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Showing papers on "Spectral density estimation published in 1998"


Journal ArticleDOI
TL;DR: An iterative nonparametric approach to spectral estimation that is particularly suitable for estimation of line spectra is presented, which minimizes a cost function derived from Bayes' theorem.
Abstract: We present an iterative nonparametric approach to spectral estimation that is particularly suitable for estimation of line spectra. This approach minimizes a cost function derived from Bayes' theorem. The method is suitable for line spectra since a "long tailed" distribution is used to model the prior distribution of spectral amplitudes. Since the data themselves are used as constraints, phase information can also be recovered and used to extend the data outside the original window. The objective function is formulated in terms of hyperparameters that control the degree of fit and spectral resolution. Noise rejection can also be achieved by truncating the number of iterations. Spectral resolution and extrapolation length are controlled by a single parameter. When this parameter is large compared with the spectral powers, the algorithm leads to zero extrapolation of the data, and the estimated Fourier transform yields the periodogram. When the data are sampled at a constant rate, the algorithm uses one Levinson recursion per iteration. For irregular sampling, the algorithm uses one Cholesky decomposition per iteration. The performance of the algorithm is illustrated with three different problems that arise in geophysical data: (1) harmonic retrieval from a time series contaminated with noise; (2) linear event detection from a finite aperture array of receivers, (3) interpolation/extrapolation of gapped data. The performance of the algorithm as a spectral estimator is tested with the Kay and Marple (1981) data set.

351 citations


Journal ArticleDOI
TL;DR: A comprehensive comparison of 2D spectral estimation methods for SAR imaging shows that MVM, ASR, and SVA offer significant advantages over Fourier methods for estimating both scattering intensity and interferometric height, and allow empirical comparison of the accuracies of Fouriers.
Abstract: Discusses the use of modern 2D spectral estimation algorithms for synthetic aperture radar (SAR) imaging. The motivation for applying power spectrum estimation methods to SAR imaging is to improve resolution, remove sidelobe artifacts, and reduce speckle compared to what is possible with conventional Fourier transform SAR imaging techniques. This paper makes two principal contributions to the field of adaptive SAR imaging. First, it is a comprehensive comparison of 2D spectral estimation methods for SAR imaging. It provides a synopsis of the algorithms available, discusses their relative merits for SAR imaging, and illustrates their performance on simulated and collected SAR imagery. Some of the algorithms presented or their derivations are new, as are some of the insights into or analyses of the algorithms. Second, this work develops multichannel variants of four related algorithms, minimum variance method (MVM), reduced-rank MVM (RRMVM), adaptive sidelobe reduction (ASR) and space variant apodization (SVA) to estimate both reflectivity intensity and interferometric height from polarimetric displaced-aperture interferometric data. All of these interferometric variants are new. In the interferometric contest, adaptive spectral estimation can improve the height estimates through a combination of adaptive nulling and averaging. Examples illustrate that MVM, ASR, and SVA offer significant advantages over Fourier methods for estimating both scattering intensity and interferometric height, and allow empirical comparison of the accuracies of Fourier, MVM, ASR, and SVA interferometric height estimates.

212 citations


Journal ArticleDOI
TL;DR: This paper reviews some novel spectral analysis techniques that are useful for neurological signals in general and EEG signals in particular and presents an auto-regressive (AR) modeling based spectral estimation procedure to overcome the problems of lower resolution and 'leakage' effects inherent in the FFT algorithm.

184 citations


Journal ArticleDOI
01 Oct 1998
TL;DR: Range-Doppler images of manoeuvring aircraft produced by conventional Fourier analysis are compared with those produced by time-varying spectral analysis, and a quantitative simulation illustrates the benefit of using the latter.
Abstract: Fourier transforms are the basis for conventional radar range-Doppler imaging. Target rotation during the coherent integration time results in a time-varying Doppler frequency shift that produces, after Fourier transform, a smeared Doppler spectrum and a blurred image. Sophisticated motion compensation algorithms must be applied to obtain focused images using Fourier techniques. However, image blurring can be mitigated without resorting to sophisticated focusing algorithms by using time-varying spectral analysis in place of the Fourier analysis for Doppler processing. Various methods of time-varying spectral analysis are described and compared. Range-Doppler images of manoeuvring aircraft produced by conventional Fourier analysis are then compared with those produced by time-varying spectral analysis. A quantitative simulation illustrates the benefit of using the latter.

