Showing papers on "Multidimensional signal processing published in 2003"

Nonuniform fast Fourier transforms using min-max interpolation

Abstract: The fast Fourier transform (FFT) is used widely in signal processing for efficient computation of the FT of finite-length signals over a set of uniformly spaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e., a nonuniform FT. Several papers have described fast approximations for the nonuniform FT based on interpolating an oversampled FFT. This paper presents an interpolation method for the nonuniform FT that is optimal in the min-max sense of minimizing the worst-case approximation error over all signals of unit norm. The proposed method easily generalizes to multidimensional signals. Numerical results show that the min-max approach provides substantially lower approximation errors than conventional interpolation methods. The min-max criterion is also useful for optimizing the parameters of interpolation kernels such as the Kaiser-Bessel function.

Signal Analysis: Time, Frequency, Scale and Structure

Abstract: Preface. Acknowledgments. 1 Signals: Analog, Discrete, and Digital. 1.1 Introduction to Signals. 1.1.1 Basic Concepts. 1.1.2 Time-Domain Description of Signals. 1.1.3 Analysis in the Time-Frequency Plane. 1.1.4 Other Domains: Frequency and Scale. 1.2 Analog Signals. 1.2.1 Definitions and Notation. 1.2.2 Examples. 1.2.3 Special Analog Signals. 1.3 Discrete Signals. 1.3.1 Definitions and Notation. 1.3.2 Examples. 1.3.3 Special Discrete Signals. 1.4 Sampling and Interpolation. 1.4.1 Introduction. 1.4.2 Sampling Sinusoidal Signals. 1.4.3 Interpolation. 1.4.4 Cubic Splines. 1.5 Periodic Signals. 1.5.1 Fundamental Period and Frequency. 1.5.2 Discrete Signal Frequency. 1.5.3 Frequency Domain. 1.5.4 Time and Frequency Combined. 1.6 Special Signal Classes. 1.6.1 Basic Classes. 1.6.2 Summable and Integrable Signals. 1.6.3 Finite Energy Signals. 1.6.4 Scale Description. 1.6.5 Scale and Structure. 1.7 Signals and Complex Numbers. 1.7.1 Introduction. 1.7.2 Analytic Functions. 1.7.3 Complex Integration. 1.8 Random Signals and Noise. 1.8.1 Probability Theory. 1.8.2 Random Variables. 1.8.3 Random Signals. 1.9 Summary. 1.9.1 Historical Notes. 1.9.2 Resources. 1.9.3 Looking Forward. 1.9.4 Guide to Problems. References. Problems. 2 Discrete Systems and Signal Spaces. 2.1 Operations on Signals. 2.1.1 Operations on Signals and Discrete Systems. 2.1.2 Operations on Systems. 2.1.3 Types of Systems. 2.2 Linear Systems. 2.2.1 Properties. 2.2.2 Decomposition. 2.3 Translation Invariant Systems. 2.4 Convolutional Systems. 2.4.1 Linear, Translation-Invariant Systems. 2.4.2 Systems Defined by Difference Equations. 2.4.3 Convolution Properties. 2.4.4 Application: Echo Cancellation in Digital Telephony. 2.5 The l p Signal Spaces. 2.5.1 l p Signals. 2.5.2 Stable Systems. 2.5.3 Toward Abstract Signal Spaces. 2.5.4 Normed Spaces. 2.5.5 Banach Spaces. 2.6 Inner Product Spaces. 2.6.1 Definitions and Examples. 2.6.2 Norm and Metric. 2.6.3 Orthogonality. 2.7 Hilbert Spaces. 2.7.1 Definitions and Examples. 2.7.2 Decomposition and Direct Sums. 2.7.3 Orthonormal Bases. 2.8 Summary. References. Problems. 3 Analog Systems and Signal Spaces. 3.1 Analog Systems. 3.1.1 Operations on Analog Signals. 3.1.2 Extensions to the Analog World. 3.1.3 Cross-Correlation, Autocorrelation, and Convolution. 3.1.4 Miscellaneous Operations. 3.2 Convolution and Analog LTI Systems. 3.2.1 Linearity and Translation-Invariance. 3.2.2 LTI Systems, Impulse Response, and Convolution. 