Julius O. Smith

A flexible sampling-rate conversion method

A digital resampling method is proposed which allows non-uniform and time-varying resampling. The method is based on interpolated look-up in a large table of filter coefficients. One filter table handles all conversion factors. Formulas are given for determining the size of look-up table needed for a given precision requirement.

Physical Modeling Synthesis Update

Recent research in physical modeling of musical instruments for purposes of sound synthesis is reviewed. Recent references, results, and outstanding problems are highlighted for models of strings, winds, brasses, percussion, and acoustic spaces. Emphasis is placed on digital waveguide models and the musical acoustics research on which they are based.

Circulant and elliptic feedback delay networks for artificial reverberation

The feedback delay network (FDN) has been proposed for digital reverberation, The digital waveguide network (DWN) is also proposed with similar advantages. This paper notes that the commonly used FDN with an N/spl times/N orthogonal feedback matrix is isomorphic to a normalized digital waveguide network consisting of one scattering junction joining N reflectively terminated branches. Generalizations of FDNs and DWNs are discussed. The general case of a lossless FDN feedback matrix is shown to be any matrix having unit-modulus eigenvalues and linearly independent eigenvectors. A special class of FDNs using circulant matrices is proposed. These structures can be efficiently implemented and allow control of the time and frequency behavior. Applications of circulant feedback delay networks in audio signal processing are discussed.

The 2-D digital waveguide mesh

An extremely efficient method for modeling wave propagation in a membrane is provided by the multidimensional extension of the digital waveguide. The 2-D digital waveguide mesh is constructed out of bi-directional delay units and scattering junctions. We show that it coincides with the standard finite difference scheme in the lossless case. Wave propagation in the mesh is compared with wave propagation in an ideal membrane; the dissipation and dispersion error is derived.<<ETX>>

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.

Principles of Digital Waveguide Models of Musical Instruments

Basic principles of digital waveguide modeling of musical instruments are presented in a tutorial introduction intended for graduate students in electrical engineering with a solid background in signal processing and acoustics. The vibrating string is taken as the principal illustrative example, but the formulation is unified with that for acoustic tubes. Modeling lossy stiff strings using delay lines and relatively low-order digital filters is described. Various choices of wave variables are discussed, including velocity waves, force waves, and root-power waves. Signal scattering at an impedance discontinuity is derived for an arbitrary number of waveguides intersecting at a junction. Various computational forms are discussed, including the Kelly-Lochbaum, one-multiply, and normalized scattering junctions. A relatively new three-multiply normalized scattering junction is derived using a two-multiply transformer to normalize a one-multiply scattering junction. Conditions for strict passivity of the model are discussed. Use of commutativity of linear, time-invariant elements to greatly reduce computational cost is described. Applications are summarized, and models of the clarinet and bowed-string are described in some detail. The reed-bore and bow-string interactions are modeled as nonlinear scattering junctions attached to the bore/string acoustic waveguide.

The simulation of piano string vibration: From physical models to finite difference schemes and digital waveguides

A model of transverse piano string vibration, second order in time, which models frequency-dependent loss and dispersion effects is presented here. This model has many desirable properties, in particular that it can be written as a well-posed initial-boundary value problem (permitting stable finite difference schemes) and that it may be directly related to a digital waveguide model, a digital filter-based algorithm which can be used for musical sound synthesis. Techniques for the extraction of model parameters from experimental data over the full range of the grand piano are discussed, as is the link between the model parameters and the filter responses in a digital waveguide. Simulations are performed. Finally, the waveguide model is extended to the case of several coupled strings.

A switched parametric and transform audio coder

In this paper, we present a system of sines+transients+noise modeling techniques that dynamically switches between parametric representations and transform coding based representations. The sines and noise are represented by parametric models using multiresolution sinusoidal modeling and Bark-band noise modeling, respectively. The transients are modeled by short regions of transform coding. In addition, new methods are presented for selection and quantization of sinusoidal trajectories based on trajectory length and signal-to-masking thresholds. This system is useful for both low bitrate audio coding (20-40 kbps) and compressed-domain processing, such as time-scale modification.

Adaptive Interpolated Time-Delay Estimation

An adaptive delay-estimation (ADE) algorithm is proposed for the continuous tracking of time-delay. The method uses an adaptive delay line which is interpolated by a first-order filter. Two delay-line interpolating filters are considered, each having a single coefficient which is estimated in real time. The first implements linear interpolation, and the second interpolates using a first-order allpass filter. Since the ADE algorithm is derived from recursive Gauss-Newton optimization, it can be viewed as a recursive maximum likelihood (RML) algorithm for time-delay estimation.

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.