Showing papers on "Spectral density estimation published in 2006"

On spectral linear stochastic estimation

Abstract: An extension to classical stochastic estimation techniques is presented, following the formulations of Ewing and Citriniti (1999), whereby spectral based estimation coefficients are derived from the cross spectral relationship between unconditional and conditional events. This is essential where accurate modeling using conditional estimation techniques are considered. The necessity for this approach stems from instances where the conditional estimates are generated from unconditional sources that do not share the same grid subset, or possess different spectral behaviors than the conditional events. In order to filter out incoherent noise from coherent sources, the coherence spectra is employed, and the spectral estimation coefficients are only determined when a threshold value is achieved. A demonstration of the technique is performed using surveys of the dynamic pressure field surrounding a Mach 0.30 and 0.60 axisymmetric jet as the unconditional events, to estimate a combination of turbulent velocity and turbulent pressure signatures as the conditional events. The estimation of the turbulent velocity shows the persistence of compact counter-rotating eddies that grow with quasi-periodic spacing as they convect downstream. These events eventually extend radially past the jet axis where the potential core is known to collapse.

Adaptive filtering primer with MATLAB

Abstract: INTRODUCTION Signal Processing An Example Outline of the Text DISCRETE-TIME SIGNAL PROCESSING Discrete Time Signals Transform-Domain Representation of Discrete-Time Signals The Z-Transform Discrete-Time Systems Problems Hints-Solutions-Suggestions RANDOM VARIABLES, SEQUENCES, AND STOCHASTIC PROCESSES Random Signals and Distributions Averages Stationary Processes Special Random Signals and Probability Density Functions Wiener-Khinchin Relations Filtering Random Processes Special Types of Random Processes Nonparametric Spectra Estimation Parametric Methods of power Spectral Estimation Problems Hints-Solutions-Suggestions WIENER FILTERS The Mean-Square Error The FIR Wiener Filter The Wiener Solution Wiener Filtering Examples Problems Hints-Solutions-Suggestions EIGENVALUES OF RX - PROPERTIES OF THE ERROR SURFACE The Eigenvalues of the Correlation Matrix Geometrical Properties of the Error Surface Problems Hints-Solutions-Suggestions NEWTON AND STEEPEST-DESCENT METHOD One-Dimensional Gradient Search Method Steepest-Descent Algorithm Problems Hints-Solutions-Suggestions THE LEAST MEAN-SQUARE (LMS) ALGORITHM Introduction Derivation of the LMS Algorithm Examples Using the LMS Algorithm Equation Performance Analysis of the LMS Algorithm Equation Learning Curve Complex Representation of LMS Algorithm Problems Hints-Solutions-Suggestions VARIATIONS OF LMS ALGORITHMS The Sign Algorithms Normalized LMS (NLMS) Algorithm Variable Step-Size LMS (VSLMS) Algorithm The Leaky LMS Algorithm Linearly Constrained LMS Algorithm Self-Correcting Adaptive Filtering (SCAF) Transform Domain Adaptive LMS Filtering Error Normalized LMS Algorithms Problems Hints-Solutions-Suggestions LEAST SQUARES AND RECURSIVE LEAST-SQUARES SIGNAL PROCESSING Introduction to Least Squares Least-Square Formulation Least-Squares Approach Orthogonality Principle Projection Operator Least-Squares Finite Impulse Response Filter Introduction to RLS Algorithm Problems Hints-Solutions-Suggestions ABBREVIATIONS BIBLIOGRAPHY APPENDIX A: MATRIX ANALYSIS INDEX

