Jonathan S. Abel

Bio: Jonathan S. Abel is an academic researcher from Stanford University. The author has contributed to research in topics: Reverberation & Filter design. The author has an hindex of 30, co-authored 156 publications receiving 3965 citations. Previous affiliations of Jonathan S. Abel include Ames Research Center & Massachusetts Institute of Technology.

Closed-form least-squares source location estimation from range-difference measurements

Abstract: Three noniterative techniques are presented for localizing a single source given a set of noisy range-difference measurements. The localization formulas are derived from linear least-squares "equation error" minimization, and in one case the maximum likelihood bearing estimate is approached. Geometric interpretations of the equation error norms minimized by the three methods are given, and the statistical performances of the three methods are compared via computer simulation.

Bark and ERB bilinear transforms

Abstract: Use of a bilinear conformal map to achieve a frequency warping nearly identical to that of the Bark frequency scale is described Because the map takes the unit circle to itself, its form is that of the transfer function of a first-order allpass filter Since it is a first-order map, it preserves the model order of rational systems, making it a valuable frequency warping technique for use in audio filter design A closed-form weighted-equation-error method is derived that computes the optimal mapping coefficient as a function of sampling rate, and the solution is shown to be generally indistinguishable from the optimal least-squares solution The optimal Chebyshev mapping is also found to be essentially identical to the optimal least-squares solution The expression 08517[arctan(006583fs)]/sup 1/2/-0916 is shown to accurately approximate the optimal allpass coefficient as a function of sampling rate f/sub s/ in kHz for sampling rates greater than 1 kHz A filter design example is included that illustrates improvements due to carrying out the design over a Bark scale Corresponding results are also given and compared for approximating the related "equivalent rectangular bandwidth (ERB) scale" of Moore and Glasberg (ACTA Acustica, vo82, p335-45, 1996) using a first-order allpass transformation Due to the higher frequency resolution called for by the ERB scale, particularly at low frequencies, the first-order conformal map is less able to follow the desired mapping, and the error is two to three times greater than the Bark-scale case, depending on the sampling rate

Fifty Years of Artificial Reverberation

Abstract: The first artificial reverberation algorithms were proposed in the early 1960s, and new, improved algorithms are published regularly. These algorithms have been widely used in music production since the 1970s, and now find applications in new fields, such as game audio. This overview article provides a unified review of the various approaches to digital artificial reverberation. The three main categories have been delay networks, convolution-based algorithms, and physical room models. Delay-network and convolution techniques have been competing in popularity in the music technology field, and are often employed to produce a desired perceptual or artistic effect. In applications including virtual reality, predictive acoustic modeling, and computer-aided design of acoustic spaces, accuracy is desired, and physical models have been mainly used, although, due to their computational complexity, they are currently mainly used for simplified geometries or to generate reverberation impulse responses for use with a convolution method. With the increase of computing power, all these approaches will be available in real time. A recent trend in audio technology is the emulation of analog artificial reverberation units, such as spring reverberators, using signal processing algorithms. As a case study we present an improved parametric model for a spring reverberation unit.

The spherical interpolation method of source localization

Abstract: A closed-form least squares approximate maximum likelihood method for localization of broad-band emitters from time-difference-of-arrival (TDOA) measurements, called the spherical interpolation (SI) method, is presented. The localization formula is derived from least squares "equation-error" minimization. Computer simulation results show that the SI method has variance approaching the Cramer-Rap lower bound.

Existence and uniqueness of GPS solutions

Abstract: The existence and uniqueness of positions computed from global positioning system (GPS) pseudorange measurements is studied. Contrary to the claims of S. Bancroft (1985) and L.O. Krause (1987), in the case of n=4 satellites a fix may not exist, and, if a fix exists, it is not guaranteed to be unique. In the case of n>or=5 satellites, a unique fix is assured, except in certain degenerate cases such as coplanar satellites. An alternate formulation of the direct n=4 pseudorange to three-space position solutions of Bancroft and Krause is presented, and simple tests for existence and uniqueness are derived. >

A simple and efficient estimator for hyperbolic location

Abstract: An effective technique in locating a source based on intersections of hyperbolic curves defined by the time differences of arrival of a signal received at a number of sensors is proposed. The approach is noniterative and gives an explicit solution. It is an approximate realization of the maximum-likelihood estimator and is shown to attain the Cramer-Rao lower bound near the small error region. Comparisons of performance with existing techniques of beamformer, spherical-interpolation, divide and conquer, and iterative Taylor-series methods are made. The proposed technique performs significantly better than spherical-interpolation, and has a higher noise threshold than divide and conquer before performance breaks away from the Cramer-Rao lower bound. It provides an explicit solution form that is not available in the beamforming and Taylor-series methods. Computational complexity is comparable to spherical-interpolation but substantially less than the Taylor-series method. >

