scispace - formally typeset
Search or ask a question

Showing papers on "Spectral density estimation published in 1995"


Journal ArticleDOI
N.J. Kasdin1
01 May 1995
TL;DR: A new digital model for power law noises is presented, which allows for very accurate and efficient computer generation of 1/f/sup /spl alpha// noises for any /splalpha// noises.
Abstract: This paper discusses techniques for generating digital sequences of noise which simulate processes with certain known properties or describing equations. Part I of the paper presents a review of stochastic processes and spectral estimation (with some new results) and a tutorial on simulating continuous noise processes with a known autospectral density or autocorrelation function. In defining these techniques for computer generating sequences, it also defines the necessary accuracy criteria. These methods are compared to some of the common techniques for noise generation and the problems, or advantages, of each are discussed. Finally, Part I presents results on simulating stochastic differential equations. A Runge-Kutta (RK) method is presented for numerically solving these equations. Part II of the paper discusses power law, or 1/f/sup /spl alpha//, noises. Such noise processes occur frequently in nature and, in many cases, with nonintegral values for /spl alpha/. A review of 1/f noises in devices and systems is followed by a discussion of the most common continuous 1/f noise models. The paper then presents a new digital model for power law noises. This model allows for very accurate and efficient computer generation of 1/f/sup /spl alpha// noises for any /spl alpha/. Many of the statistical properties of this model are discussed and compared to the previous continuous models. Lastly, a number of approximate techniques for generating power law noises are presented for rapid or real time simulation. >

466 citations



01 May 1995
TL;DR: In this article, a comprehensive comparison of 2D spectral estimation methods for SAR imaging is presented, and a theoretical analysis of the impact of the adaptive sidelobe reduction (ASR) algorithm on target to clutter ratio is provided.
Abstract: : This report discusses the use of modern 2-D spectral estimation algorithms for SAR imaging, and makes two principal contributions to the field of adaptive SAR imaging. First, it is a comprehensive comparison of 2-D 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. The discussion of autoregressive linear predictive techniques (ARLP), including the Tufts Kumaresan variant, is somewhat more general than appears in most of the literature, in that it allows the prediction element to be varied throughout the subaperture. This generality leads to a theoretical link between ARLP and one of Pisarenko's methods. The report also provides a theoretical analysis that predicts the impact of the adaptive sidelobe reduction (ASR) algorithm on target to clutter ratio and provides insight into order and constraint selection. Second, this work develops multi-channel variants of three related algorithms, minimum variance method (MVM), reduced rank MVM (RRMVM), and ASR to estimate both reflectivity intensity and interferometric height from polarimetric displaced-aperture interferometric data. Examples illustrate that MVM and ASR both offer significant advantages over Fourier methods for estimating both scattering intensity and interferometric height, and allow empirical comparison of the accuracies of Fourier, MVM, and- ometric height estimates.

226 citations


Journal ArticleDOI
TL;DR: In this paper, an intuitive method for the reduction in the bias of a nonparametric spectral estimator is presented, which results in bias-corrected estimators that are related to kernel estimators with trapezoidal shape.
Abstract: . The theory of nonparametric spectral density estimation based on an observed stretch X1,…, XN from a stationary time series has been studied extensively in recent years. However, the most popular spectral estimators, such as the ones proposed by Bartlett, Daniell, Parzen, Priestley and Tukey, are plagued by the problem of bias, which effectively prohibits ✓N-convergence of the estimator. This is true even in the case where the data are known to be m-dependent, in which case ✓N-consistent estimation is possible by a simple plug-in method. In this report, an intuitive method for the reduction in the bias of a nonparametric spectral estimator is presented. In fact, applying the proposed methodology to Bartlett's estimator results in bias-corrected estimators that are related to kernel estimators with lag-windows of trapezoidal shape. The asymptotic performance (bias, variance, rate of convergence) of the proposed estimators is investigated; in particular, it is found that the trapezoidal lag-window spectral estimator is ✓N-consistent in the case of moving-average processes, and ✓(N/log/N)-consistent in the case of autoregressive moving-average processes. The finite-sample performance of the trapezoidal lag-window estimator is also assessed by means of a numerical simulation.

160 citations


Journal ArticleDOI
TL;DR: In this paper, the same rules can be applied to create a new type of fractional-order Fourier transform which results in a smooth transition of a function when transformed between the real and Fourier spaces.

112 citations


Journal ArticleDOI
TL;DR: The asymptotic covariance matrix and bias of the estimators of dsω(t)/dts, s = 0,1,2,…, m − 1, are obtained for the frequency with bounded m-derivative and the estimator is shown to be strongly consistent and Gaussian for a polynomial frequency.

