Stanley P. Lipshitz

An improved acoustic model for active noise control in a duct

This paper presents a model of sound propagation in a duct, for the purpose of active noise control. A physical model generally different from those explored in much of the literature is derived, with non-constant acoustic load impedance at the one end, and a coupled disturbance loudspeaker model at the other end. Experimental results are presented which validate the derived transfer function.

Dithered quantizers with and without feedback

It is shown that quantizing systems without feedback respond to the use of particular spectrally-shaped dither signals quite differently from those with feedback paths. For each type of system, conditions are given which ensure that the quantization error will be wide-sense stationary with no input dependence and with a predictable power spectral density function.<<ETX>>

Using computer algebra to explore sound-wave propagation in spherical cavities

This article shows how we have used the Maple computer algebra system to solve a classical problem in mathematical physics-that of analyzing sound-wave propagation in spherical cavities using the Fourier method to solve the wave equation. Our approach lets users easily generate and visualize solutions starting from various initial conditions for this conceptually difficult problem. To illustrate our approach, we perform a careful analysis of the propagation and reflection of spherically symmetrical sound waves for a specific initial condition.

Random rounding in redundant representations

This paper investigates the performance of randomly dithered first and higher-order sigma-delta quantization applied to the frame coefficients of a vector in a infinite-dimensional Hilbert space. We compute the mean square error resulting from linear reconstruction with the quantized frame coefficients. When properly dithered, this computation simplifies in the same way as under the assumption of the white-noise hypothesis. The results presented here are valid for a uniform mid-tread quantizer operating in the no-overload regime. We estimate the large-redundancy asymptotics of the error for each family of tight frames obtained from regular sampling of a bounded, differentiable path in the Hilbert space. In order to achieve error asymptotics that are comparable to the quantization of oversampled band-limited functions, we require the use of smoothly terminated frame paths.