3.2.3 Convolution Properties. 3.2.4 Dirac Delta Properties. 3.2.5 Splines. 3.3 Analog Signal Spaces. 3.3.1 L p Spaces. 3.3.2 Inner Product and Hilbert Spaces. 3.3.3 Orthonormal Bases. 3.3.4 Frames. 3.4 Modern Integration Theory. 3.4.1 Measure Theory. 3.4.2 Lebesgue Integration. 3.5 Distributions. 3.5.1 From Function to Functional. 3.5.2 From Functional to Distribution. 3.5.3 The Dirac Delta. 3.5.4 Distributions and Convolution. 3.5.5 Distributions as a Limit of a Sequence. 3.6 Summary. 3.6.1 Historical Notes. 3.6.2 Looking Forward. 3.6.3 Guide to Problems. References. Problems. 4 Time-Domain Signal Analysis. 4.1 Segmentation. 4.1.1 Basic Concepts. 4.1.2 Examples. 4.1.3 Classification. 4.1.4 Region Merging and Splitting. 4.2 Thresholding. 4.2.1 Global Methods. 4.2.2 Histograms. 4.2.3 Optimal Thresholding. 4.2.4 Local Thresholding. 4.3 Texture. 4.3.1 Statistical Measures. 4.3.2 Spectral Methods. 4.3.3 Structural Approaches. 4.4 Filtering and Enhancement. 4.4.1 Convolutional Smoothing. 4.4.2 Optimal Filtering. 4.4.3 Nonlinear Filters. 4.5 Edge Detection. 4.5.1 Edge Detection on a Simple Step Edge. 4.5.2 Signal Derivatives and Edges. 4.5.3 Conditions for Optimality. 4.5.4 Retrospective. 4.6 Pattern Detection. 4.6.1 Signal Correlation. 4.6.2 Structural Pattern Recognition. 4.6.3 Statistical Pattern Recognition. 4.7 Scale Space. 4.7.1 Signal Shape, Concavity, and Scale. 4.7.2 Gaussian Smoothing. 4.8 Summary. References. Problems. 5 Fourier Transforms of Analog Signals. 5.1 Fourier Series. 5.1.1 Exponential Fourier Series. 5.1.2 Fourier Series Convergence. 5.1.3 Trigonometric Fourier Series. 5.2 Fourier Transform. 5.2.1 Motivation and Definition. 5.2.2 Inverse Fourier Transform. 5.2.3 Properties. 5.2.4 Symmetry Properties. 5.3 Extension to L 2 (R). 5.3.1 Fourier Transforms in L 1 (R) &cap L 2 (R). 5.3.2 Definition. 5.3.3 Isometry. 5.4 Summary. 5.4.1 Historical Notes. 5.4.2 Looking Forward. References. Problems. 6 Generalized Fourier Transforms of Analog Signals. 6.1 Distribution Theory and Fourier Transforms. 6.1.1 Examples. 6.1.2 The Generalized Inverse Fourier Transform. 6.1.3 Generalized Transform Properties. 6.2 Generalized Functions and Fourier Series Coefficients. 6.2.1 Dirac Comb: A Fourier Series Expansion. 6.2.2 Evaluating the Fourier Coefficients: Examples. 6.3 Linear Systems in the Frequency Domain. 6.3.1 Convolution Theorem. 6.3.2 Modulation Theorem. 6.4 Introduction to Filters. 6.4.1 Ideal Low-pass Filter. 6.4.2 Ideal High-pass Filter. 6.4.3 Ideal Bandpass Filter. 6.5 Modulation. 6.5.1 Frequency Translation and Amplitude Modulation. 6.5.2 Baseband Signal Recovery. 6.5.3 Angle Modulation. 6.6 Summary. References. Problems. 7 Discrete Fourier Transforms. 7.1 Discrete Fourier Transform. 7.1.1 Introduction. 7.1.2 The DFT's Analog Frequency-Domain Roots. 7.1.3 Properties. 7.1.4 Fast Fourier Transform. 7.2 Discrete-Time Fourier Transform. 7.2.1 Introduction. 7.2.2 Properties. 7.2.3 LTI Systems and the DTFT. 7.3 The Sampling Theorem. 7.3.1 Band-Limited Signals. 7.3.2 Recovering Analog Signals from Their Samples. 7.3.3 Reconstruction. 7.3.4 Uncertainty Principle. 7.4 Summary. References. Problems. 8 The z-Transform. 8.1 Conceptual Foundations. 8.1.1 Definition and Basic Examples. 8.1.2 Existence. 8.1.3 Properties. 8.2 Inversion Methods. 8.2.1 Contour Integration. 8.2.2 Direct Laurent Series Computation. 8.2.3 Properties and z-Transform Table Lookup. 8.2.4 Application: Systems Governed by Difference Equations. 8.3 Related Transforms. 8.3.1 Chirp z-Transform. 