Showing papers on "Impulse response published in 1995"

Introduction to ultra-wideband radar systems

Abstract: Ultra-Wideband Radar Overview, J.D. Taylor Introduction Ultra-Wideband Radar Terminology and Concepts Potential Applications of UWB Radar UWB Systems Frequency Spectrum Sharing and Interference Issues Book Conclusion References Technical Issues in Ultra-Wideband Radar Systems, H.F. Engler, Jr. Introduction Fundamental Radar Principles Classification of Radar Waveforms Technical Issues in UWB Radar System Design Summary References Appendices: Signal Characteristics Governing Range and Velocity Measurement Resolution Range Accuracy Requirements for Velocity Estimation from Differential Time Delay The Concept of Nonlinearity Analytical Techniques for Ultra-Wideband Signals, M. Rangaswamy and T.K. Sarkar Preface Part 1: Fourier Analysis of Signals Introduction Information and Bandwidth Fourier Analysis of Signals Properties of the Fourier Transform Dirac-Delta Function Fourier Transform of Periodic Signals Numerical Computation of the Fourier Transform Spectral Density Times Correlation of Power Signals Power Spectral Density of Random Signals Conclusion References Part 2: Laplace Transforms and Signal Analysis Introduction Laplace Transforms Inverse Laplace Transform Properties of Laplace Transform One-Sided Laplace Transform Applications of the Two-Sided Laplace Transform Pulse Propagation in a Long Medium Conclusion References Part 3: Limitations of Time and Frequency Approaches Introduction Consideration in Performing Time-Domain Measurements Data Acquisition Processing Considerations Transformations from the Discrete to the Continuous Domain Experimental Verification Characterization of Objects in the Frequency Domain Conclusion References Transmitters Power Supply Design, D. Platts Introduction Considerations for Power Supply Design Pulsed Power Supplies Switching Techniques for Pulsed Power Supplies Conclusion References Light-Activated Semiconductor Switches for UWB Radar, O.S.F. Zucker and I.A. McIntyre Introduction The Evolution of the Requirements Digital Synthesis of UWB Signals by Sequential Switching Digital Synthesis: Experimental Results Switches and Their Limits Switch Optical Requirements Switch Choice Conclusion Acknowledgments References Ultra-Wideband Antenna Technology Introduction and Overview Antennas and UWB Signals, P.R. Foster Introduction Antenna Elements Aperture Antennas References Array Antenna Calculations in the Time Domain Using Pseudorandomly Coded Signals, J.D. Halsey Introduction Impulse Signal Design Correlating Receivers Fundamentals of Beamforming in the Time Domain Numerical Simulation Conclusions References Appendix: A Discussion of Time-Domain Field Equations Ultra-Wideband Impulse Antennas, M.G.M. Hussain Introduction Relative Bandwidth The Large-Current Radiator Field Strengths and Magnetic Flux of the Large-Current Radiator Measured Antenna Patterns References Linear Array Beam Forming with Nonsinusoidal Waves, M.G.M. Hussain Introduction Array Beamforming with Sinusoidal Waves Beamforming with Nonsinusoidal Waves Frequency Domain Array Beamforming Transfer Function and Impulse Response of Linear Array Synthesis of Antenna Array Beam Patterns Summary References Direct Radiating Systems A Basic UWB Design and Experiments: Blumlein Impulse Generator and TEM Radiator, W.C. Nunnally and R.N. Edwards Practical UWB Impulse Generators and Radiators Description of Transverse Electromagnetic Transmitter Basic Impulse Radiation Considerations Experimental Results Conclusions References Design and Analysis of an Example of NEMP Radiating Antenna, D. Giri Introduction Design and Analysis of an Example of NEMP Radiating Antenna Radiating NEMP Simulators Antenna Concepts for UWB Radar Acknowledgments References Propagation and Energy Transfer RF Propagation in the Atmosphere, R. Roussel-Dupre Introduction UWB Propagation Low-Power Propagation through a Background Plasma High-Power Propagation in Nonlinear Media References Energy Transfer through Media and Sensing of the Media, T.W. Barrett Introduction to Energy Transfer Concepts Advanced Theory of Dielectrics and Transmissions through Media Pulse Envelope Effects Soliton Waves, Group Theory, and Electromagnetic Missile Concepts References Appendices: Further Developments in Self-Induced Transparency The Nonlinear Wave Equations and Solitons Relation of U(1) and SU(2) Symmetry Groups Transmitter Signature and Target Signature of Radar Signals, H.F. Harmuth Introduction Features of Carrier-Free Radar Signals Position Coding and Large Target Signature Character Coding and Large Target Signature Conclusions References Appendix: Continuous and Transient Response of Resonant Circuits Radar Cross Section and Target Scattering, M.L. VanBlaricum Introduction Radar Cross Section The Scattering Matrix Frequency Dependence of RCS Relationships among CW, Transient, and Wideband Scattering The Singularity Expansion Formulation Resonance Based Target Identification References Ultra-Wideband Radar Receivers, J.D. Taylor and E.C. Kisenwether Introduction Narrowband and UWB Signal Receiver Concepts UWB Threshold Signal Detection Correlation Detection UWB Radar Receivers and Signal Processing References Appendices: Narrowband Receiver Sensitivity to UWB Signals Computation of Correlator Output vs. SNR High Order Signal Processing for Ultra-Wideband Radar Signals, V.Z. Marmarelis, D. Sheby, E.C. Kisenwether, and T.A. Erdley Introduction Background Methodology Experiment Results Conclusions Acknowledgments References Performance Prediction and Modeling, T.W. Barrett Introduction and Overview Theoretical Background for Time Domain Signal Processing Radar Performance Prediction Principles Comparison Analysis of Frequency Domain and Time Domain Signals Time Domain Radar Performance Prediction Rules for Time Domain Radar Performance Equation Practical Example of a Time Domain Radar System and Analysis References Appendices: Periodic, Aperiodic, and Random Signals The Gaussian Approximation: Heterodyne vs. Homodyne Reception Boundary Diffraction

