Showing papers in "IEEE Signal Processing Magazine in 1991"

Wavelets and signal processing

Abstract: A simple, nonrigorous, synthetic view of wavelet theory is presented for both review and tutorial purposes. The discussion includes nonstationary signal analysis, scale versus frequency, wavelet analysis and synthesis, scalograms, wavelet frames and orthonormal bases, the discrete-time case, and applications of wavelets in signal processing. The main definitions and properties of wavelet transforms are covered, and connections among the various fields where results have been developed are shown. >

Exploitation of spectral redundancy in cyclostationary signals

Abstract: It is shown that the cyclostationarity attribute, as it is reflected in the periodicities of (second-order) moments of the signal, can be interpreted in terms of the property that allows generation of spectral lines from the signal by putting it through a (quadratic) nonlinear transformation. The fundamental link between the spectral-line generation property and the statistical property called spectral correlation, which corresponds to the correlation that exists between the random fluctuations of components of the signal residing in distinct spectral bands, is explained. The effects on the spectral-correlation characteristics of some basic signal processing operations, such as filtering, product modulation, and time sampling, are examined. It is shown how to use these results to derive the spectral-correlation characteristics for various types of man-made signals. Some ways of exploiting the inherent spectral redundancy associated with spectral correlation to perform various signal processing tasks involving detection and estimation of highly corrupted man-made signals are described. >

Adaptive polynomial filters

Abstract: Adaptive nonlinear filters equipped with polynomial models of nonlinearity are explained. The polynomial systems considered are those nonlinear systems whose output signals can be related to the input signals through a truncated Volterra series expansion or a recursive nonlinear difference equation. The Volterra series expansion can model a large class of nonlinear systems and is attractive in adaptive filtering applications because the expansion is a linear combination of nonlinear functions of the input signal. The basic ideas behind the development of gradient and recursive least-squares adaptive Volterra filters are first discussed. Adaptive algorithms using system models involving recursive nonlinear difference equations are then treated. Such systems may be able to approximate many nonlinear systems with great parsimony in the use of coefficients. Also discussed are current research trends and new results and problem areas associated with these nonlinear filters. A lattice structure for polynomial models is described. >

Computationally efficient algorithms for cyclic spectral analysis

Abstract: Two computationally efficient algorithms for digital cyclic spectral analysis, the FFT accumulation method (FAM) and the strip spectral correlation algorithm (SSCA), are developed from a series of modifications on a simple time smoothing algorithm. The signal processing, computational, and structural attributes of time smoothing algorithms are presented with emphasis on the FAM and SSCA. As a vehicle for examining the algorithms the problem of estimating the cyclic cross spectrum of two complex-valued sequences is considered. Simplifications of the resulting expressions to special cases of the cross cyclic spectrum of two complex-valued sequences, such as the cyclic spectrum of a single real-valued sequence, are easily found. Computational and structural simplifications arising from the specialization are described. >

Orthogonal approaches to time-series analysis and system identification

Abstract: Some recent, efficient approaches to nonlinear system identification, ARMA modeling, and time-series analysis are described and illustrated. Sufficient detail and references are furnished to enable ready implementation, and examples are provided to demonstrate superiority over established classical techniques. The ARMA identification algorithm presented does not require a priori knowledge of, or assumptions about, the order of the system to be identified or signal to be modeled. A suboptimal, recursive, pairwise search of the orthogonal candidate data records is conducted, until a given least-squares criterion is satisfied. In the case of nonlinear systems modeling, discrete-time Volterra series is stressed, or rather a more efficient parallel-cascade approach. The model is constructed by adding parallel paths (each consisting of the cascade of dynamic linear and static nonlinear systems). In the case of time-series analysis, a non-Fourier sinusoidal series approach is stressed. The relevant frequencies are estimated by an orthogonal search procedure. A search of the candidate sinusoids is conducted until a given mean-square criterion is satisfied. >

New forms of Levinson and Schur algorithms

Abstract: The Levinson and Schur solutions to the adaptive filtering and parameter estimation problem of recursive least squares processing are described. Unnormalized versions of a newly developed Schur RLS adaptive filter are presented. A systolic array of the Schur RL adaptive filter is devised and its performance is illustrated with a typical example. The classical Levinson and Schur algorithms drop out as special cases of the more general Levinson and Schur RLS adaptive filtering algorithms. The recently introduced split Levinson and Schur algorithms, which are obtained by exploiting the symmetry in the Toeplitz-structured extended normal equations, are reviewed. >