8.3.2 Zak Transform. 8.4 Summary. 8.4.1 Historical Notes. 8.4.2 Guide to Problems. References. Problems. 9 Frequency-Domain Signal Analysis. 9.1 Narrowband Signal Analysis. 9.1.1 Single Oscillatory Component: Sinusoidal Signals. 9.1.2 Application: Digital Telephony DTMF. 9.1.3 Filter Frequency Response. 9.1.4 Delay. 9.2 Frequency and Phase Estimation. 9.2.1 Windowing. 9.2.2 Windowing Methods. 9.2.3 Power Spectrum Estimation. 9.2.4 Application: Interferometry. 9.3 Discrete filter design and implementation. 9.3.1 Ideal Filters. 9.3.2 Design Using Window Functions. 9.3.3 Approximation. 9.3.4 Z-Transform Design Techniques. 9.3.5 Low-Pass Filter Design. 9.3.6 Frequency Transformations. 9.3.7 Linear Phase. 9.4 Wideband Signal Analysis. 9.4.1 Chirp Detection. 9.4.2 Speech Analysis. 9.4.3 Problematic Examples. 9.5 Analog Filters. 9.5.1 Introduction. 9.5.2 Basic Low-Pass Filters. 9.5.3 Butterworth. 9.5.4 Chebyshev. 9.5.5 Inverse Chebyshev. 9.5.6 Elliptic Filters. 9.5.7 Application: Optimal Filters. 9.6 Specialized Frequency-Domain Techniques. 9.6.1 Chirp-z Transform Application. 9.6.2 Hilbert Transform. 9.6.3 Perfect Reconstruction Filter Banks. 9.7 Summary. References. Problems. 10 Time-Frequency Signal Transforms. 10.1 Gabor Transforms. 10.1.1 Introduction. 10.1.2 Interpretations. 10.1.3 Gabor Elementary Functions. 10.1.4 Inversion. 10.1.5 Applications. 10.1.6 Properties. 10.2 Short-Time Fourier Transforms. 10.2.1 Window Functions. 10.2.2 Transforming with a General Window. 10.2.3 Properties. 10.2.4 Time-Frequency Localization. 10.3 Discretization. 10.3.1 Transforming Discrete Signals. 10.3.2 Sampling the Short-Time Fourier Transform. 10.3.3 Extracting Signal Structure. 10.3.4 A Fundamental Limitation. 10.3.5 Frames of Windowed Fourier Atoms. 10.3.6 Status of Gabor's Problem. 10.4 Quadratic Time-Frequency Transforms. 10.4.1 Spectrogram. 10.4.2 Wigner-Ville Distribution. 10.4.3 Ambiguity Function. 10.4.4 Cross-Term Problems. 10.4.5 Kernel Construction Method. 10.5 The Balian-Low Theorem. 10.5.1 Orthonormal Basis Decomposition. 10.5.2 Frame Decomposition. 10.5.3 Avoiding the Balian-Low Trap. 10.6 Summary. 10.6.1 Historical Notes. 10.6.2 Resources. 10.6.3 Looking Forward. References. Problems. 11 Time-Scale Signal Transforms. 11.1 Signal Scale. 11.2 Continuous Wavelet Transforms. 11.2.1 An Unlikely Discovery. 11.2.2 Basic Theory. 11.2.3 Examples. 11.3 Frames. 11.3.1 Discretization. 11.3.2 Conditions on Wavelet Frames. 11.3.3 Constructing Wavelet Frames. 11.3.4 Better Localization. 11.4 Multiresolution Analysis and Orthogonal Wavelets. 11.4.1 Multiresolution Analysis. 11.4.2 Scaling Function. 11.4.3 Discrete Low-Pass Filter. 11.4.4 Orthonormal Wavelet. 11.5 Summary. References. Problems. 12 Mixed-Domain Signal Analysis. 12.1 Wavelet Methods for Signal Structure. 12.1.1 Discrete Wavelet Transform. 12.1.2 Wavelet Pyramid Decomposition. 12.1.3 Application: Multiresolution Shape Recognition. 12.2 Mixed-Domain Signal Processing. 12.2.1 Filtering Methods. 12.2.2 Enhancement Techniques. 12.3 Biophysical Applications. 12.3.1 David Marr's Program. 12.3.2 Psychophysics. 12.4 Discovering Signal Structure. 12.4.1 Edge Detection. 12.4.2 Local Frequency Detection. 12.4.3 Texture Analysis. 12.5 Pattern Recognition Networks. 12.5.1 Coarse-to-Fine Methods. 12.5.2 Pattern Recognition Networks. 12.5.3 Neural Networks. 12.5.4 Application: Process Control. 12.6 Signal Modeling and Matching. 12.6.1 Hidden Markov Models. 12.6.2 Matching Pursuit. 12.6.3 Applications. 12.7 Afterword. References. Problems. Index.