120 citations


Journal ArticleDOI
TL;DR: It is shown by means of a higher order expansion technique that the one-dimensional (1-D) Capon estimator underestimates the true spectrum, whereas the 1-D APES method is unbiased; it is shown that the bias of the forward-backward Capon is half that of theforward-only Capon (to within a second-order approximation).
Abstract: The problem of complex spectral estimation is of great interest in many applications. This paper studies the general class of the forward-backward matched-filterbank (MAFI) spectral estimators including the widely used Capon as well as the more recently introduced amplitude and phase estimation of a sinusoid (APES) methods. In particular, we show by means of a higher order expansion technique that the one-dimensional (1-D) Capon estimator underestimates the true spectrum, whereas the 1-D APES method is unbiased; we also show that the bias of the forward-backward Capon is half that of the forward-only Capon (to within a second-order approximation). Furthermore. We show that these results can be extended to the two-dimensional (2-D) Capon and APES estimators. Numerical examples are also presented to demonstrate quantitatively the properties of and the relation between these MAFI estimators.

118 citations


Journal ArticleDOI
TL;DR: In this paper, the authors make use of a matched filter bank (MAFI) approach to derive spectral estimators for stationary signals with mixed spectra, and they show that the Capon spectral estimator as well as the more recently recently proposed CCA estimator can be computed using the same approach.

98 citations


Journal ArticleDOI
TL;DR: It is concluded that the AR modelling approach can produce tremor spectra that are superior to those from FFT-based methods for short data sequences and for providing information about the physiological mechanisms of tremor generation are not yet clear.

82 citations


Journal ArticleDOI
TL;DR: In this article, the Capon and APES estimators belong to the class of matched-filterbank spectral estimators and can be used to obtain complex spectral estimates that have more narrow spectral peaks and lower sidelobe levels than the fast Fourier transform (FFT) methods.
Abstract: Both the Capon and APES estimators can be shown to belong to the class of matched-filterbank spectral estimators and can be used to obtain complex spectral estimates that have more narrow spectral peaks and lower sidelobe levels than the fast Fourier transform (FFT) methods. It can also be shown that APES has better statistical performance than Capon. In this paper, we address the issue of how to efficiently implement Capon and APES for spectral estimation.

79 citations


Journal ArticleDOI
TL;DR: In this paper, a non-biased estimator of power spectral density (PSD) is introduced for data obtained from a zeroth order interpolated laser Doppler anemometer (LDA) data set.
Abstract: A non-biased estimator of power spectral density (PSD) is introduced for data obtained from a zeroth order interpolated laser Doppler anemometer (LDA) data set. The systematic error, sometimes referred to as the “particle-rate filter” effect, is removed using an FIR filter parameterized using the mean particle rate. Independent from this, a procedure for estimating the measurement system noise is introduced and applied to the estimated spectra. The spectral estimation is performed in the domain of the autocorrelation function and assumes no further process parameters. The new technique is illustrated using simulated and measured data, in the latter case with direct comparison to simultaneously acquired hot-wire data.

76 citations


Proceedings ArticleDOI
04 Oct 1998
TL;DR: It is found that such a signal can almost surely be reconstructed from its multi-coset samples provided that a universal pattern is used and the scheme can attain the Landau-Nyquist minimum density asymptotically.
Abstract: We address the problem of sampling of 2D signals with sparse multi-band spectral structure. We show that the signal can be sampled at a fraction of the its Nyquist density determined by the occupancy of the signal in its frequency domain, but without explicit knowledge of its spectral structure. We find that such a signal can almost surely be reconstructed from its multi-coset samples provided that a universal pattern is used. Also, the scheme can attain the Landau-Nyquist minimum density asymptotically. The spectrum blind feature of our reconstruction scheme has potential applications in Fourier imaging. We apply the sampling scheme on a test image to demonstrate its performance.