An optimum computer-generated pulse signal suitable for the measurement of very long impulse responses

Abstract: Transfer functions of acoustic systems often exhibit wide dynamic ranges and very long impulse responses. A ‘‘time‐stretched’’ pulse as proposed by Aoshima (ATSP), though originally given in a very specific form seems to be one of the most promising signals to measure transfer functions with characteristics of acoustic system mentioned as above. In this paper, this pulse (ATSP) is first generalized and then optimized for the measurement of long impulse responses. This optimized ATSP (OATSP) has an almost ideal characteristic to measure impulse responses shorter than its specific length N. Moreover, it is newly shown in this paper that OATSP has also a good characteristic to measure impulse responses longer than N. Discussion is presented on how to design OATSP suitable for a specific situation of measurement by analyzing errors, when the pulse is used to measure impulse responses longer than N.

Time-domain uniform geometrical theory of diffraction for a curved wedge

Abstract: A time-domain version of the uniform geometrical theory of diffraction (TD-UTD) is developed to describe, in closed form, the transient electromagnetic scattering from a perfectly conducting, arbitrarily curved wedge excited by a general time impulsive astigmatic wavefront. This TD-UTD impulse response is obtained by a Fourier inversion of the corresponding frequency domain UTD solution. An analytic signal representation of the transient fields is used because it provides a very simple procedure to avoid the difficulties that result when inverting frequency domain UTD fields associated with rays that traverse line or smooth caustics. The TD-UTD response to a more general transient wave excitation of the wedge may be found via convolution. A very useful representation for modeling a general pulsed astigmatic wave excitation is also developed which, in particular, allows its convolution with the TD-UTD impulse response to be done in closed form. Some numerical examples illustrating the utility of these developments are presented.