Automatic reduction of hyperspectral imagery using wavelet spectral analysis

Abstract: Hyperspectral imagery provides richer information about materials than multispectral imagery. The new larger data volumes from hyperspectral sensors present a challenge for traditional processing techniques. For example, the identification of each ground surface pixel by its corresponding spectral signature is still difficult because of the immense volume of data. Conventional classification methods may not be used without dimension reduction preprocessing. This is due to the curse of dimensionality, which refers to the fact that the sample size needed to estimate a function of several variables to a given degree of accuracy grows exponentially with the number of variables. Principal component analysis (PCA) has been the technique of choice for dimension reduction. However, PCA is computationally expensive and does not eliminate anomalies that can be seen at one arbitrary band. Spectral data reduction using automatic wavelet decomposition could be useful. This is because it preserves the distinctions among spectral signatures. It is also computed in automatic fashion and can filter data anomalies. This is due to the intrinsic properties of wavelet transforms that preserves high- and low-frequency features, therefore preserving peaks and valleys found in typical spectra. Compared to PCA, for the same level of data reduction, we show that automatic wavelet reduction yields better or comparable classification accuracy for hyperspectral data, while achieving substantial computational savings.

Approximating a bandlimited function using very coarsely quantized data: A family of stable sigma-delta modulators of arbitrary order

Abstract: Digital signal processing has revolutionized the storage and transmission of audio and video signals as well as still images, in consumer electronics and in more scientific settings (such as medical imaging). The main advantage of digital signal processing is its robustness: although all the operations have to be implemented with, of necessity, not quite ideal hardware, the a priori knowledge that all correct outcomes must lie in a very restricted set of well-separated numbers makes it possible to recover them by rounding off appropriately. Bursty errors can compromise this scenario (as is the case in many communication channels, as well as in memory storage devices), making the “perfect” data unrecoverable by rounding off. In this case, knowledge of the type of expected contamination can be used to protect the data, prior to transmission or storage, by encoding them with error correcting codes; this is done entirely in the digital domain. These advantages have contributed to the present widespread use of digital signal processing. Many signals, however, are not digital but analog in nature; audio signals, for instance, correspond to functions f(t), modeling rapid pressure oscillations, which depend on the “continuous” time t (i.e. t ranges over or an interval in , and not over a discrete set), and the range of f typically also fills an interval in .F or this reason, the first step in any digital processing of such signals must consist in a conversion of the analog signal to the digital world, usually abbreviated as A/D conversion. For different types of signals, different A/D schemes are used; in this paper, we restrict our attention to a particular class of A/D conversion schemes adapted to audio signals. Note that at the end of the chain, after the signal has been processed, stored, retrieved, transmitted, ..., all in digital form, it needs to be reconverted to an analog signal that can be understood by a human hearing system; we thus need a D/A conversion there.

Robust, efficient, localization system

Abstract: Replica correlation processing, and associated representative signal-data reduction and reconstruction techniques, are used to detect signals of interest and obtain robust measures of received-signal parameters, such as time differences of signal arrival and directional angles of arrival, that can be used to estimate the location of a cellularized-communications signal source. The new use in the present invention of signal-correlation processing for locating communications transmitters. This enables accurate and efficient extraction of parameters for a particular signal even in a frequency band that contains multiple received transmissions, such as occurs with code-division-multiple-access (CDMA) communications. Correlation processing as disclosed herein further enables extended processing integration times to facilitate the effective detection of desired communications-signal effects and replication measurement of their location-related parameters, even for the communications signals modulated to convey voice conversations or those weakened through propagation effects. Using prior, constructed, signal replicas in the correlation processing enables elimination of the inter-site communications of the signal representations that support the correlation analyses. Reduced-data representations of the modulated signals for voiced conversation, or for the variable components of data communications, are used to significantly reduce the inter-site communications that support the correlation analyses.