Detection and estimation theory and its applications

Abstract: Part I Review Chapters Chapter 1 Review of Probability 1.1 Chapter Highlights 1.2 Definition of Probability 1.3 Conditional Probability 1.4 Bayes' Theorem 1.5 Independent Events 1.6 Random Variables 1.7 Conditional Distributions and Densities 1.8 Functions of One Random Variable 1.9 Moments of a Random Variable 1.10 Distributions with Two Random Variables 1.11 Multiple Random Variables 1.12 Mean-Square Error (MSE) Estimation 1.13 Bibliographical Notes 1.14 Problems Chapter 2 Stochastic Processes 2.1 Chapter Highlights 2.2 Stationary Processes 2.3 Cyclostationary Processes 2.4 Averages and Ergodicity 2.5 Autocorrelation Function 2.6 Power Spectral Density 2.7 Discrete-Time Stochastic Processes 2.8 Spatial Stochastic Processes 2.9 Random Signals 2.10 Bibliographical Notes 2.11 Problems Chapter 3 Signal Representations and Statistics 3.1 Chapter Highlights 3.2 Relationship of Power Spectral Density and Autocorrelation Function 3.3 Sampling Theorem 3.4 Linear Time-Invariant and Linear Shift-Invariant Systems 3.5 Bandpass Signal Representations 3.6 Bibliographical Notes 3.7 Problems Part II Detection Chapters Chapter 4 Single Sample Detection of Binary Hypotheses 4.1 Chapter Highlights 4.2 Hypothesis Testing and the MAP Criterion 4.3 Bayes Criterion 4.4 Minimax Criterion 4.5 Neyman-Pearson Criterion 4.6 Summary of Detection-Criterion Results Used in Chapter 4 Examples 4.7 Sequential Detection 4.8 Bibliographical Notes 4.9 Problems Chapter 5 Multiple Sample Detection of Binary Hypotheses 5.1 Chapter Highlights 5.2 Examples of Multiple Measurements 5.3 Bayes Criterion 5.4 Other Criteria 5.5 The Optimum Digital Detector in Additive Gaussian Noise 5.6 Filtering Alternatives 5.7 Continuous Signals-White Gaussian Noise 5.8 Continuous Signals-Colored Gaussian Noise 5.9 Performance of Binary Receivers in AWGN 5.10 Further Receiver-Structure Considerations 5.11 Sequential Detection and Performance 5.12 Bibliographical Notes 5.13 Problems Chapter 6 Detection of Signals with Random Parameters 6.1 Chapter Highlights 6.2 Composite Hypothesis Testing 6.3 Unknown Phase 6.4 Unknown Amplitude 6.5 Unknown Frequency 6.6 Unknown Time of Arrival 6.7 Bibliographical Notes 6.8 Problems Chapter 7 Multiple Pulse Detection with Random Parameters 7.1 Chapter Highlights 7.2 Unknown Phase 7.3 Unknown Phase and Amplitude 7.4 Diversity Approaches and Performances 7.5 Unknown Phase, Amplitude, and Frequency 7.6 Bibliographical Notes 7.7 Problems Chapter 8 Detection of Multiple Hypotheses 8.1 Chapter Highlights 8.2 Bayes Criterion 8.3 MAP Criterion 8.4 M-ary Detection Using Other Criteria 8.5 M-ary Decisions with Erasure 8.6 Signal-Space Representations 8.7 Performance of M-ary Detection Systems 8.8 Sequential Detection of Multiple Hypotheses 8.9 Bibliographical Notes 8.10 Problems Chapter 9 Nonparametric Detection 9.1 Chapter Highlights 9.2 Sign Tests 9.3 Wilcoxon Tests 9.4 Other Nonparametric Tests 9.5 Bibliographical Notes 9.6 Problems Part III Estimation Chapters Chapter 10 Fundamentals of Estimation Theory 10.1 Chapter Highlights 10.2 Formulation of the General Parameter Estimation Problem 10.3 Relationship between Detection and Estimation Theory 10.4 Types of Estimation Problems 10.5 Properties of Estimators 10.6 Bayes Estimation 10.7 Minimax Estimation 10.8 Maximum-Likelihood Estimation 10.9 Comparison of Estimators of Parameters 10.10 Bibliographical Notes 10.11 Problems Chapter 11 Estimation of Specific Parameters 11.1 Chapter Highlights 11.2 Parameter Estimation in White Gaussian Noise 11.3 Parameter Estimation in Nonwhite Gaussian Noise 11.4 Amplitude Estimation in the Coherent Case with WGN 11.5 Amplitude Estimation in the Noncoherent Case with WGN 11.6 Phase Estimation in WGN 11.7 Time-Delay Estimation in WGN 11.8 Frequency Estimation in WGN 11.9 Simultaneous Parameter