Identification of State-Space Models from Time and Frequency Data

Abstract: This dissertation considers the identication of linear multivariable systems using finite dimensional time-invariant state-space models.Parametrization of multivariable state-space models is considered. A full parametrization, where all elements in the state-space matrices are parameters, is introduced. A model structure with full parametrization gives two important implications; low sensitivity realizations can be used and the structural issues of multivariable canonical parametrizations are circumvented. Analysis reveals that additional estimated parameters do not increase the variance of the transfer function estimate if the resulting model class is not enlarged.Estimation and validation issues for the case of impulse response data are discussed. Identication techniques based on realization theory are linked to the prediction error method. The combination of these techniques allows for the estimation of high quality models for systems with many oscillative modes. A new model quality measure, Modal Coherence Indicator, is introduced. This indicator gives an independent quality tag for each identified mode and provides information useful for model validation and order estimation.Two applications from the aircraft and space industry are considered. Both problems are concerned with vibrational analysis of mechanical structures. The first application is from an extensive experimental vibrational study of the airframe structure of the Saab 2000 commuter aircraft. The second stems from vibrational analysis of a launcher-satellite separation system. In both applications multi-output discrete time state-space models are estimated, which are then used to derive resonant frequencies and damping ratios.New multivariable frequency domain identification algorithms are also introduced. Assuming primary data consist of uniformly spaced frequency response measurements, an identification algorithm based on realization theory is derived. The algorithm is shown to be robust against bounded noise as well as being consistent. The resulting estimate is shown to be asymptotically normal, and an explicit variance expression is determined. If data originate from an infinite dimensional system, it is shown that the estimated transfer function converges to the transfer function of the truncated balanced realization.Frequency domain subspace based algorithms are also derived and analyzed when the data consist of samples of the Fourier transform of the input and output signals. These algorithms are the frequency domain counterparts of the time domain subspace based algorithms.The frequency domain identification methods developed are applied to measured frequency data from a mechanical truss structure which exhibits many lightly damped oscillative modes. With the new methods, high quality state-space models are estimated both in continuous and discrete time.

Photonic wideband array antennas

Abstract: Presents an introduction to the optical control of array antennas by using fiber optic links for remote control and a photonic time shift network for wide instantaneous bandwidth. An overview of the development of a wideband conformal array designed for airborne surveillance radars is given. The paper covers the system design and the performance of an L-band (850-1400 MHz) M-element array controlled by photonics. Packaging techniques of the photonic components and the array aperture are discussed. The wideband performance of the system is highlighted. A nano-second impulse response has been measured to demonstrate a 50% instantaneous bandwidth (550 MHz, 30 cm range resolution) for target ID and imaging. A built-in signal injection technique based on time-domain impulse measurement was used to calibrate the wideband components in the time-shift beamforming network. >

The generalized multidelay adaptive filter: structure and convergence analysis

Abstract: Frequency-domain adaptive filters have long been recognized as an attractive alternative to time-domain algorithms when dealing with systems with large impulse response and/or correlated input. New frequency-domain LMS adaptive schemes have been proposed. These algorithms essentially retain the attractive features of frequency-domain implementations, while requiring a processing delay considerably smaller than the length of the impulse response. The authors show that these algorithms can be seen as particular implementations of a more general scheme, the generalized multidelay filter (GMDF). Within this general class of algorithms, we focus on implementations based on the weighted overlap and add reconstruction algorithms; these variants, overlooked in previous contributions, provide an independent control of the overall processing delay and of the rate of update of the filter coefficients, allowing a trade-off between the computational complexity and the rate of convergence. We present a comprehensive analysis of the performance of this new scheme and to provide insight into the influence of impulse response segmentation on the behavior of the adaptive algorithm. Exact analytical expressions for the steady-state mean-square error are first derived. Necessary and sufficient conditions for the convergence of the algorithm to the optimal solution within finite variance are then obtained, and are translated into bounds for the stepsize parameter. Simulations are presented to support our analysis and to demonstrate the practical usefulness of the GMDF algorithm in applications where large impulse response has to be processed. >