Digital Signal and Image Processing

Abstract: Chapter 1. Fundamental Concepts.Chapter 2. Fourier Analysis.Chapter 3. Z-Transform and Digital Filters.Chapter 4. Filter Design and Implementation.Chapter 5. Multivariate Signal Processing.Chapter 6. Finite-Wordlength Effects.Chapter 7. Adaptive Signal Processing.Chapter 8. Least-Squares Adaptive Algorithms.Chapter 9. Linear Prediction.Chapter 10. Image Processing Fundamentals.Chapter 11. Image Compression and Coding.Appendix. Concepts of Linear Algebra.Index.

Magnetotelluric data processing with a robust statistical procedure having a high breakdown point

Abstract: SUMMARY A new robust magnetotelluric (MT) data processing algorithm is described, involving Siegel estimation on the basis of a repeated median (RM) algorithm for maximum protection against the influence of outliers and large errors. The spectral transformation is performed by means of a fast Fourier transformation followed by segment coherence sorting. To remove outliers and gaps in the time domain, an algorithm of forward autoregression prediction is applied. The processing technique is tested using two 7 day long synthetic MT time-series prepared within the framework of the COMDAT processing software comparison project. The first test contains pure MT signals, whereas in the second test the same signal is superimposed on different types of noise. To show the efficiency of the algorithm some examples of real MT data processing are also presented.

Complex signal processing is not - complex

Abstract: Wireless systems often make use of the quadrature relationship between pairs of signals to effectively cancel out-of-band and interfering in-band signal components. The understanding of these systems is often simplified by considering both the signals and system transfer-functions as 'complex' quantities. The complex approach is especially useful in highly-integrated multi-standard receivers where the use of narrow-band fixed-coefficient filters at the RF and high IF frequencies must be minimized. A tutorial review of complex signal processing for wireless applications emphasizing a graphical and pictorial description rather than an equation-based approach is first presented. Next, a number of classical modulation architectures are described using this formulation. Finally, more recent developments such as complex filters, image-reject mixers, low-IF receivers, and over-sampling A/D converters are discussed.

Frequency-domain source identification and manipulation in stereo mixes for enhancement, suppression and re-panning applications

Abstract: We describe a frequency-domain framework for source identification, separation and manipulation in stereo music recordings. Based on a simplified model of the stereo mix, we describe how a similarity measure between the short-time Fourier transforms (STFT) of the input signals is used to identify time-frequency regions occupied by each source based on the panning coefficient assigned to it during the mix. Individual sources are identified and manipulated by clustering the time-frequency components with a given panning coefficient. After modification, an inverse STFT is used to synthesize a time-domain processed signal. We describe applications of the technique in source suppression, enhancement and re-panning.

Continuous-time digital signal processing

Abstract: Digitally processing quantised (but not sampled) signals produces no aliasing and reduces the in-band quantisation error. Techniques for accomplishing such processing are proposed. Experimental evidence is included.

CFAR detection of multidimensional signals: an invariant approach

Abstract: The paper deals with constant false alarm rate (CFAR) detection of multidimensional signals embedded in Gaussian noise with unknown covariance. We attack the problem by resorting to the principle of invariance,which proves a valuable statistical tool for ensuring a priori, namely at the design stage, the CFAR property. In this context, we determine a maximal invariant statistic with respect to a proper group of transformations that leave unaltered the hypothesis-testing problem under study, devise the optimum invariant detector, and show that no uniformly most powerful invariant (UMPI) test exists. Thus, we establish the conditions an invariant detector must fulfill in order to ensure the CFAR property. Finally, we discuss several suboptimal (implementable) invariant receivers and, remarkably, show that the generalized likelihood ratio test (GLRT) detector is a member of this class. The performance analysis, which has been carried out in the presence of a Gaussian signal array, shows that the proposed detectors exhibit a quite acceptable loss with respect to the optimum Neyman-Pearson detector.

Direction of arrival estimation for multiple source signals using independent component analysis

Abstract: This paper presents a new method for estimating the directions of source signals. We assume a situation in which multiple source signals are mixed in a reverberant condition and observed at several sensors. The new method is based on independent component analysis, which separates mixed signals into original source signals. It can be applied where the number of sources is equal to the number of sensors, whereas the conventional methods based on subspace analysis, such as the MUSIC algorithm, are applicable where there are fewer sources than sensors. Even in cases where the MUSIC algorithm can be applied, the new method is better at estimating the directions of sources if they are closely placed.