75 citations


Journal ArticleDOI
TL;DR: In this article, the authors used local polynomial techniques to fit Whittle's likelihood for spectral density estimation, and showed that the Whittle likelihood-based estimator has advantages over the least-squares based log-periodogram.
Abstract: This article uses local polynomial techniques to fit Whittle's likelihood for spectral density estimation. Asymptotic sampling properties of the proposed estimators are derived, and adaptation of the proposed estimator to the boundary effect is demonstrated. We show that the Whittle likelihood-based estimator has advantages over the least-squares based log-periodogram. The bandwidth for the Whittle likelihood-based method is chosen by a simple adjustment of a bandwidth selector proposed in Fan & Gijbels (1995). The effectiveness of the proposed procedure is demonstrated by a few simulated and real numerical examples. Our simulation results support the asymptotic theory that the likelihood based spectral density and log-spectral density estimators are the most appealing among their peers

Journal ArticleDOI
TL;DR: It is shown that multitapering, or using sine or Slepian tapers, produces much better results than using the periodogram and is attractive compared with other competing methods when the technique is applied to a geophysical estimation problem.
Abstract: In many branches of science, particularly astronomy and geophysics, power spectra of the form f/sup -/spl beta//, where /spl beta/ is a positive power-law exponent, are common. This form of spectrum is characterized by a sharp increase in the spectral density as the frequency f decreases toward zero. A power spectrum analysis method that has proven very powerful wherever the spectrum of interest is detailed and/or varies rapidly with a large dynamic range is the multitaper method. With multitaper spectral estimation, a set of orthogonal tapers are applied to the time series, and the resulting direct spectral estimators ("eigenspectra") are averaged, thus, reducing the variance. One class of processes with spectra of the power-law type are fractionally differenced Gaussian processes that are stationary and can model certain types of long-range persistence. Spectral decay f/sup -/spl beta// can be modeled for 0

Journal ArticleDOI
18 May 1998
TL;DR: This analysis is limited to the spectral analysis of stationary stochastic processes with unknown spectral density, and a single time series model will be chosen with a statistical criterion from three previously estimated and selected models: the best autoregressive (AR), the best moving average (MA) model, and the best combined ARMA model.
Abstract: This analysis is limited to the spectral analysis of stationary stochastic processes with unknown spectral density. The main spectral estimation methods are: parametric with time series models, or nonparametric with a windowed periodogram. A single time series model will be chosen with a statistical criterion from three previously estimated and selected models: the best autoregressive (AR) model, the best moving average (MA) model, and the best combined ARMA model. The accuracy of the spectrum, computed from this single selected time series model, is compared with the accuracy of some windowed periodogram estimates. The time series model generally gives a spectrum that is better than the best possible windowed periodogram. It is a fact that a single good time series model can be selected automatically for statistical data with unknown spectral density. It is fiction that objective choices between windowed periodograms can be made.

Journal ArticleDOI
TL;DR: The preliminary results obtained with the proposed time-variant methods, compared with the classical short-time Fourier analysis and the short- time auto-regressive (AR) analysis, are superior in terms of standard deviation of the attenuation coefficient estimate.
Abstract: In the field of biological tissue characterization, fundamental acoustic attenuation properties have been demonstrated to have diagnostic importance. Attenuation caused by scattering and absorption shifts the instantaneous spectrum to the lower frequencies. Due to the time-dependence of the spectrum, the attenuation phenomenon is a time-variant process. This downward shift may be evaluated either by the maximum energy frequency of the spectrum or by the center frequency. In order to improve, in strongly attenuating media, the results given by the short-time Fourier analysis and the short-time parametric analysis, we propose two approaches adapted to this time-variant process: an adaptive method and a time-varying method. Signals backscattered by an homogeneous medium of scatterers are modeled by a computer algorithm with attenuation values ranging from 1 to 5 dB/cm MHz and a 45 MHz transducer center frequency. Under these conditions, the preliminary results obtained with the proposed time-variant methods, compared with the classical short-time Fourier analysis and the short-time auto-regressive (AR) analysis, are superior in terms of standard deviation (SD) of the attenuation coefficient estimate. This study, based on nonstationary AR spectral estimation, promises encouraging perspectives for in vitro and in vivo applications both in weakly and highly attenuating media.

Proceedings ArticleDOI
12 May 1998
TL;DR: A full generalization is presented where both the autocorrelation function and power spectral density are defined in terms of a general basis set and a partial generalization where the density is the Fourier transform of the characteristic function but the characteristicfunction is defined in Terms of an arbitrary basis set.
Abstract: We generalize the Wiener-Khinchin theorem. A full generalization is presented where both the autocorrelation function and power spectral density are defined in terms of a general basis set. In addition, we present a partial generalization where the density is the Fourier transform of the autocorrelation function but the autocorrelation function is defined in terms of an arbitrary basis set. Both the deterministic and random cases are considered.