Volume, Volatility, and Leverage: A Dynamic Analysis

Abstract: This paper uses dynamic impulse response analysis to investigate the interrelationships among stock price volatility, trading volume, and the leverage effect. Dynamic impulse response analysis is a technique for analyzing the multistep ahead characteristics of a non-parametric estimate of the one-step conditional density of a strictly stationary process. The technique is the generalization to a nonlinear process of Sims-style impulse response analysis for linear models. In this paper, we refine the technique and apply it to a long panel of daily observations on the price and trading volume of four stocks actively traded on the NYSE: Boeing, Coca-Cola, IBM, and MMM.

Method and apparatus for multi-channel acoustic echo cancellation

Abstract: In a multi-channel acoustic echo cancellation, received signals in a plurality of channels are radiated as acoustic signals by a plurality of loudspeakers, received signal vectors in these channels are combined into a combined vector and a rearranged received signal vector in the case of at least two channels being exchanged is generated. By inputting the combined received signal vector into an echo replica generating part which simulates echo paths from the loudspeakers to at least one microphone, an echo replica is generated. The echo replica is subtracted from an echo output from the microphone to obtain a residual echo. Based on the relationship between the received signal vector and the corresponding residual echo and between the rearranged received signal vector and the corresponding approximated residual echo, an adjustment vector is obtained which is used to adjust the estimated echo path vector representing an impulse response of the echo replica generating part.

Slow asymptotic convergence of LMS acoustic echo cancelers

Abstract: In most acoustic echo canceler (AEC) applications, an adaptive finite impulse response (FIR) filter is employed with coefficients that are computed using the LMS algorithm. The paper establishes a theoretical basis for the slow asymptotic convergence that is often noted in practice for such applications. The analytical approach expresses the mean-square error trajectory in terms of eigenmodes and then applies the asymptotic theory of Toeplitz matrices to obtain a solution that is based on a general characterization of the actual room impulse response. The method leads to good approximations even for a moderate number of taps (N>16) and applies to both full-band and subband designs. Explicit mathematical expressions of the mean-square error convergence are derived for bandlimited white noise, a first-order Markov process, and, more generally, pth-order rational spectra and a direct power-law model, which relates to lowpass FIR filters. These expressions show that the asymptotic convergence is generally slow, being at best of order 1/t for bandlimited white noise. It is argued that input filter design cannot do much to improve slow convergence. However, the theory suggests postfiltering as a remedy that would be useful for the full-band LMS AEC and may also be applicable to subband designs. >

Slope transforms: theory and application to nonlinear signal processing

Abstract: Fourier transforms are among the most useful linear signal transformations for quantifying the frequency content of signals and for analyzing their processing by linear time-invariant systems. Some nonlinear signal transforms are developed that can provide information about the slope content of signals and are useful analytic tools for large classes of nonlinear systems. Many of their theoretical properties are examined, showing a striking conceptual resemblance to Fourier transforms and their application to linear systems. These novel transforms, called slope transforms, are originally derived from the eigenvalues of morphological dilation and erosion systems, where the corresponding eigenfunctions are lines /spl alpha/t+b parameterized by their slope /spl alpha/. They obey a nonlinear superposition principle of the supremum- or infimum-of-sums type. Applied to the impulse response of dilation or erosion systems, the slope transforms provide a slope response function for these systems, which allows their analysis and design in a transform domain, the slope domain. Applied to arbitrary signals, the slope transforms provide information about upper or lower tangents to the signal's graph at varying slopes. The upper or lower envelopes of the signal can be obtained from the inverse transforms. Overall, the slope transforms provide a new transform domain for signals and morphological systems where time lines become slope impulses, time cones become slope bandpass filters, and time dilation/erosion transform into addition of slope transforms. Their application to the design of slope-selective filters is also presented. >