Design of multidimensional signal constellations

Abstract: An algorithmic technique intended for signal constellation design for an N-dimensional Euclidean signal space is presented. Such signals are used for reliable and efficient digital communications on an additive white Gaussian noise channel. The minimum Euclidean distance between signals and the constellation-constrained capacity are used as performance measures. The basic idea is to spread out the signal vectors using an iterative method modelling the behaviour of equally charged particles in free space. Initially, the vectors are randomly distributed. The vectors reach equilibrium after a few iterations. Numerical calculations for N=2, 3, 4 and 5 dimensions and M=N+1, N+2, ...,20 signals show that the generated codes are nearly as good as previously known codes, and in some cases even better

Interpolated rectangular 3-D digital waveguide mesh algorithms with frequency warping

Abstract: Various interpolated three-dimensional (3-D) digital waveguide mesh algorithms are elaborated. We introduce an optimized technique that improves a formerly proposed trilinearly interpolated 3-D mesh and renders the mesh more homogeneous in different directions. Furthermore, various sparse versions of the interpolated mesh algorithm are investigated, which reduce the computational complexity at the expense of accuracy. Frequency-warping techniques are used to shift the frequencies of the output signal of the mesh in order to cancel the effect of dispersion error. The extensions improve the accuracy of 3-D digital waveguide mesh simulations enough so that in the future it can be used for acoustical simulations needed in the design of listening rooms, for example.

Method and system for performing digital beam forming at intermediate frequency on the radiation pattern of an array antenna

Abstract: A method of performing digital beam forming on the radiation pattern of an array antenna (34) comprising a plurality of antenna elements (34a-34c), each antenna element being coupled to a signal processing chain, said method comprising a weighting phase in which at least a complex weight coefficient (Wr, Wi) is applied to a digital signal in a corresponding signal processing chain, characterised in that said digital signal is an intermediate frequency digital signal (SIF; SIFW), and in that said weighting phase comprises the following steps: a) duplicating said digital signal into a first and a second digital signal; b) processing said first and second digital signals by: - multiplying (15, 17) said first and second digital signals respectively by a real (Wr) and an imaginary (Wi) part of said complex weight coefficient; - applying a Hilbert transform (14) to that signal which is multiplied by the imaginary part (Wi) of said complex weight coefficient; c) combining (18) said processed first and second digital signals into a weighted digital intermediate frequency signal (SIF; SIFW) by subtracting said second signal from said first signal.

Energy-efficient soft error-tolerant digital signal processing

Abstract: In this paper, we present energy-efficient soft error (SE)-tolerant techniques for digital signal processing (DSP) systems. The proposed technique, referred to as algorithmic soft error-tolerance (ASET), employs an low-complexity estimator of a main DSP block to guarantee reliability in presence of soft errors either in the MDSP or the estimator. For FIR filtering, it is shown that the proposed technique provides robustness to soft error rates of up to P/sub er/=10/sup -2/ in single-event upset (SEU). It is also shown that the proposed techniques provide 40%/spl sim/61% savings in power dissipation over that achieved via triple modula redundancy (TMR) when the desired signal-to-noise ratio SNR/sub des/=25/spl sim/35 dB.

Audio Signal Classification: History and Current Techniques

Abstract: Audio signal classification (ASC) consists of extracting relevant features from a sound, and of using these features to identify into which of a set of classes the sound is most likely to fit. The feature extraction and grouping algorithms used can be quite diverse depending on the classification domain of the application. This paper presents background necessary to understand the general research domain of ASC, including signal processing, spectral analysis, psychoacoustics and auditory scene analysis. Also presented are the basic elements of classification systems. Perceptual and physical features are discussed, as well as clustering algorithms and analysis duration. Neural nets and hidden Markov models are discussed as they relate to ASC. These techniques are presented with an overview of the current state of the ASC research literature.

A new algorithm for the estimation of the frequency of a complex exponential in additive Gaussian noise

Abstract: The letter presents a new algorithm for the precise estimation of the frequency of a complex exponential signal in additive, complex, white Gaussian noise. The discrete Fourier transform (DFT)-based algorithm performs a frequency interpolation on the results of an N point complex fast Fourier transform. For large N and large signal to noise ratio, the frequency estimation error variance obtained is 0.063 dB above the Cramer-Rao bound. The algorithm has low computational complexity and is well suited for real time digital signal processing applications, including communications, radar and sonar.