Estimation in WGN 11.10 Whittle Approximation 11.11 Bibliographical Notes 11.12 Problems Chapter 12 Estimation of Multiple Parameters 12.1 Chapter Highlights 12.2 ML Estimation for a Discrete Linear Observation Model 12.3 MAP Estimation for a Discrete Linear Observation Model 12.4 Sequential Parameter Estimation 12.5 Bibliographical References 12.6 Problems Chapter 13 Distribution-Free Estimation-Wiener Filters 13.1 Chapter Highlights 13.2 Orthogonality Principle 13.3 Autoregressive Techniques 13.4 Discrete Wiener Filter 13.5 Continuous Wiener Filter 13.6 Generalization of Discrete and Continuous Filter Representations 13.7 Bibliographical Notes 13.8 Problems Chapter 14 Distribution-Free Estimation-Kalman Filter 14.1 Chapter Highlights 14.2 Linear Least-Squares Methods 14.3 Minimum-Variance Weighted Least-Squares Methods 14.4 Minimum-Variance Least-Squares or Kalman Algorithm 14.5 Kalman Algorithm Computational Considerations 14.6 Kalman Algorithm for Signal Estimation 14.7 Continuous Kalman Filter 14.8 Extended Kalman Filter 14.9 Comments and Extensions 14.10 Bibliographical Notes 14.11 Problems Part IV Application Chapters Chapter 15 Detection and Estimation in Non-Gaussian Noise Systems 15.1 Chapter Highlights 15.2 Characterization of Impulsive Noise 15.3 Detector Structures in Non-Gaussian Noise 15.4 Selected Examples of Noise Models, Receiver Structures, and Error-Rate Performance 15.5 Estimation of Non-Gaussian Noise Parameters 15.6 Bibliographical Notes 15.7 Problems Chapter 16 Direct-Sequence Spread-Spectrum Signals in Fading Multipath Channels 16.1 Chapter Highlights 16.2 Introduction to Direct-Sequence Spread Spectrum Communications 16.3 Fading Multipath Channel Models 16.4 Receiver Structures with Known Channel Parameters 16.5 Receiver Structures without Knowledge of Phase 16.6 Receiver Structures without Knowledge of Amplitude or Phase 16.7 Receiver Structures and Performance with No Channel Knowledge 16.8 Bibliographical Notes 16.9 Problems Chapter 17 Multiuser Detection 17.1 Chapter Highlights 17.2 Introduction 17.3 Synchronous Multiuser Direct-Sequence CDMA 17.4 Asynchronous Multiuser Direct-Sequence CDMA 17.5 Speculative Summary 17.6 Bibliographical Notes 17.7 Problems Chapter 18 Low-Probability-of-Intercept Communications 18.1 Chapter Highlights 18.2 LPI System Model 18.3 Interceptor Detector Structures 18.4 Filter-Bank Combiners 18.5 Feature Detectors 18.6 Bibliographical Notes 18.7 Problems Chapter 19 Spectrum Estimation 19.1 Chapter Highlights 19.2 Overview of Power Spectral Estimation 19.3 Periodogram Techniques 19.4 Parametric Spectral Estimation Techniques 19.5 Examples of Spectral Estimation from MATLAB 19.6 Bibliographical Notes 19.7 Problems Appendix A Properties of Distribution and Density Functions Appendix B Common pdfs, cdfs, and Characteristic Functions B.1 One Point B.2 Zero-One B.3 Binomial B.4 Poisson B.5 Uniform B.6 Exponential B.7 Gaussian-Based Distributions B.8 Compilation of Mean, Variance, and Characteristic Function Appendix C Multiple Normal Random Variables C.1 Zero-Mean Jointly Normal Real Random Variables C.2 Nonzero-Mean Jointly Normal Real Random Variables C.3 Linear Transformation of Zero-Mean Jointly Normal Real Random Variables C.4 Central Limit Theorem 609 C.5 Nonzero Mean Jointly Normal Complex Random Variables Appendix D Properties of Autocorrelation and Power Spectral Density Functions D.1 Autocorrelation Functions-Continuous Processes D.2 Power Spectral Density Functions-Continuous Process D.3 Properties of Discrete Processes Appendix E Equivalence of LTI and LSI Bandlimited Systems Appendix F Theory of Random Sums Appendix G Evaluations Useful for Chapters 6, 7, and 16 Appendix H Gram-Charlier Type Series Appendix I Mobile User Detection I.1 Overview of Commercial Cellular Networks I.2 CDMA I.3 Bibliographical Notes Bibliography Glossary List of Symbols Index

