has led to consideration of new time-frequency distributions affiliated with the affine group of clock changes. Due to their origin these distributions involve stretched forms of the signals which are not easy to compute by standard techniques. An attempt is made to solve this difficulty by giving efficient algorithms founded on the use of the fast Mellin transform. >

The fast time frequency transform (F.T.F.T.): A novel on-line approach to the instantaneous spectrum

Abstract: This paper describes a concept for fast on-line transformation of signals into the combined time-frequency domain. Assuming a limited number of narrow-band signal components equidistantly spaced on the frequency axis, the number of computations required is minimized and an optimal time and frequency resolution is accomplished at the same time. Typically, for a postulated N-number of components, N being a power of 2, instantaneous amplitudes and frequencies are presented at each Nth input sample. From the fluctuations of the frequency over time, a measure for instantaneous bandwidth is derived that can be interpreted as the reciprocal of instantaneous signal-to-noise ratio. Instantaneous output of the FTFT may allow improved recognition of short transient patterns in noisy signals such as the Electro-Encephalo-Gram (EEG) and optimized feature coding and data compression compared to techniques, that average over a period of time. Using integer arithmetic and a high level programming language, the throughput rate on a single 20 MHz microprocessor is better than 1.5 KHz.

SAR ocean image representation using wavelets

Abstract: The utility of wavelet analysis as a tool for geophysical research is examined using both continuous and discrete versions of the wavelet transform. In both cases, waveform decomposition and reconstruction is possible using somewhat different computational procedures. The theoretical background of each procedure is briefly described and applied using a specific 'wavelet'. The wavelet used is based on a Gaussian function, and provides simultaneous time-frequency (or space-wavenumber) localization that meets the lower limit of the uncertainty principle. A representation of this type is ideally suited for the analysis of waveforms that arise from nonstationary processes. The properties of wavelet analysis are examined by expanding an FM-chirp waveform and azimuth cuts taken from two different SAR ocean images. The performance and ease of implementation are compared for the continuous and discrete formulations, and the effects of filtering in wavelet phase space using the discrete case are also examined. >

Matrix reformulation of the Gabor transform

Abstract: We have observed that if one restricts the von Neumann lattice to N points on the time axis and M points in the frequency axis there are, by definition, only MN independent Gabor coefficients. If the data is sampled such thatthere are exactly MN samples, then the forward and inverse Gabor transforms should be representable as linear transformations in C MN , the MN -dimensional vector space over the complex numbers, and the relationships that hold become matrix equations. These matrix equations are formulated, and some conclusions are drawn about the relative merits of using some methods as opposed to others, i.e., speed versus accuracy as well as whether or not the coefficients that are obtained via some methods are true Gabor coefficients.

Uncertainty Principles for Time-Frequency Operators

Abstract: This paper explores some of the connections between classical Fourier analysis and time-frequency operators, as related to the role of the uncertainty principle in Gabor and wavelet basis expansions.

Time-scale modification of speech using an incremental time-frequency approach with waveform structure compensation

Abstract: The authors try to identify the primary sources of distortion in a non-recursive time-scale modification (TSM) algorithm which is based on the short-time Fourier transform (STFT). A simpler version of this TSM algorithm is then proposed for processing speech, where incremental estimators eliminate the need for explicit linear time-scaling operations. Also featured in the design is a waveform structure compensation stage to prevent excessive deterioration of the rate-changed output. A polar (i.e., magnitude-phase) synthesis equation is used for increased efficiency. The TSM method is capable of generating high-quality rate-changed speech at a reasonable computational cost. >

The wave packet transform (WPT) as applied to signal processing

Abstract: The wave packet transform (WPT) is introduced. It uses the Weyl operator and wave packet functions, i.e., functions that are similar to wavelets, in a linear form to compute coefficients in a two-dimensional space of time and frequency. The importance of the Weyl operator in the WPT and its use with different wave packets are discussed. It is shown that the energetic form of the WPT, the wavepacketgram, i.e., the modulus square of the WPT, is a member of Cohen's class of time-frequency distributions. It is also shown that the wavepacketgram is a positive time-frequency distribution. >

SAR ocean image decomposition using the Gabor expansion

Abstract: Demonstrates the utility of the Gabor expansion as a new tool in geophysical research. The Gabor expansion provides good time-frequency (or space-wavenumber) localization and is ideally suited to represent nonstationary processes. The properties of this tool are demonstrated by expanding an FM-chirp waveform, and azimuth cuts taken from two different SAR ocean images. The effects of filtering in Gabor phase space are also investigated. >

Window matching in the time-frequency plane and the adaptive spectrogram

Abstract: Aspects of generating spectrograms which may be used in the preliminary steps of time-frequency analysis are discussed. It is shown that the major problem with the application of the spectrogram is its nonunique nature, i.e., the use of an arbitrary window for analysis. The concept of window matching is introduced, whereby the selection of the window used for analysis depends on the instantaneous signal characteristics at the given time-frequency point under analysis. Generalized instantaneous parameters are derived and subsequently used to demonstrate how the window matching may be applied. An adaptive window-matched spectrogram is generated. Practical data results are given. >

The ambiguity function of a linear signal space and its application to maximum-likelihood range/Doppler estimation

Abstract: The concept of the ambiguity function (AF) is extended to linear signal spaces. Some properties of the AF of a linear signal space, its relations with other space representations, and the results obtained for some specific signal spaces are discussed. It is shown that the AF of a signal space describes the performance of the maximum likelihood (ML) range/Doppler estimator for a slowly fluctuating point target when a series of orthogonal signal pulses are transmitted. This multipulse estimator is more accurate than a conventional signal-pulse estimator since the AF of a linear signal space may have arbitrarily good thumbtack shape. >

The wave packet transform (WPT) as applied to signal processing

Abstract: The wave packet transform (WPT) uses the Weyl operator and wave packet functions, i.e., functions that are similar to wavelets, in a linear form to compute coefficients in a two-dimensional space of time and frequency. The importance of the Weyl operator in the WPT and its use with different wave packets is discussed. It is shown that the energetic form of the WPT, the wavepacketgram, i.e., the modulus square of the WPT, is a member of Cohen's class of time-frequency distributions which are called the wave packet Cohen class distributions. It is shown that the wavepacketgram is a positive time-frequency distribution. >