High-Resolution and Robust Signal Processing

Abstract: High-Resolution and Robust Signal Processing describes key methodological and theoretical advances achieved in this domain over the last twenty years, placing emphasis on modern developments and recent research pursuits. Applications-grounded, this sophisticated resource links theoretical background with high-resolution methods used in wireless communications, brain signal analysis, and space-time radar signal processing. Chapter extras include theorem proofs, derivations, and computational shortcuts, as well as open problems, numerical measurement, and performance examples, and simulation results Sixteen illustrious field leaders invest High-Resolution and Robust Signal Processing with: in-depth reviews of parametric high-resolution estimation and detection techniques; robust array processing solutions for adaptive beam forming and high-resolution direction finding; Parafac techniques for high-resolution array processing and specific areas of application; high-resolution nonparametric methods and implementation tactics for spectral analysis; multidimensional high-resolution data models and discussion of R-D unitary ESPRIT with colored noise; multidimensional high-resolution parameter estimation techniques applicable to channel sounding; estimation procedures for high-resolution space-time radar signal processing using 2-D or 1-D/1-D models; and models and methods for EEG/MEG space-time dipole source estimation and sensory array design.

Signal Processing of Ground Penetrating Radar Using Spectral Estimation Techniques to Estimate the Position of Buried Targets

Abstract: Super-resolution is very important for the signal processing of GPR (ground penetration radar) to resolve closely buried targets. However, it is not easy to get high resolution as GPR signals are very weak and enveloped by the noise. The MUSIC (multiple signal classification) algorithm, which is well known for its super-resolution capacity, has been implemented for signal and image processing of GPR. In addition, conventional spectral estimation technique, FFT (fast Fourier transform), has also been implemented for high-precision receiving signal level. In this paper, we propose CPM (combined processing method), which combines time domain response of MUSIC algorithm and conventional IFFT (inverse fast Fourier transform) to obtain a super-resolution and high-precision signal level. In order to support the proposal, detailed simulation was performed analyzing SNR (signal-to-noise ratio). Moreover, a field experiment at a research field and a laboratory experiment at the University of Electro-Communications, Tokyo, were also performed for thorough investigation and supported the proposed method. All the simulation and experimental results are presented.

Near-field broadband beamformer design via multidimensional semi-infinite-linear programming techniques

Abstract: Broadband microphone arrays has important applications such as hands-free mobile telephony, voice interface to personal computers and video conference equipment. This problem can be tackled in different ways. In this paper, a general broadband beamformer design problem is considered. The problem is posed as a Chebyshev minimax problem. Using the l/sub 1/-norm measure or the real rotation theorem, we show that it can be converted into a semi-infinite linear programming problem. A numerical scheme using a set of adaptive grids is applied. The scheme is proven to be convergent when a certain grid refinement is used. The method can be applied to the design of multidimensional digital finite-impulse response (FIR) filters with arbitrarily specified amplitude and phase.

Power spectrum analysis for DNA sequences

Abstract: Certain biological functions are related to observe periodic behavior in DNA sequences, for example the period-3 behavior in exons. Appropriately, the field of digital signal processing has begun to contribute to the gene identification problem by allowing for discoveries in terms of these periodicities. This work presents known spectral analysis techniques that are applied in a new manner to find DNA sequences that exhibit periodic behavior in the residues. Improvements to the standard DFT power spectrum are shown by intuitively choosing new sequence alphabets. We also illustrate how power spectrums of the warped DFT and the Walsh-Hadamard transform provide useful frequency domain representations for finding such periodic behavior. Examples are given to illustrate the value of the competing techniques and to visually display comparisons.

A SR-based radon transform to extract weak lines from noise images

Abstract: The Radon transform is able to transform two dimensional images with lines into a space of line parameters, where each line in the image will give a peak positioned at the corresponding line parameters. This has led to many line detection applications in image processing, computer vision and array processing. But when the lines are embedded in very strong noise background, using the Radon transform directly is not so effective. In this paper we present a SR-based Radon transform, in which a bistable stochastic resonance structure is introduced into the Radon transform. Using this kind of transform, we can easily extract weak lines from noise images. We also give applications in the bearing-time record and the LOFAR display.