Spectral extrapolation of spatially bounded images [MRI application]

Abstract: A spectral extrapolation algorithm for spatially bounded images is presented. An image is said to be spatially bounded when it is confined to a closed region and is surrounded by a background of zeros. With prior knowledge of the spatial domain zeros, the extrapolation algorithm extends the image's spectrum beyond a known interval of low-frequency components. The result, which is referred to as the finite support solution, has space variant resolution; features near the edge of the support region are better resolved than those in the center. The resolution of the finite support solution is discussed as a function of the number of known spatial zeros and known spectral components. A regularized version of the finite support solution is included for handling the case where the known spectral components are noisy. For both the noiseless and noisy cases, the resolution of the finite support solution is measured in terms of its impulse response characteristics, and compared to the resolution of the zerofilled and Nyquist solutions. The finite support solution is superior to the zerofilled solution for both the noisy and noiseless data cases. When compared to the Nyquist solution, the finite support solution may be preferred in the noisy data case. Examples using medical image data are provided. >

Effects of Amplitude and Phase Mismatching Errors in the Generation of a Kinoform for Pattern Recognition

Abstract: A model to determine the influence of the phase and amplitude mismatching on the diffraction orders is proposed. The coupling between amplitude and phase in liquid crystal televisions (LCTV) is also considered. The effect on the impulse response of the nonlinearities is studied from experimentally determined amplitude and phase modulations. It is shown that even with these nonlinearities one of the orders corresponds to the impulse response of the kinoform. The proper diffractional order may be separated by adding phase codes. Experimental results of impulse responses and correlations are given for different configurations of the spatial light modulator (SLM).

Broadband sampling oscilloscope characterization with the "Nose-to-Nose" calibration procedure: a theoretical and practical analysis

Abstract: In the past the "nose-to-nose" calibration procedure has been introduced as probably the most accurate method to determine the impulse response of broadband sampling oscilloscopes like the HP54124T. The method is based on the hypothesis "sampler kick-out equals oscilloscope impulse response". This hypothesis was originally based on an intuitive approach and was later verified experimentally (comparison with power measurements) as well as with SPICE simulations. Until now, however, there was no generalized mathematical evidence supporting this basic hypothesis. In this paper a mathematical theory is developed, which starts from a generalized sampler equivalent scheme, and which shows that, under conditions which are valid in practice, the sampler kick-out indeed equals the sampler impulse response. Experimental results are reported concerning the accuracy and precision of the calibration procedure. These experiments involve the investigation of experiment repeatability, noise, sampler linearity and timebase effects. >

Time-domain equalization for multicarrier communication

Abstract: Multicarrier communication, without time-domain equalizer (TEQ), over a channel whose impulse response duration is of the same order as the inverse carrier spacing, requires a long guard interval yielding a considerable loss in both power and bandwidth efficiency. A smaller guard interval (yielding a smaller loss) can be allowed when using at the receiver a TEQ that shortens the impulse response of the cascade of channel plus TEQ. In this contribution the impulse response of a FIR TEQ is determined according to a MMSE criterion, resulting in an eigenvalue problem. Numerical performance results as a function of TEQ complexity are presented, assuming both upstream and downstream asymmetric digital subscriber line (ADSL) communication over twisted pair cable.

Optimization of adaptive filter tap settings for subband acoustic echo cancellers in teleconferencing

Abstract: A subband acoustic echo canceller for a telecommunications teleconferencing room is equiped with subband adaptive filters and filter taps associated with said subbands. A data store is provided containing a weight list for controlling allocation of the filter taps among the subbands. An optimum tap profile as determined by the weights is a composite of room acoustic impulse response and weighting adjustments based on one or more measures of perceived human acoustic sensitivity experienced by far-end users. An active periodic adjustment of the weights responsive to detection of sibilant energy in the incoming path further improves echo cancellation. Active measurement and updating of the room acoustic impulse response provides further refinement.