87 citations


Journal ArticleDOI
TL;DR: The ability of the optimal kernel to suppress interference is quite remarkable, thus making the proposed framework potentially useful for interference suppression via time-frequency filtering.
Abstract: Current theories of a time-varying spectrum of a nonstationary process all involve, either by definition or by difficulties in estimation, an assumption that the signal statistics vary slowly over time. This restrictive quasistationarity assumption limits the use of existing estimation techniques to a small class of nonstationary processes. We overcome this limitation by deriving a statistically optimal kernel, within Cohen's (1989) class of time-frequency representations (TFR's), for estimating the Wigner-Ville spectrum of a nonstationary process. We also solve the related problem of minimum mean-squared error estimation of an arbitrary bilinear TFR of a realization of a process from a correlated observation. Both optimal time-frequency invariant and time-frequency varying kernels are derived. It is shown that in the presence of any additive independent noise, optimal performance requires a nontrivial kernel and that optimal estimation may require smoothing filters that are very different from those based on a quasistationarity assumption. Examples confirm that the optimal estimators often yield tremendous improvements in performance over existing methods. In particular, the ability of the optimal kernel to suppress interference is quite remarkable, thus making the proposed framework potentially useful for interference suppression via time-frequency filtering. >

86 citations


Journal ArticleDOI
TL;DR: In this article, the authors show that the standard asymptotic results for periodograms do not apply and that using the periodogram of the raw data can yield highly misleading results.
Abstract: The periodogram for a spatial process observed on a lattice is often used to estimate the spectral density. The bases for such estimators are two asymptotic properties that periodograms commonly possess: (1) the periodogram at a particular frequency is approximately unbiased for the spectral density, and (2) the correlation of the periodogram at distinct frequencies is approximately zero. For spatial data, it is often appropriate to use fixed-domain asymptotics in which the observations get increasingly dense in some fixed region as their number increases. Using fixed-domain asymptotics, this article shows that standard asymptotic results for periodograms do not apply and that using the periodogram of the raw data can yield highly misleading results. But by appropriately filtering the data before computing the periodogram, it is possible to obtain results similar to the standard asymptotic results for spatial periodograms.

67 citations


ReportDOI
TL;DR: Den Haan et al. as discussed by the authors proposed a parametric spectral estimation procedure for constructing heteroskedasticity and autocorrelation consistent (HAC) covariance matrices, and established the consistency of this procedure under very general conditions similar to those considered in previous research.
Abstract: In this paper, we propose a parametric spectral estimation procedure for constructing heteroskedasticity and autocorrelation consistent (HAC) covariance matrices. We establish the consistency of this procedure under very general conditions similar to those considered in previous research, and we demonstrate that the parametric estimator converges at a faster rate than the kernel-based estimators proposed by Andrews and Monahan (1992) and Newey and West (1994). In finite samples, our Monte Carlo experiments indicate that the parametric estimator matches, and in some cases greatly exceeds, the performance of the prewhitened kernel estimator proposed by Andrews and Monahan (1992). These simulation experiments illustrate several important limitations of non-parametric HAC estimation procedures, and highlight the advantages of explicitly modeling the temporal properties of the error terms. Wouter J. den Haan Andrew Levin Depa

65 citations


Journal ArticleDOI
TL;DR: In this article, an effective bandwidth measure for multitaper spectral estimators, a relatively new and very powerful class of estimators proving to be very valuable whenever the spectrum of interest is detailed and/or varies rapidly with a large dynamic range.
Abstract: SUMMARY The bandwidth of a spectral estimator is a measure of the minimum separation in frequency between approximately uncorrelated spectral estimates. We determine an effective bandwidth measure for multitaper spectral estimators, a relatively new and very powerful class of spectral estimators proving to be very valuable whenever the spectrum of interest is detailed and/or varies rapidly with a large dynamic range. The multitaper spectral estimator is the average of several direct spectral estimators, each of which uses one of a set of orthogonal tapers. We show that the equivalent width of the autocorrelation of the overall spectral window is a suitable measure of the effective bandwidth of a multitaper spectral estimator and illustrate its use in the case of both Slepian and sinusoidal orthogonal tapers. This measure allows a unified treatment of bandwidth for the class of quadratic spectral estimators. Hence, for example, it is now possible properly to compare multitaper spectral estimators with traditional lag window spectral estimators, by assigning a fixed and equal effective bandwidth to both methods. An application is given to the spectral analysis of ocean wave data.