Random sampling of evolution time space and Fourier transform processing.

Abstract: Application of Fourier Transform for processing 3D NMR spectra with random sampling of evolution time space is presented. The 2D FT is calculated for pairs of frequencies, instead of conventional sequence of one-dimensional transforms. Signal to noise ratios and linewidths for different random distributions were investigated by simulations and experiments. The experimental examples include 3D HNCA, HNCACB and (15)N-edited NOESY-HSQC spectra of (13)C (15)N labeled ubiquitin sample. Obtained results revealed general applicability of proposed method and the significant improvement of resolution in comparison with conventional spectra recorded in the same time.

An evaluation of autoregressive spectral estimation model order for brain-computer interface applications

Abstract: Autoregressive (AR) spectral estimation is a popular method for modeling the electroencephalogram (EEG), and therefore the frequency domain EEG phenomena that are used for control of a brain-computer interface (BCI). Several studies have been conducted to evaluate the optimal AR model order for EEG, but the criteria used in these studies does not necessarily equate to the optimal AR model order for sensorimotor rhythm (SMR)-based BCI control applications. The present study confirms this by evaluating the EEG spectra of data obtained during control of SMR-BCI using different AR model orders and model evaluation criteria. The results indicate that the AR model order that optimizes SMR-BCI control performance is generally higher than the model orders that are frequently used in SMR-BCI studies.

Spectral Density Estimation and Robust Hypothesis Testing Using Steep Origin Kernels Without Truncation

Abstract: Author(s): Phillips, Peter C.B.; Sun, Yixiao; Jin, Sainan | Abstract: In this paper, we construct a new class of kernel by exponentiating conventional kernels and use them in the long run variance estimation with and without smoothing. Depending on whether the exponent is allowed to grow with the sample size, we establish different asymptotic approximations to the sampling distribution of the proposed estimator. When the exponent is passed to infinity with the sample size, the new estimator is consistent and shown to be asymptotically normal. When the exponent is fixed, the new estimator is inconsistent and has a nonstandard limiting distribution. It is shown via Monte Carlo experiments that, when the chosen exponent is small in practical applications, the nonstandard limit theory provides better approximations to the finite sampling distributions of the spectral density estimator and the associated test statistic in regression settings.

Spectral Analysis of Signals:The Missing Data Case

Abstract: Spectral estimation is important in many fields including astronomy, meteorology, seismology, communications, economics, speech analysis, medical imaging, radar, sonar, and underwater acoustics. Most existing spectral estimation algorithms are devised for uniformly sampled complete-data sequences. However, the spectral estimation for data sequences with missing samples is also important in many applications ranging from astronomical time series analysis to synthetic aperture radar imaging with angular diversity. For spectral estimation in the missing-data case, the challenge is how to extend the existing spectral estimation techniques to deal with these missing-data samples. Recently, nonparametric adaptive filtering based techniques have been developed successfully for various missing-data problems. Collectively, these algorithms provide a comprehensive toolset for the missing-data problem based exclusively on the nonparametric adaptive filter-bank approaches, which are robust and ac urate, and can provide high resolution and low sidelobes. In this book, we present these algorithms for both one-dimensional and two-dimensional spectral estimation problems.

Comparison of AR and Welch Methods in Epileptic Seizure Detection

Abstract: Brain is one of the most critical organs of the body. Synchronous neuronal discharges generate rhythmic potential fluctuations, which can be recorded from the scalp through electroencephalography. The electroencephalogram (EEG) can be roughly defined as the mean electrical activity measured at different sites of the head. EEG patterns correlated with normal functions and diseases of the central nervous system. In this study, EEG signals were analyzed by using autoregressive (parametric) and Welch (non-parametric) spectral estimation methods. The parameters of autoregressive (AR) method were estimated by using Yule---Walker, covariance and modified covariance methods. EEG spectra were then used to compare the applied estimation methods in terms of their frequency resolution and the effects in determination of spectral components. The variations in the shape of the EEG power spectra were examined in order to epileptic seizures detection. Performance of the proposed methods was evaluated by means of power spectral densities (PSDs). Graphical results comparing the performance of the proposed methods with that of Welch technique were given. The results demonstrate consistently superior performance of the covariance methods over Yule---Walker AR and Welch methods.