Fourier Transforms in Radar and Signal Processing

Abstract: Introduction. Rules and Pairs. Pulse Spectra. Sampling Theory. Periodic Waveforms. Interpolation for Delayed Waveform Time Series. Equalization. Array Beamforming.

Correlators and cross-correlators using tapped optical fibers

Abstract: A Tapped Optical-Fibers Processor (TOP) for correlation and autocorrelation facilitates the processing if radar and SAR (synthetic aperture radar) signals, allowing fine resolution to be obtained without fast front-end sampling while significantly reducing digital computational burdens. Particularly in conjunction with radar signal processing, the input signal may be composed of the sum of at least two or more signals, in which case the output may include the autocorrelations of both inputs as well as the generation of a cross-correlation of the two autocorrelations. In terms of hardware, a signal processor according to the invention preferably includes a coherent laser source operating at a carrier frequency; a modulator to insert an input RF signal into the carrier; an optical fiber radiator composed of a fiber with taps that radiate the modulated optical signal; a lens to perform a spatial Fourier transformation on the radiated signal; and a detector array to output the transformed signal to a digital processor for additional signal processing. In any case, the two input signals may be electronically or optically combined.

Efficient multibeam synthesis with interference nulling for large arrays

Abstract: This paper describes a class of multibeam synthesis algorithms that are useful for large arrays when simultaneous nulling of interference is required. In these algorithms, the computational cost is kept small by using fast Fourier transform (FFT) beamforming, while at the same time interference is nulled using spatial projections. Once the interference steering vectors are determined, these algorithms have a computational cost per output which is only slightly greater than that of the FFT with no interference nulling. In addition, techniques are derived that allow the Fourier beams to be protected against distortion by constraining the patterns, reducing the pattern variation, or both. These techniques may be particularly well suited for some new radiotelescopes now in the planning stages.

Digital signal processing : mathematical and computational methods, software development and applications

Abstract: Part I Mathematical Methods for Signal Analysis Introduction to complex analysis the delta function and the Green's function Fourmet series the Fourier transform, convolution and correlation, the sampling theorem, the Laplace transform the Hilbert transform and quadrature detection, modulation and demodulation, the wavelet transform, the z-transform, the Wigner transform. Part II Computational Techniques in Linear Algebra Basic linear algebra, types of linear systems, formal methods of solution direct methods of solution iterative improvement vector and matrix norms, conditioning and the condition number, the least squares method iterative methods of solution the conjugate gradient method the computation of eigen values and eigen vectors. Part III Programming and Software Engineering Number systems and numerical error, programming languages, software design methods, structured and modular programming software engineering for DSP in C. Part IV Digital Signal Processing Methods Algorithms and Building a Library Digital frequency filtering, the DFT and FFT, computing with the FFT, spectral leakage and windowing inverse filters, the Wiener filter, the matched filter, constrained deconvolution, homomorphic filtering noise and chaos Bayesian estimation methods, the maximum entropy method, spectral extrapolation FIR and IIR filters, non-stationary signal processing random fractal and multi-random-fractal signals.

A general solution to the maximization of the multidimensional generalized Rayleigh quotient used in linear discriminant analysis for signal classification

Abstract: A more general solution and a new didactic demonstration of the maximization of the multidimensional case of the generalized Rayleigh quotient are described. This solution is not only the well-known eigenvectors solution widely available in the literature but also a general transformation that is not necessarily orthogonal. The demonstration uses only basic linear algebra and simple Lagrangian maximization to find the transformation matrix that maximizes the multidimensional generalized Rayleigh quotient for linear discriminant analysis, widely used in signal classification applications.

Implementation of FPGA based fast DOA estimator using unitary MUSIC algorithm [cellular wireless base station applications]

Abstract: This paper proposes the practical implementation of a DOA estimation system, using an FPGA (field programmable gate array), that is a key technique in the realization of the DOA-based adaptive array antenna for cellular wireless base-stations. It incorporates the spectral unitary MUSIC (multiple signal classification) algorithm, which is one of the representative super resolution DOA estimation techniques. This paper describes the DSP design and real hardware implementation of the unitary MUSIC algorithm. This system achieves a high performance in the eigenvalue decomposition (EVD) and MUSIC angular spectra computation with a cyclic Jacobi processor based on CORDIC (coordinate rotation digital computer) and spatial DFT (discrete Fourier transform), respectively. All DSP functions are computed by only fixed-point operation with finite bit-length to meet the requirements of fast processing and low power consumption due to the simplified and optimized architecture.