64 citations


Journal ArticleDOI
TL;DR: The fractional Fourier transform can also be helpful for lens design, especially for specifying a lens cascade, according to its role in wave propagation and signal processing.
Abstract: The fractional Fourier transform has been used in optics so far for wave propagation and for signal processing. Now we show that this new transform can also be helpful for lens design, especially for specifying a lens cascade.

Proceedings ArticleDOI
10 Sep 1995
TL;DR: An algorithm for automatic segmentation of the heart sound using an autoregressive (AR) model to estimate the power spectral density of the signal as well as the energy in certain frequency bands for consecutive overlapping frames is presented.
Abstract: The objective of this paper is to present an algorithm for automatic segmentation of the heart sound. The algorithm utilises an autoregressive (AR) model to estimate the power spectral density (PSD) of the signal as well as the energy in certain frequency bands for consecutive overlapping frames. The starting and end points of each event are then calculated by filtering the tracking level using a morphological transform and estimating the boundary of its dominant peaks. The algorithm was tested for 960 cycles of heart sound recorded front all four popular auscaltatory areas of 30 patients. Results indicate the capability of this algorithm to isolate desired events in subjects with various pathological conditions.

Journal ArticleDOI
TL;DR: A novel data-adaptive estimator for the evolutionary spectrum of non stationary signals that possesses desirable properties in terms of time-frequency resolution and positivity and is robust in the spectral estimation of noisy nonstationary data.
Abstract: We present a novel data-adaptive estimator for the evolutionary spectrum of nonstationary signals. We model the signal at a frequency of interest as a sinusoid with a time-varying amplitude, which is accurately represented by an orthonormal basis expansion. We then compute a minimum mean-squared error estimate of this amplitude and use it to estimate the time-varying spectrum at that frequency, all while minimizing the interference from the signal components at other frequencies. Repeating the process over all frequencies, we obtain a power distribution that is consistent with the Wold-Cramer evolutionary spectrum and reduces to Capon's (1969) method for the stationary case. Our estimator possesses desirable properties in terms of time-frequency resolution and positivity and is robust in the spectral estimation of noisy nonstationary data. We also propose a new estimator for the autocorrelation of nonstationary signals. This autocorrelation estimate is needed in the data-adaptive spectral estimation. We illustrate the performance of our estimator using simulation examples and compare it with the recently presented evolutionary periodogram and the bilinear time-frequency distribution with exponential kernels. >

Journal ArticleDOI
TL;DR: This work shows that the original bulk-optics configuration for performing the fractional-Fourier-transform operation provides a scaled output using a fixed lens and suggests an asymmetrical setup for obtaining a non-scaled output.
Abstract: Recently two optical interpretations of the fractional Fourier transform operator were introduced. We address implementation issues of the fractional-Fourier-transform operation. We show that the original bulk-optics configuration for performing the fractional-Fourier-transform operation [J. Opt. Soc. Am. A 10, 2181 (1993)] provides a scaled output using a fixed lens. For obtaining a non-scaled output, an asymmetrical setup is suggested and tested. For comparison, computer simulations were performed. A good agreement between computer simulations and experimental results was obtained.

Journal ArticleDOI
TL;DR: In this article, several autoregressive (AR) methods for spectral estimation were applied toward the task of estimating ultrasonic backscatter coefficients from small volumes of tissue, including Burg's algorithm, the Modified Covariance algorithm, and the Recursive Maximum Likelihood Estimation algorithm.
Abstract: Several autoregressive (AR) methods for spectral estimation were applied toward the task of estimating ultrasonic backscatter coefficients from small volumes of tissue. Data were acquired from a homogeneous tissue-mimicking phantom and from a normal human liver in vivo. AR methods performed better at short record lengths than the traditional DFT (discrete Fourier Transform) approach. The DFT method consistently underestimated backscatter coefficients at small gate lengths. Burg's algorithm, the Modified Covariance algorithm, and the Recursive Maximum Likelihood Estimation algorithm performed comparably. The Yule-Walker algorithm did not perform as well as these but offered a slight improvement over the DFT. Several order determination methods were tested. These included residual variance (RV), final prediction error (FPE), Akaike information criterion (AIC), and Minimum Description Length (MDL). The AIC and MDL produced misleading results at higher orders. The RV and FPE yielded better results. The autoregressive method offers promise for enhanced spatial resolution and accuracy in ultrasonic tissue characterization and nondestructive evaluation of materials. >