Introduction to Applied Statistical Signal Analysis: Guide to Biomedical and Electrical Engineering Applications

Abstract: Introduction to Terminology Empirical Modeling and Approximation Fourier Analysis Probability Concepts and Signal Characteristics Random Processes and Signal Correlation Random Signals, Linear Systems, and Power Spectra Spectral Analysis for Random Signals Random Signal Modeling and Modern Spectral Estimation Theory and Application of Cross Correlation and Coherence

Estimation of the Coherence Function with the MVDR Approach

Abstract: The minimum variance distortionless response (MVDR), originally developed by Capon for frequency-wavenumber analysis, is a very well established method in array processing. It is also used in spectral estimation. The aim of this paper is to show how the MVDR method can be used to estimate the magnitude squared coherence (MSC) function, which is very useful in so many applications but so few methods exist to estimate it. Simulations show that our algorithm gives much more reliable results than the one based on the popular Welch's method.

Spectral-domain covariance estimation with a priori knowledge

Abstract: A knowledge-aided spectral-domain approach to estimating the interference covariance matrix used in space-time adaptive processing (STAP) is proposed. Prior knowledge of the range-Doppler clutter scene is used to identify geographic regions with homogeneous scattering statistics. Then, minimum-variance spectral estimation is used to arrive at a spectral-domain clutter estimate. Finally, space-time steering vectors are used to transform the spectral-domain estimate into a data-domain estimate of the clutter covariance matrix. The proposed technique is compared with ideal performance and to the fast maximum likelihood technique using simulated results. An investigation of the performance degradation that can occur due to various inaccurate knowledge assumptions is also presented

Processing of ND NMR spectra sampled in polar coordinates: a simple Fourier transform instead of a reconstruction.

Abstract: In order to reduce the acquisition time of multidimensional NMR spectra of biological macromolecules, projected spectra (or in other words, spectra sampled in polar coordinates) can be used. Their standard processing involves a regular FFT of the projections followed by a reconstruction, i.e. a non-linear process. In this communication, we show that a 2D discrete Fourier transform can be implemented in polar coordinates to obtain directly a frequency domain spectrum. Aliasing due to local violations of the Nyquist sampling theorem gives rise to base line ridges but the peak line-shapes are not distorted as in most reconstruction methods. The sampling scheme is not linear and the data points in the time domain should thus be weighted accordingly in the polar FT; however, artifacts can be reduced by additional data weighting of the undersampled regions. This processing does not require any parameter tuning and is straightforward to use. The algorithm written for polar sampling can be adapted to any sampling scheme and will permit to investigate better compromises in terms of experimental time and lack of artifacts.

Regularization operators for natural images based on nonlinear perception models

Abstract: Image restoration requires some a priori knowledge of the solution. Some of the conventional regularization techniques are based on the estimation of the power spectrum density. Simple statistical models for spectral estimation just take into account second-order relations between the pixels of the image. However, natural images exhibit additional features, such as particular relationships between local Fourier or wavelet transform coefficients. Biological visual systems have evolved to capture these relations. We propose the use of this biological behavior to build regularization operators as an alternative to simple statistical models. The results suggest that if the penalty operator takes these additional features in natural images into account, it will be more robust and the choice of the regularization parameter is less critical.

Spectral analysis of a signal driven sampling scheme

Abstract: This work is a part of a drastic revolution in the classical signal processing chain required in mobile systems. The system must be low power as it is powered by a battery. Thus a signal driven sampling scheme based on level crossing is adopted, delivering non-uniformly spaced out in time sampled points. In order to analyse the non-uniformly sampled signal obtained at the output of this sampling scheme a new spectral analysis technique is devised. The idea is to combine the features of both uniform and non-uniform signal processing chains in order to obtain a good spectrum quality with low computational complexity. The comparison of the proposed technique with General Discrete Fourier transform and Lomb's algorithm shows significant improvements in terms of spectrum quality and computational complexity.

Power measurement in digital wireless communication systems through parametric spectral estimation

Abstract: Power measurement in digital wireless communication systems often suffers from poor repeatability, usually accompanied by a low accuracy. To face the problem, the use of parametric spectral estimators is investigated in this paper. In particular, a new method is proposed, which first estimates the power spectral density (PSD) of the analyzed signal through Burg's solution, and then evaluates the power by applying straightforward measurement algorithms to the estimated PSD. The results of a number of experiments, carried out on both laboratory and actual signals peculiar to digital wireless communication systems, assess the efficacy and reliability of the method. Moreover, a comparison of the achieved performance to that offered by an alternative measurement solution, already proposed by the authors and based on nonparametric PSD estimation, shows that the method allows for a significant reduction of measurement time, while exhibiting the same repeatability.