Discrete-Time Speech Signal Processing: Principles and Practice

Abstract: (NOTE: Each chapter begins with an introduction and concludes with a Summary, Exercises and Bibliography.) 1. Introduction. Discrete-Time Speech Signal Processing. The Speech Communication Pathway. Analysis/Synthesis Based on Speech Production and Perception. Applications. Outline of Book. 2. A Discrete-Time Signal Processing Framework. Discrete-Time Signals. Discrete-Time Systems. Discrete-Time Fourier Transform. Uncertainty Principle. z-Transform. LTI Systems in the Frequency Domain. Properties of LTI Systems. Time-Varying Systems. Discrete-Fourier Transform. Conversion of Continuous Signals and Systems to Discrete Time. 3. Production and Classification of Speech Sounds. Anatomy and Physiology of Speech Production. Spectrographic Analysis of Speech. Categorization of Speech Sounds. Prosody: The Melody of Speech. Speech Perception. 4. Acoustics of Speech Production. Physics of Sound. Uniform Tube Model. A Discrete-Time Model Based on Tube Concatenation. Vocal Fold/Vocal Tract Interaction. 5. Analysis and Synthesis of Pole-Zero Speech Models. Time-Dependent Processing. All-Pole Modeling of Deterministic Signals. Linear Prediction Analysis of Stochastic Speech Sounds. Criterion of "Goodness". Synthesis Based on All-Pole Modeling. Pole-Zero Estimation. Decomposition of the Glottal Flow Derivative. Appendix 5.A: Properties of Stochastic Processes. Random Processes. Ensemble Averages. Stationary Random Process. Time Averages. Power Density Spectrum. Appendix 5.B: Derivation of the Lattice Filter in Linear Prediction Analysis. 6. Homomorphic Signal Processing. Concept. Homomorphic Systems for Convolution. Complex Cepstrum of Speech-Like Sequences. Spectral Root Homomorphic Filtering. Short-Time Homomorphic Analysis of Periodic Sequences. Short-Time Speech Analysis. Analysis/Synthesis Structures. Contrasting Linear Prediction and Homomorphic Filtering. 7. Short-Time Fourier Transform Analysis and Synthesis. Short-Time Analysis. Short-Time Synthesis. Short-Time Fourier Transform Magnitude. Signal Estimation from the Modified STFT or STFTM. Time-Scale Modification and Enhancement of Speech. Appendix 7.A: FBS Method with Multiplicative Modification. 8. Filter-Bank Analysis/Synthesis. Revisiting the FBS Method. Phase Vocoder. Phase Coherence in the Phase Vocoder. Constant-Q Analysis/Synthesis. Auditory Modeling. 9. Sinusoidal Analysis/Synthesis. Sinusoidal Speech Model. Estimation of Sinewave Parameters. Synthesis. Source/Filter Phase Model. Additive Deterministic-Stochastic Model. Appendix 9.A: Derivation of the Sinewave Model. Appendix 9.B: Derivation of Optimal Cubic Phase Parameters. 10. Frequency-Domain Pitch Estimation. A Correlation-Based Pitch Estimator. Pitch Estimation Based on a "Comb Filter<170. Pitch Estimation Based on a Harmonic Sinewave Model. Glottal Pulse Onset Estimation. Multi-Band Pitch and Voicing Estimation. 11. Nonlinear Measurement and Modeling Techniques. The STFT and Wavelet Transform Revisited. Bilinear Time-Frequency Distributions. Aeroacoustic Flow in the Vocal Tract. Instantaneous Teager Energy Operator. 12. Speech Coding. Statistical Models of Speech. Scaler Quantization. Vector Quantization (VQ). Frequency-Domain Coding. Model-Based Coding. LPC Residual Coding. 13. Speech Enhancement. Introduction. Preliminaries. Wiener Filtering. Model-Based Processing. Enhancement Based on Auditory Masking. Appendix 13.A: Stochastic-Theoretic parameter Estimation. 14. Speaker Recognition. Introduction. Spectral Features for Speaker Recognition. Speaker Recognition Algorithms. Non-Spectral Features in Speaker Recognition. Signal Enhancement for the Mismatched Condition. Speaker Recognition from Coded Speech. Appendix 14.A: Expectation-Maximization (EM) Estimation. Glossary.Speech Signal Processing.Units.Databases.Index.About the Author.