Journal ArticleDOI
TL;DR: A new method for on-line spectral estimation of nonstationary time series via autoregressive (AR) model construction is proposed and demonstrated by computer simulation study and applying to the actual data of electroencephalogram (EEG).
Abstract: A new method for on-line spectral estimation of nonstationary time series via autoregressive (AR) model construction is proposed. The method consists of on-line parameter estimation based on the recursive least squares ladder estimation algorithm with a forgetting factor and on-line order determination based on AIC with some modifications. The effectiveness of the proposed method is demonstrated by computer simulation study and applying to the actual data of electroencephalogram (EEG). >

Journal ArticleDOI
TL;DR: By analysing a windowing signal with Fourier transform, the leakage-induced phase error is investigated, and the phase error distribution is indicated, and a practical approach to correct leakage in a discrete frequency signal to obtain accurate phase information is presented.

Journal ArticleDOI
TL;DR: In this paper, the spectral density function of a stationary process is approximated by polynomial splines and the approximation is chosen to maximize the expected log-likelihood based on the asymptotic properties of the periodogram.
Abstract: . The logarithm of the spectral density function for a stationary process is approximated by polynomial splines. The approximation is chosen to maximize the expected log-likelihood based on the asymptotic properties of the periodogram. Estimates of this approximation are shown to possess the usual nonparametric rate of convergence when the number of knots suitably increases to infinity.

Journal Article
TL;DR: In this paper, a method of characterizing bread-crumb grain was developed, based on the Fourier transform analysis of images captured by a standard document scanner, which was achieved by estimating the spectral character of an average cell within a localized area.
Abstract: A method of characterizing bread-crumb grain was developed, based on the Fourier transform analysis of images captured by a standard document scanner. The characterization was achieved by estimating the spectral character of an average cell within a localized area, using a classic spectral estimation technique. Quantities characterizing the basic cell structure then were extracted from the spectral estimate and verified by experienced bakers. Crumb score parameters included composite cell fineness and elongation. Volume estimates were calculated, based on the area of the slices scanned and product length. Crust thickness and crust contrast (darkness) were also computed.

Journal ArticleDOI
TL;DR: The adaptive subband decomposition guarantees the benefits of estimation from a sub band decomposition without the inconveniences of the aliasing effects.

Proceedings ArticleDOI
09 May 1995
TL;DR: A generalized TKEF (GTKEF) is proposed to reduce the noise sensitivity and it turns out that the generalization can be used to enhance the sum frequency tone as well, which enables the GTKEF to apply to resolve of two closely-spaced tones.
Abstract: Based on physical considerations, Kaiser (1990) proposed a new energy function for discrete time signals, known as the Teager-Kaiser energy function (TKEF). An interesting property of the TKEF is that if the input signal consists of two closely-spaced tones (amplitude modulated signal), the TKEF produces the difference frequency tone (envelope signal). However, a drawback is that the TKEF is highly sensitive to additive noise. We propose a generalized TKEF (GTKEF) to reduce the noise sensitivity. Fortunately, it turns out that the generalization can be used to enhance the sum frequency tone as well. This enables us to apply the GTKEF to resolve of two closely-spaced tones. The result can be viewed as an interesting nonlinear preprocessing scheme that can be used to transform a signal consisting of two closeby frequencies at f/sub 1/ and f/sub 2/ into a signal consisting of frequencies at (f/sub 1/-f/sub 2/) and (f/sub 1/+f/sub 2/). Clearly, it is much easier to resolve the latter frequencies, whichever spectral analysis method is used.

Journal ArticleDOI
TL;DR: The technique of Fourier synthesis holography to image through scattering materials is analyzed in detail and post-data-acquisition processing such as selection of the gating time delay and autocorrelation shaping are demonstrated.
Abstract: The technique of Fourier synthesis holography to image through scattering materials is analyzed in detail. A broad spectral source is decomposed into its Fourier components, and a hologram is formed at each wavelength and stored in the computer. Upon synthesis in the computer, a clear image can be formed of the obscured object. Post-data-acquisition processing such as selection of the gating time delay and autocorrelation shaping are also demonstrated.

Proceedings ArticleDOI
09 May 1995
TL;DR: A method is presented for classifying multi-level PSK signals in the presence of additive white Gaussian noise (AGWN) based on the Discrete Fourier Transform of a phase histogram, which performs well at low SNR.
Abstract: A method is presented for classifying multi-level PSK signals in the presence of additive white Gaussian noise (AGWN). The technique is based on the Discrete Fourier Transform (DFT) of a phase histogram. The probability of correct classification is given and it is found that the technique performs well at low SNR. The benefits of this technique are that it is simple to implement and requires no prior knowledge of the SNR of the signal for the classification.