Towards an Inverse Constant Q Transform

Abstract: The Constant Q transform has found use in the analysis of musical signals due to its logarithmic frequency resolution. Unfortunately, a considerable drawback of the Constant Q transform is that there is no inverse transform. Here we show it is possible to obtain a good quality approximate inverse to the Constant Q transform provided that the signal to be inverted has a sparse representation in the Discrete Fourier Transform domain. This inverse is obtained through the use of `0 and `1 minimisation approaches to project the signal from the constant Q domain back to the Discrete Fourier Transform domain. Once the signal has been projected back to the Discrete Fourier Transform domain, the signal can be recovered by performing an inverse Discrete Fourier Transform. 1. THE CONSTANT Q TRANSFORM The Constant Q transform (CQT) was derived by Brown as a means of creating a log-frequency resolution spectrogram [1]. This has considerable advantages for the analysis of musical signals, as the frequency resolution can be set to match that of the equal tempered scale used in western music, where the frequencies are geometrically spaced, as opposed to the linear spacing that occurs in the discrete Fourier transform (DFT). The frequency components of the CQT have a constant ratio of center frequency to resolution, as opposed to the constant frequency difference and constant resolution of the DFT. This constant ratio results in a constant pattern for the spectral components making up notes played on a given instrument, and this has been used to attempt sound source separation of pitched instruments from both single channel and multi-channel mixtures of instruments[2],[3]. Given an inital minimum frequency f0 for the CQT, the center frequencies for each band can be obtained from: fk = f02 k b (k = 0, 1, ...) (1) where b is the number of bins per octave. The fixed ratio of center frequency to bandwidth is then given by Q = ( 2 1 b − 1 )−1 (2) The desired bandwidth of each frequency band is FitzGerald et al. Towards an ICQT then obtained by choosing a window of length

The OFDM System Based on the Fractional Fourier Transform

Abstract: Transmission over wireless channels can lead to intersymbol interference (ISI) as well as interchannel (or intercarrier) interference (ICI). To decrease the results of ICI, this paper proposes an OFDM system based on the fractional Fourier transform (FrFT) in which traditional Fourier transform is replaced by fractional Fourier transform to modulate and demodulate the symbols. The multiplicative filter in fractional Fourier domain has been designed to equalize the received signal. Theoretical analysis and numerical simulation results show that the proposed equalizer in optimal fractional Fourier domain can significantly improve the performance of the system as compared to the Fourier domain equalizer.

Iterative image reconstruction using prior knowledge.

Abstract: A method is proposed to reconstruct signals from incomplete data. The method, which can be interpreted both as a discrete implementation of the so-called prior discrete Fourier transform (PDFT) spectral estimation technique and as a variant of the algebraic reconstruction technique, allows one to incorporate prior information about the reconstructed signal to improve the resolution of the signal estimated. The context of diffraction tomography and image reconstruction from samples of the far-field scattering amplitude are used to explore the performance of the method. On the basis of numerical computations, the optimum choice of parameters is determined empirically by comparing image reconstructions of the noniterative PDFT algorithm and the proposed iterative scheme.

Time-Frequency Analysis of Systems with Changing Dynamic Properties

Abstract: Time-frequency analysis methods transform a time series into a two-dimensional representation of frequency content with respect to time. The Fourier Transform identifies the frequency content of a signal (as a sum of weighted sinusoidal functions) but does not give useful information regarding changes in the character of the signal, as all temporal information is encoded in the phase of the transform. A time-frequency representation, by expressing frequency content at different sections of a record, allows for analysis of evolving signals. The time-frequency transformation most commonly encountered in seismology and civil engineering is a windowed Fourier Transform, or spectrogram; by comparing the frequency content of the first portion of a record with the last portion of the record, it is straightforward to identify the changes between the two segments. Extending this concept to a sliding window gives the spectrogram, where the Fourier transforms of successive portions of the record are assembled into a time-frequency representation of the signal. The spectrogram is subject to an inherent resolution limitation, in accordance with the uncertainty principle, that precludes a perfect representation of instantaneous frequency content. The wavelet transform was introduced to overcome some of the shortcomings of Fourier analysis, though wavelet methods are themselves unsuitable for many commonly encountered signals. The Wigner-Ville Distribution, and related refinements, represent a class of advanced time-frequency analysis tools that are distinguished from Fourier and wavelet methods by an increase in resolution in the time-frequency plane. I introduce several time-frequency representations and apply them to various synthetic signals as well as signals from instrumented buildings. vi For systems of interest to engineers, investigating the changing properties of a system is typically performed by analyzing vibration data from the system, rather than direct inspection of each component. Nonlinear elastic behavior in the forcedisplacement relationship can decrease the apparent natural frequencies of the system - these changes typically occur over fractions of a second in moderate to strong excitation and the system gradually recovers to pre-event levels. Structures can also suffer permanent damage (e.g., plastic deformation or fracture), permanently decreasing the observed natural frequencies as the system loses stiffness. Advanced time-frequency representations provide a set of exploratory tools for analyzing changing frequency content in a signal, which can then be correlated with damage patterns in a structure. Modern building instrumentation allows for an unprecedented investigation into the changing dynamic properties of structures: a framework for using time-frequency analysis methods for instantaneous system identification is discussed.