Computer simulation of radio channels using a harmonic decomposition technique

Abstract: Based on a harmonic decomposition of stochastic processes, a new approach for approximating the time variant radio channel impulse response, given an arbitrary Doppler power density spectrum is presented. The basic idea is to use a Fourier expansion with uncorrelated coefficients to approximate the actual radio fading process. An upper bound on the mean square error between the actual and approximated fading as a function of the number of terms in the expansion is also given. The proposed method is particularly adapted for simulating broadband radio channels. >

Deconvolution and total least squares in finding the impulse response of an electromagnetic system from measured data

Abstract: Total least squares (TLS) is a method of solving over-determined sets of linear equations AX/spl ap/b when there are errors both in the observation vector b(m/spl times/1) and in the data matrix A(m/spl times/n). This method is particularly useful when the data matrix A is singular or highly ill conditioned. We present the method of finding the TLS by applying the singular value decomposition to the discrete deconvolution problem. Numerical results are presented for finding the impulse response of a transmission line from experimental data. The advantage of this approach is that this method can be automated based on the signal to noise ratio of the measured data. >

Performance monitoring of control systems using likelihood methods

Abstract: Evaluating deterioration in performance of control systems using closed loop operating data is addressed. A framework is proposed in which acceptable performance is expressed by constraints on the closed loop transfer function impulse response coefficients. Using likelihood methods, a hypothesis test is outlined to determine if control deterioration has occurred, and several threshold selection methods are enumerated.

Method at ofdm-reception for correction of frequency, time window, sampling clock and slow phase variations

Abstract: The present invention relates to a method for correction of frequency, time window error, sampling clock and phase error at OFDM-receivers. The information which is transmitted in a signal which includes several carriers in digital form, includes consecutive frames comprising a number of symbols. In respective frames at least one up-chirp and one down-chirp is arranged. Correction of the frequency is made based on analysis of the up- and down-chirps. Further the main focus of the weighted impulse response is determined. The position of the main focus is used for correction of the time window and the sampling clock. Further the vectors from the location of the received carriers are registred in relation to their ideal location in a matrix. The angles between the received vector and the ideally located vector are determined and are weighed together with regard to the amplitude of the transmission function at the frequency of the carrier and the distance of the vector to the origin of coordinates. An average is after that made of the weighed angle distances. The obtained average is used for correction of the phase error. Further, the knowledge of the obtained phase error and previous phase errors is used for estimation of the coming phase error in the following reception.

Method and apparatus for providing reduced complexity echo cancellation in a multicarrier communication system

Abstract: A data communication system is provided including a multicarrier transmitter which encodes and modulates input data into a plurality of carriers, a channel which distorts signals input to it by the transmitter, an echo path which also distorts signals, and a multicarrier receiver which receives signals from the channel and minimizes the distortions through the use of a SIRF. The method of determining the set of time domain SIRF parameters generally includes the steps of approximating the original channel and echo impulse responses, optionally modeling the channel impulse response, optionally modeling the echo impulse response, computing SIRF coefficients based upon the combined approximated or modeled channel impulse response and the approximated or modeled echo impulse response, calculating a SSNR for the calculated SIRF coefficients, and repeating the steps a predetermined number of times to determine those coefficients with the best

Modulation classification of signals in unknown ISI environments

Abstract: Modulation classification is an important component of non-cooperative communication theory in which the received signal type is unknown but may be restricted to a finite set of possibilities. We develop two classification techniques for digitally modulated signals affected by intersymbol interference (ISI). The initial development of the classification tests is derived assuming a known-channel impulse response. In order to address signal classification in an unknown ISI environment, we employ per-survivor processing (PSP), a technique for estimating both the data sequence and the unknown parameters of a communications signal which exhibits memory.