Journal ArticleDOI
TL;DR: In this article, the authors proposed a spectral algorithm for generating sets of random fields which are correlated with one another. But the algorithm is based on a discrete version of the Fourier-Stieltjes representation for multidimensional random fields.

Patent
17 Feb 1998
TL;DR: In this paper, a post-processing method for a speech decoder is proposed, which gives a decoded speech signal in the time domain in order to obtain high frequency resolution from a frequency spectrum having nonharmonic and noise deficiencies.
Abstract: A post-processing method for a speech decoder (1) which gives a decoded speech signal in the time domain in order to obtain high frequency resolution from a frequency spectrum having non-harmonic and noise deficiencies. The method comprises the following steps: a) transforming (21) the decoded time domain signal to a frequency domain signal by means of a high frequency resolution transform (FFT); b) analysing (5) the energy distribution of said frequency domain signal throughout its frequency area (4 kHz) to find the disturbing frequency components and to prioritize such frequency components which are situated in the higher part of the frequency spectrum; c) finding (6) the suppression degree for said disturbing frequency components based on said prioritizing; d) controlling a post-filtering (31) of said transform in dependence of said finding (6); and e) inverse transforming (4) the post-filtered transform in order to obtain a post-filtered decoded speech signal in the time domain.

Proceedings ArticleDOI
18 May 1998
TL;DR: The method, based on a spectral estimation of the differential secondary signal, has been implemented using a floating point Digital Signal Processor and a fourteen-bit Analog Interface Circuit to generate the primary signal and to process the primary and the secondary signals.
Abstract: This paper presents a new method for signal processing of Linear Variable Differential Transformer (LVDT) position sensors. The method, based on a spectral estimation of the differential secondary signal, has been implemented using a floating point Digital Signal Processor (DSP) and a fourteen-bit Analog Interface Circuit (AIC) to generate the primary signal and to process the primary and the secondary signals. The resulting accuracy improves if compared with the classic solution based on synchronous demodulation. Also, the lack of need of heavy filtering, except for the antialiasing function, can decrease the measuring time and offers diagnostic capability.

Journal ArticleDOI
01 Sep 1998
TL;DR: The Cramér-Rao bound for a general nonparametric spectral estimation problem is derived under a local smoothness condition and under the aforementioned condition the Thomson method (TM) and Daniell method (DM) for power spectral density (PSD) estimation can be interpreted as approximations of the maximum likelihood PSD estimator.
Abstract: In this paper the Cramer-Rao bound (CRB) for a general nonparametric spectral estimation problem is derived under a local smoothness condition (more exactly, the spectrum is assumed to be well approximated by a piecewise constant function). Furthermore it is shown that under the aforementioned condition the Thomson (TM) and Danieli (DM) methods for power spectral density (PSD) estimation can be interpreted as approximations of the maximum likelihood PSD estimator. Finally the statistical efficiency of the TM and DM as nonparametric PSD estimators is examined and also compared to the CRB for ARMA-based PSD estimation. In particular for broadband signals, the TM and DM almost achieve the derived nonparametric performance bound and can therefore be considered to be nearly optimal.

Journal ArticleDOI
TL;DR: A recursive algorithm to implement phase retrieval from two intensities in the fractional Fourier transform domain is proposed that can significantly simplify computational manipulations and does not need an initial phase estimate compared with conventional iterative algorithms.
Abstract: We first discuss the discrete fractional Fourier transform and present some essential properties. We then propose a recursive algorithm to implement phase retrieval from two intensities in the fractional Fourier transform domain. This approach can significantly simplify computational manipulations and does not need an initial phase estimate compared with conventional iterative algorithms. Simulation results show that this approach can successfully recover the phase from two intensities.

Journal ArticleDOI
TL;DR: A full generalization is presented where both the autocorrelation function and power spectral density are defined in terms of a general basis set and a partial generalization where the density is the Fourier transform of the characteristic function but the characteristicfunction is defined in Terms of an arbitrary basis set.
Abstract: We generalize the concept of the autocorrelation function and give the generalization of the Wiener-Khinchin theorem. A full generalization is presented where both the autocorrelation function and power spectral density are defined in terms of a general basis set. In addition, we present a partial generalization where the density is the Fourier transform of the characteristic function but the characteristic function is defined in terms of an arbitrary basis set. Both the deterministic and random cases are considered.