Evaluation of an autoregressive spectral estimator for modal wave number estimation in range-dependent shallow water waveguides

Abstract: In shallow water, geoacoustic properties of the seabed can be inferred from knowledge of acoustic normal modes propagating in the waveguide. For range-varying waveguides, modal content varies locally in response to changes in the environment. The problem becomes estimating the local modal content of a propagating field. For acoustic fields measured on horizontal arrays, resolution of closely spaced modal eigenvalues depends on the data aperture length. Therefore, range variability in a waveguide can only be detected for range scales of order of the resolvability of the individual modes. When only short data apertures are available for modal estimation, high-resolution methods must be used. In this paper, a high-resolution autoregressive (AR) spectral estimation method for extracting the modal information from measurements of a continuous wave acoustic field made on a horizontal array is evaluated. Performance is discussed for estimation accuracy and resolution in the presence of noise. Results are compared to previous work characterizing high-resolution wave number estimators. The AR estimator performance is comparable to other high-resolution methods and does not require prior information about the number of propagating modes. In addition, range/wave number plots obtained using a sliding window technique yield a robust method for identifying propagating modes and any changes with range.

Estimating time-series models from irregularly spaced data

Abstract: Maximum-likelihood estimation of the parameters of a continuous-time model for irregularly sampled data is very sensitive to initial conditions. Simulations may converge to a good solution if the true parameters are used as starting values for the nonlinear search of the minimum of the negative log likelihood. From realizable starting values, the convergence to a continuous-time model with an accurate spectrum is rare if more than three parameters have to be estimated. A discrete-time spectral estimator that applies a new algorithm for automatic equidistant missing-data analysis to irregularly spaced data is introduced. This requires equidistant resampling of the data. A slotted nearest neighbor (NN) resampling method replaces a true irregular observation time instant by the nearest equidistant resampling time point if and only if the distance to the true time is within half the slot width. It will be shown that this new resampling algorithm with the slotting principle has favorable properties over existing schemes such as NN resampling. A further improvement is obtained by using a slot width that is only a fraction of the resampling time

Adaptive windowed Fourier transform in 3-D shape measurement

Abstract: An adaptive windowed Fourier transform method in 3-D measurement based on a wavelet transform is proposed, in which, by applying a wavelet ridge, a series of scaling factors are calculated to determine the series of prime windows needed in the windowed Fourier transform method. Because the spectrum of each local fringe is simpler than that of the whole fringe, even though there is frequency aliasing as far as the whole fringe is concerned, the fundamental spectrum may separate into components in each local fringe. It is easy to filter out one of the fundamental frequency components from the local spectra. Adding these local fundamental components, the full fundamental component can be obtained correctly. The advantage of the method is that it not only eliminates the frequency aliasing, but also obtains the modulation distribution function to guide phase unwrapping.

Algorithm to Remove Spectral Leakage, Close-in Noise, and Its Application to Converter Test

Abstract: A fundamental condition of using Discrete Fourier is that the signal being transformed needs to be periodic and transform is performed on an integer number of these periods. In practice, due to some physical limitations, this condition is not always satisfied. A phenomenon known as leakage will occur and cause serous distortion in the transformed signal. Window functions are generally used at the expense of a reduced spectral resolution. Other alternative methods have also been proposed, but none of them offers the quality of direct Fourier transform of a periodic signal. This paper presents a new algorithm, called FXT, which produces equivalent spectral result with non -periodic signal as if the signal was periodic.