Short-time Fourier transforms using cascade filter structures

Abstract: A wide class of short-time Fourier transforms (STFT's), or spectrograms, can be obtained by applying an infinite-length analysis window, corresponding to an impulse response of an IIR filter, at every data sample and then taking the Fourier transform. The use of the cascade form realization of the analysis window allows simple and recursive generations of a number of distinct STFT's with different tradeoff between temporal and spectral resolutions. The temporal-spectral resolution diversity of all STFT's (spectrograms) associated with the same window is a function of its poles and zeros as well as their order of cascade. Closed-form expressions of such diversity are derived for the case of multiple-pole and all pole analysis windows. >

Simulation of indoor propagation channel at infrared frequencies in furnished office environments

Abstract: Diffused infrared communication is a potential candidate for providing wireless service to portable computers inside buildings. The details of a model that estimates the impulse response and frequency response of the infrared channel in indoor environments of different shapes and sizes are described. An important feature of the model is inclusion of the effect of office furniture and people in the room on the channel's impulse response. The developed simulation package has been executed under diversified sets of conditions to obtain the impulse response of the IR channel in rooms of arbitrary shape, with and without furniture. The corresponding results have been compared with each other, and with some empirical data. The major conclusions are: (i) room furniture may have a great effect on the impulse response under certain conditions, (ii) there is general good match between the simulated and empirical frequency response functions of the channel.

Radar target identification using the bispectrum: a comparative study

Abstract: Radar target identification is performed using time-domain bispectral features. The classification performance is compared with the performance of other classifiers that use either the impulse response or frequency domain response of the unknown target. The classification algorithms developed here are based on the spectral or the bispectral energy of the received backscatter signal. Classification results are obtained using simulated radar returns derived from measured scattering data from real radar targets. The performance of classifiers in the presence of additive Gaussian (colored or white), exponential noise, and Weibull noise are considered, along with cases where the azimuth position of the target is unknown. Finally, the effect on classification performance of responses horn extraneous point scatterers is investigated. >

Diversity receiver in which reception characteristics can be improved

Abstract: In a diversity receiver provided with diversity branches (51 and 52) which have a predetermined distance therebetween and each of which produces a received signal sequence in response to reception of a radio signal directed to the diversity receiver with a symbol rate, each of samplers (56 and 57) samples the received signal sequence with plural times of the symbol rate to produce a sampled serial signal sequence. Each of serial-to-conversion circuits (58 and 59) converts the sampled serial signal sequence into parallel signals. With reference to the parallel signals, channel impulse response estimation circuits (61 and 62, or 63 and 64) estimate channel impulse responses, respectively. In accordance with each of the estimated impulse response signals and each of the parallel signals, branch metric calculation circuits (66, 67, 68, and 69) calculate branch metrics. A branch metric combining circuit (71) combines the branch metrics into a combined branch metric. A Viterbi processor (72) carries out maximum likelihood sequence estimation in accordance with the combined branch metric.

Generalized acoustic diffraction tomogra phy1

Abstract: A generalized diffraction tomography algorithm is developed, which in principle can handle irregularly spaced data, curved acquisition lines and non-uniform background models. By direct comparison with medical diffraction tomography, it is shown that the generalized method involves the same two processing steps: data filtering and back-propagation. The filter handles the irregular sampling of the model space and the uneven energy coverage, while the back-propagation operator removes the wave propagation effects. Paraxial ray-tracing techniques are employed to compute both these quantities. In medical diffraction tomography, the resolution vector (i.e. the Fourier vector of the model space) is defined by the incident and scattered plane-wave directions. It is shown here that a similar relationship exists for a non-uniform background, where the resolution vector at a particular image point is defined by the incident and scattered ray directions. Consequently, the impulse response of the generalized algorithm becomes space variant. Finally, a general processing procedure for transmission mode seismic data, based on this generalized algorithm, is proposed. The potential of the method is demonstrated using synthetic cross-hole data.