Jonathan S. Abel

Fifty Years of Artificial Reverberation

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.

Method and apparatus for measuring head-related transfer functions

A method and apparatus is capable of accurately deriving acoustic transfer functions such as head-related transfer functions (HRTF) at low cost. Various aspects of the invention include constraining the reflection geometry of a measurement system to facilitate removal of reflection effects, establishing ambient noise level and ambient reverberation time to calibrate test signals, generating soundfields using Golay code test signals, invalidating measurements by detecting test subject movement and short-duration ambient sounds, deriving distance and/or interaural time difference (ITD) using minimum-phase forms of impulse responses, and deriving equalized HRTF suitable for use in acoustic displays without knowing output or input transducer acoustical properties. Spatial resampling of derived HRTF and spectral shaping of test signals are discussed.

Optimal sensor placement for passive source localization

Estimating the position of a source given the signals received at a sensor array is a basic problem in the fields of acoustics and geophysics. Of interest is how to place the sensors so that the source can be most accurately localized. The Cramer-Rao bound is used as a gauge of the accuracy of source position estimators. A simple geometric interpretation of the Cramer-Rao bound is developed, and subject to geometric constraints, sensor arrangements minimizing bound variance are found. Carters optimal arrays yielding minimum range, bearing, and position bound variance subject to the constraint that the sensors lie along a line segment are reproduced without tedious algebraic manipulations or computer-aided maximization. The bound variance of the optimal arrays is seen to be roughly a factor of three smaller than that of commonly used uniformly spaced arrays.<<ETX>>

The Bark bilinear transform

Use of a bilinear conformal map to achieve a frequency warping nearly identical to the Bark scale is described. Because the map takes the unit circle to itself, its form is that of an allpass transfer function. Since it is a first-order map, it preserves the model order of rational systems. A direct-form expression for computing the optimal allpass coefficient as a function of sampling rate is developed, and a filter design example is presented.

Restoring a clipped signal

The restoration of a band-limited signal which has undergone amplitude clipping is studied. This problem can be viewed as that of recovery from signal drop-outs (missing samples over an interval of time), with the extrapolated signal constrained to lie outside the clipping interval during the drop out. If the signal is oversampled, and the clipping threshold moderate, a unique reconstruction often results from application of signal matching and bandwidth constraints. More generally, however, candidate reconstructions are seen to lie on or inside a polyhedron in the space of sampled signals. In contrast to the case of extrapolation through missing samples, upper and lower limits typically can be placed on the reconstructed signal at every sample point. In light of this finding, methods for choosing a unique reconstruction are discussed. Finally, the case of noise is considered.<<ETX>>

Source range and depth estimation from multipath range difference measurements

A prefilter is developed that converts range differences into position estimates for the case of multipath range differences or simple range differences measured to a collinear element array. Lower bounds are placed on the variance of position estimates. The sensor placement providing the minimum bound variance is discussed, and an estimator-achieving the variance lower bound in the limit of small estimation errors-is presented. The estimator is the minimizer of a weighted equation error norm, and is a closed-form function of the measured range differences; analytic expressions for its bias and variance are given. >

Automated Physical Modeling of Nonlinear Audio Circuits For Real-Time Audio Effects—Part I: Theoretical Development

This paper presents a procedural approach to derive nonlinear filters from schematics of audio circuits for the purpose of digitally emulating analog musical effects circuits in real time. This work, the first in a two-part series, extends a well-known efficient nonlinear continuous-time state-space formulation for physical modeling of musical acoustics to real-time modeling of nonlinear circuits. Rules for applying the formulation are given, as well as a procedure to derive simulation parameters automatically from circuit netlists. Furthermore, a related nonlinear discrete-time state-space algorithm is proposed to alleviate problems in solving particular circuit configurations. These methods were devised to solve non-convergence problems in the simulation of strongly saturated, nonparametric guitar distortion circuits such as the saturating diode clipper, which is presented as an example derivation. Experimental considerations and sonic performance on various other circuits will be presented in a subsequent paper.

Method and apparatus for efficient presentation of high-quality three-dimensional audio including ambient effects

Spatialization of soundfields is accomplished by filtering audio signals using filters having unvarying frequency response characteristics and amplifying signals using amplifier gains adapted in response to signals representing sound source location and/or listener position. The filters are derived using a singular value decomposition process which finds the best set of component impulse responses to approximate a given target set of impulse responses corresponding to head related transfer functions. Efficient implementations for rendering reflection effects, air absorption losses and other ambient effects, and for spatializing multiple sound sources and/or generating multiple output signals are disclosed.

Numerical methods for simulation of guitar distortion circuits

Electric guitarists prefer analog distortion effects over many digital implementations. This article suggests reasons for this and proposes that detailed study of the electrical physics of guitar distortion circuits provides insight to design more accurate emulations. This work introduces real- time emula- tion applied to guitar audio amplifi ers in the form of a tutorial about relevant numerical methods and a case study. The results here make a compelling case for simulating musical electronics using numerical methods in real time. Analog guitar distortion effect devices known as solid- state distortion boxes commonly include a diode clipper circuit with an embedded low- pass fi lter. These distortion- effect devices can be mod- eled and accurately simulated as Ordinary Differen- tial Equations (ODEs). A survey and a comparison of the basic numerical integration methods are presented as they apply to simulating circuits for audio processing, with the widely used diode clipper presented as an example. A dedicated simulator for the diode clipper has been developed to compare several numerical integration methods and their real- time feasibility. We found that implicit or semi- implicit solvers are preferred, although the prefi lter / static nonlinearity approximation comes surprisingly close to the actual solution.

Alias-Suppressed Oscillators Based on Differentiated Polynomial Waveforms

An efficient approach to the generation of classical synthesizer waveforms with reduced aliasing is proposed. This paper introduces two new classes of polynomial waveforms that can be differentiated one or more times to obtain an improved version of the sampled sawtooth and triangular signals. The differentiated polynomial waveforms (DPW) extend the previous differentiated parabolic wave method to higher polynomial orders, providing improved alias-suppression. Suitable polynomials of order higher than two can be derived either by analytically integrating a previous lower order polynomial or by solving the polynomial coefficients directly from a set of equations based on constraints. We also show how rectangular waveforms can be easily produced by differentiating a triangular signal. Bandlimited impulse trains can be obtained by differentiating the sawtooth or the rectangular signal. An objective evaluation using masking and hearing threshold models shows that a fourth-order DPW method is perceptually alias-free over the whole register of the grand piano. The proposed methods are applicable in digital implementations of subtractive sound synthesis.