Proceedings ArticleDOI
06 Jul 1998
TL;DR: The authors explore an image reconstruction method proposed by Webb and Munson and applies ESPRIT and RELAX to simulated 3D data for a maximum of 2 and 4 elevations to compare the performance of the image reconstruction algorithms with the Cramer-Rao lower bound.
Abstract: The authors consider the problem of synthetic aperture radar (SAR) imaging of 3D targets, given a limited amount of measured data. They explore an image reconstruction method proposed by Webb and Munson. This approach employs interpolation and a series of 2D inverse FFTs to cast the 3D imaging problem into the form of a high-resolution spectral estimation problem. The series of 1D spectral estimation problems can be solved using a variety of methods. The authors apply two of those methods: ESPRIT and RELAX to simulated 3D data for a maximum of 2 and 4 elevations. They also compare the performance of the image reconstruction algorithms with the Cramer-Rao lower bound.

Journal ArticleDOI
TL;DR: The problem of estimating multiple time delays in presence of colored noise is considered, which is first converted to a high-resolution frequency estimation problem, and the sample lagged covariance matrices of the resulting signal are computed and studied in terms of their eigenstructure.
Abstract: The problem of estimating multiple time delays in presence of colored noise is considered. This problem is first converted to a high-resolution frequency estimation problem. Then, the sample lagged covariance matrices of the resulting signal are computed and studied in terms of their eigenstructure. These matrices are shown to be as effective in extracting bases for the signal and noise subspaces as the standard autocorrelation matrix, which is normally used in MUSIC and the pencil-based methods. Frequency estimators are then derived using these subspaces. The effectiveness of the method is demonstrated on two examples: a standard frequency estimation problem in presence of colored noise and a real-world problem that involves separation of multiple specular components from the acoustic backscattered from an underwater target.

Patent
13 Jul 1998
TL;DR: In this paper, the authors proposed a noise suppression apparatus consisting of a voice/non-voice discriminator for discriminating a frame signal divided into frames having a predetermined length, an amplitude spectrum subtractor for subtracting the product of an estimated noise spectrum and a predetermined coefficient from a spectrum obtained by the transform unit, and an auditory correction noise adder for adding aa audio correction noise spectrum to a spectrum outputted from the subtractor.
Abstract: A noise suppression apparatus of the present invention includes a voice/non-voice discriminator for discriminating a frame signal divided into frames having a predetermined length; a Fourier transform unit for converting a frame signal into a spectrum; a noise spectrum estimation unit for estimating a noise spectrum of a frame judged as a non-voice signal; an amplitude spectrum subtractor for subtracting the product of an estimated noise spectrum and a predetermined coefficient from a spectrum obtained by the transform unit; an auditory correction noise adder for adding aa auditory correction noise spectrum to a spectrum outputted from the subtractor; and an inverse Fourier transform unit for performing inverse Fourier transform to an output of the adder. The noise suppression apparatus further includes a negative amplitude value counter for counting the number of frequency components in an output of the subtractor whose amplitude values are negative; a subtraction coefficient setting unit for gradually decreasing a subtraction coefficient unit the counted value becomes not more than a predetermined value; an inverse Fourier transform unit for performing inverse Fourier transform to an output of the counter; and a noise spectrum estimation unit for calculating spectrum information of noise in the frame signal using different spectrum information according to the current type of frame signal.

Proceedings ArticleDOI
08 Sep 1998
TL;DR: An autocorrelation model of the slow fading process in a small urban macro cell is presented, obtained by a combination of parametric system identification and classical spectral estimation procedures, and is based on measured data.
Abstract: This paper presents an autocorrelation model of the slow fading process in a small urban macro cell. The model is obtained by a combination of parametric system identification and classical spectral estimation procedures, and is based on measured data. An analytic expression for the autocorrelation function of the resulting ARMA (2,1)-autoregressive moving average-model is given and compared to other results. The model predicts about the same overall decorrelation distance, but a faster correlation roll-off for small lags.