Proceedings ArticleDOI
23 Oct 1995
TL;DR: It is shown that spatially-variant apodization is a special version of the minimum variance spectral estimator (MVSE), and that it has limitations for reconstructing real-valued extended targets.
Abstract: Sidelobe artifact is a common problem in image reconstruction from finite-extent Fourier data. Conventional shift-invariant windows applied to the Fourier data, reduce sidelobe artifacts at the expense of worsened mainlobe resolution. Stankwitz et al. (1995) have suggested spatially-variant apodization (SVA) as a means of reducing the sidelobe artifacts, while preserving the mainlobe resolution. SVA adaptively selects windows from a set of raised-cosine weighting functions. The algorithm is heuristically motivated, and is known to be effective in synthetic aperture radar (SAR) imaging. However, this technique has received only limited analysis. In this paper, we formulate SVA as a spectral estimator, and show that SVA is a special version of the minimum variance spectral estimator (MVSE). We study the properties of SVA that are inherited from MVSE. Then, we consider the application of SVA to spectral estimation and Fourier reconstruction. Although SVA is effective in SAR, we show that it has limitations for reconstructing real-valued extended targets.

Journal ArticleDOI
TL;DR: In this article, the minimum variance of the frequency estimation is derived in terms of the noise spectral density at frequencies close to that of the signal, and the extent to which several practical methods of frequency measurement can reach this limit is analyzed.
Abstract: Consideration is given to frequency estimates for continuous data trains of a fixed length amounting to at least five oscillations of a sinusoidal signal of constant frequency accompanied by low-level noise. The minimum variance of the frequency estimation is derived in terms of the noise spectral density at frequencies close to that of the signal. The extent to which several practical methods of frequency measurement can reach this limit is analysed. The case in which the frequency of the signal source may vary slightly within each data train is also included.

Proceedings ArticleDOI
05 Jun 1995
TL;DR: In this paper, an adaptive FIR filtering approach, referred to as the APES (amplitude and phase estimation of a sinusoid), was proposed for complex spectral estimation.
Abstract: We present an adaptive FIR filtering approach, which is referred to as the APES (amplitude and phase estimation of a sinusoid), for complex spectral estimation. We compare the APES algorithm with other FIR filtering approaches including the Welch and Capon methods. We also describe how to apply the FIR filtering approaches to target range signature estimation and synthetic aperture radar (SAR) imaging. We show via both numerical and experimental examples that the adaptive FIR filtering approaches such as Capon and APES can yield more accurate spectral estimates with much lower sidelobes and narrower spectral peaks than the FFT method, which is also a special case of the FIR filtering approaches. We show that although the APES algorithnm yields somewhat wider spectral peaks than the Capon method, the former gives more accurate overall spectral estimates and SAR images that the latter and the FFT method.

Proceedings ArticleDOI
09 May 1995
TL;DR: A new algorithm, the NP algorithm, for detecting speech signals of varying quality and gain levels, which operates in the frequency domain and renders speech/no-speech decisions based on a signal-to-noise ratio derived from a sorted power spectrum.
Abstract: This paper describes a new algorithm, the NP algorithm, for detecting speech signals of varying quality and gain levels. NP operates in the frequency domain and renders speech/no-speech decisions based on a signal-to-noise ratio (SNR) derived from a sorted power spectrum. In addition to the SNR estimates, a spectral whitening process and an estimate of the variance in the ratio of the signal power to total energy are also used to identify and reject signals that are stationary or nearly stationary The key features of this algorithm are: the detection is based on a single FFT; decisions are independent of the signal gain; the process has 3 dB/octave processing gain from the transform; and frequency domain processing permits the exploitation of the signal structure.


Proceedings ArticleDOI
01 Dec 1995
TL;DR: This paper reviews statistical methods for analyzing output data from computer simulations of single systems and focuses on the problems of choosing initial conditions and estimating steady-state system parameters.
Abstract: This paper reviews statistical methods for analyzing output data from computer simulations of single systems. In particular, it focuses on the problems of choosing initial conditions and estimating steady-state system parameters. The estimation techniques include the replication/deletion approach, the regenerative method, the batch means method, the standardized time series method, the autoregressive method, and the spectral estimation method.

Journal ArticleDOI
TL;DR: This paper develops a new method for spectral estimation of Poisson-sampled stochastic processes based on exponential interpolation from the sampled process followed by resampling and usual discrete Fourier transform, and proves that this method is asymptotically unbiased.