Journal ArticleDOI
TL;DR: The aim of this paper is to estimate the parameters that characterize the sources and identify those sources that are responsible for the observed noisy pulses and yields maximum likelihood parameter estimates of the sources.
Abstract: We consider the deinterleaving of pulse trains transmitted by N independent sources. The deinterleaving problem considered has applications in spectral estimation, where N (known number) stochastic parameterized sources are sampled using a fast sensor recording the sign of the signal from each source. Due to communication constraints, the recorded signals-pulse trains or sequences of zeros and ones-are superimposed and transmitted through a single Gaussian communication channel. The aim of this paper is to estimate the parameters that characterize the sources and identify those sources that are responsible for the observed noisy pulses. Our proposed algorithm, subject to modeling assumptions, optimally combines hidden Markov model and binary time series estimation techniques and yields maximum likelihood parameter estimates of the sources.

Journal ArticleDOI
18 May 1998
TL;DR: Based on the concept of transformed domain signal processing, a fast filter-bank structure is proposed to reduce the above computational complexity of adaptive Fourier analyzers.
Abstract: Adaptive Fourier analyzers have been developed for measuring periodic signals with unknown or changing fundamental frequency. Typical applications are vibration measurements and active noise control related to rotating machinery and calibration equipment that can avoid the changes of the line frequency by adaptation. Higher frequency applications have limitations since the computational complexity of these analyzers are relatively high as the number of the harmonic components to be measured (or suppressed) is usually above 50. In this paper, based on the concept of transformed domain signal processing, a fast filter-bank structure is proposed to reduce the above computational complexity. The first step of the suggested solution is the application of the filter-bank version of the fast Fourier transform or any other fast transformations that convert input data into the transformed domain. These fast transform structures operate as single-input multiple-output filter-banks, however, they can not be adapted since their efficiency is due to their special symmetry. As a second step, the adaptation of the filter-bank is performed at the transform structure's output by adapting a simple linear combiner to the fundamental frequency of the periodic signal to be processed.

Journal ArticleDOI
TL;DR: This study emphasizes the merit of thepolygonal hold versus the sample-and-hold (zero order) and shows that polygonal interpolation results in better accuracy, especially at high frequencies.
Abstract: The power spectral density of randomly sampled signals is studied with reference to fluid velocity measured by laser Doppler velocimetry. We propose a new method for spectral estimation of Poisson-sampled stochastic processes. Our approach is based on polygonal interpolation from the sampled process followed by resampling and the usual fast Fourier transform. This study emphasizes the merit of the polygonal hold versus the sample-and-hold (zero order) and shows that polygonal interpolation results in better accuracy, especially at high frequencies. For purposes of illustrations the sampled process is assumed to be either a Kolmogorov or a Von Karman process. Numerical simulations and experimental results are given and confirm our theoretical analysis.

Journal ArticleDOI
TL;DR: In this paper, various techniques that may be used to analyse electrochemical noise data, and explores the theoretical basis of the more important methods are examined. But, their application to electrochemical data analysis is not discussed.
Abstract: This paper examines the various techniques that may be used to analyse electrochemical noise data, and explores the theoretical basis of the more important methods. Methods considered include: ○ Time domain analysis methods - including the direct measurement of the properties of transients from the time record. ○ Statistical methods - including the measurement of the mean, standard deviation/variance, noise resistance, coefficient of variation, localisation parameter and other statistical parameters. ○ Frequency domain analysis methods - including spectral estimation using various methods, including MEM and FFT, the determination of noise impedance, the determination of bispectra and wavelet analysis. ○ Discriminant analysis - this is a general method for determining the ability of a particular measurement to discriminate between alternative behaviours, and its application to electrochemical noise analysis is indicated.

Journal ArticleDOI
01 Oct 1998
TL;DR: In this article, the authors describe the application of modern spectral analysis techniques to synthetic aperture radar data, which can improve the geometrical resolution of the image with respect to the numerical values related to the compressed coded waveform and the synthetic aperture, so that subsequent classification procedures will have improved performance.
Abstract: The authors describe the application of modern spectral analysis techniques to synthetic aperture radar data. The purpose is to improve the geometrical resolution of the image with respect to the numerical values related to the compressed coded waveform and the synthetic aperture, so that subsequent classification procedures will have improved performance as well. The classical spectral estimator, i.e. the FFT, produces an image with resolution in azimuth and range bounded by the Rayleigh limits. Super-resolved images are obtained by replacing the FFT with parametric spectral estimators such as those built around an autoregressive model of the dechirped signal. The proposed processing scheme is based on a two-dimensional covariance method. The expected improvement in resolution is discussed together with the results of a simulation analysis. The application of the technique to images captured by an airborne SAR resulted in a resolution gain factor of about two. The paper concludes with a perspective on future research and applications.