P.A. Nelson

Active noise control

Active noise control exploits the long wavelengths associated with low frequency sound. It works on the principle of destructive interference between the sound fields generated by the original primary sound source and that due to other secondary sources, acoustic outputs of which can be controlled. The acoustic objectives of different active noise control systems and the electrical control methodologies that are used to achieve these objectives are examined. The importance of having a clear understanding of the principles behind both the acoustics and the electrical control in order to appreciate the advantages and limitations of active noise control is emphasized. A brief discussion of the physical basis of active sound control that concentrates on three-dimensional sound fields is presented.<<ETX>>

Fast deconvolution of multichannel systems using regularization

A very fast deconvolution method, which is based on the fast Fourier transform (FFT), can be used to control the outputs from a multichannel plant comprising any number of control sources and error sensors. The result is a matrix of causal finite impulse response filters whose performance is optimized at a large number of discrete frequencies. The paper is particularly aimed at multichannel sound reproduction and more specifically reproducing the sound field from a set of loudspeakers.

In-flight experiments on the active control of propeller-induced cabin noise

Abstract Results are presented of a series of in-flight experiments on the active contrl of propeller-induced passenger cabin noise in a B.Ae. 748 aircraft. Twenty-six configurations of up to 16 loudspeakers and 32 microphones were investigated at the first three harmonics of the blade passage frequency. Two loudspeaker distributions, which were either evenly distributed or partly concentrated in the plane of the propellers, gave similar reductions in the sum of the squares of the measured pressures at the fundamental blade passage frequency (88 Hz) of about 13 dB. Concentrating the loudspeakers near the propeller plane increased the reductions in the second and third harmonics (176 Hz and 264 Hz) from about 9 dB and 6 dB respectively for the equally distributed system, to about 12 dB for both harmonics. Subjective reductions in noise level with all three harmonics being simultaneously controlled were pronounced, with reductions of over 7 dB(A) being recorded at some seat locations. Also reported are additional experiments, with a local (two-loudspeaker, two-microphone) control system used for a single seat, and with the 16 loudspeaker, 32 microphone control system used to control the noise inside the cabin when the engines were run-up on the ground.

The active minimization of harmonic enclosed sound fields, part I: Theory

Abstract An analysis is presented of the effectiveness with which active methods can be used for producing global reductions in the amplitude of the pressure fluctuations in a harmonically excited enclosed sound field. The total time averaged acoustic potential energy is expressed as a quadratic function of the complex strengths of a number of secondary sources of sound introduced into the enclosure. For a given number and location of secondary sources, there is a unique set of source strengths which determines the minimum value of this function. The analysis is applied to the case of a lightly damped enclosure excited by a point primary source at a frequency above the Schroeder cut-off frequency. It is demonstrated that substantial reductions in the total time averaged acoustic potential energy are possible only if the secondary sources of sound are located at a distance from the primary source which is less than half a wavelength at the frequency of interest.

Fluid dynamics of a flow excited resonance, Part II: Flow acoustic interaction

Abstract This is the second of two companion papers in which the physics and detailed fluid dynamics of a flow excited resonance are examined. The approach is rather different from those previously used, in which stability theory has been applied to small wavelike disturbances in a linearly unstable shear layer, with an equivalent source driving the sound field which provides the feedback. In the approach used here, the physics of the flow acoustic interaction is explained in terms of the detailed momentum and energy exchanges occurring inside the fluid . Gross properties of the flow and resonance are described in terms of the parameters necessary to determine the behaviour of the feedback system. In this second paper it is shown that two relatively distinct momentum balances can be considered in the resonator neck region. One can be identified with the vortically induced pressure and velocity fluctuations and the other with the reciprocating potential flow. The fluctuating Coriolis force caused by the interaction of the potential and vortical flows is shown to be the only term in the linearized momentum equation which is not directly balanced by a fluctuating pressure gradient. This force provides the mechanism for the exchange of the mean energies associated with the mean and fluctuating momenta, respectively. A source and sink of energy are identified in which mean energy associated with fluctuating momentum is extracted from and returned to the mean flow, respectively. The imbalance between the source and sink is responsible for both the radiated acoustic power and the power carried away by the vortices as they convect downstream. This radiated acoustic power and vortically convected power, and the source and sink powers, are all of the same order of magnitude. With the vortex shedding and reciprocating potential flow “phase locked” the amplitude of the steady state oscillations is determined by the condition that the net power produced in the resonator neck (the source power less the sink power) is equal to the sum of the radiated acoustic power and that carried by the vortices.

Reproduction of plane wave sound fields

The problem of reproducing a desired sound field in space, not just at a number of discrete points, but over a continuous two‐dimensional area, is investigated. In theory, any sound field can be reconstructed perfectly in a given region by using a continuous monopole/dipole layer, but this is obviously not possible in practice. This paper attempts to give some quantitative measures of the extent to which a given sound field can be reproduced by using a number of discrete monopole sources. Some of the physical limitations that apply to any sound reproduction system are illustrated by studying a simple model. The desired sound field is a plane wave, the sources are ideal monopoles in a free field, and the optimal source accelerations are calculated using the traditional least‐squares method. All calculations are undertaken in the frequency domain, and three different loudspeaker arrangements are studied. The results clearly demonstrate that the quality of the reproduced sound field is mainly determined by t...

The behavior of a multiple channel active control system

The convergence behavior of an adaptive feedforward active control system is studied. This adjusts the outputs of a number of secondary sources to minimize a cost function comprising a combination of the sum of mean-square signals from a number of error sensors (the control error) and the sum of the mean-square signals fed to the secondary sources (the control effect). A steepest descent algorithm which performs this function is derived and analyzed. It is shown that some modes not only converge slowly but also require an excessive control effort for complete convergence. This ill-conditioned behavior can be controlled by the proper choice of the cost function minimized. Laboratory experiments using a 16-loudspeaker 32-microphone control system to control the harmonic sound in an enclosure are presented. The behavior of the practical system is accurately predicted from the theoretical analysis of the adaptive algorithm. The effect of errors in the assumed transfer matrix used by the steepest descent algorithm is briefly discussed. >

Adaptive inverse filters for stereophonic sound reproduction

A general theoretical basis for the design of adaptive digital filters used for the equalization of the response of multichannel sound reproduction systems is described. The approach is applied to the two-channel case and then extended to deal with arbitrary numbers of channels. The intention is to equalize not only the response of the loudspeakers and the listening room but also the crosstalk transmission from right loudspeaker to left ear and vice versa. The formulation is a generalization of the Atal-Schroeder crosstalk canceler. However, the use of a least-squares approach to the digital filter design and of appropriate modeling delays potentially allows the effective equalization of nonminimum phase components in the transmission path. A stochastic gradient algorithm which facilitates the adaptation of the digital filters to the optimal solution, thereby providing the possibility of designing the filters in situ, is presented. Some experimental results for the two-channel case are given. >

Fluid dynamics of a flow excited resonance, part I: Experiment

This is the first of two companion papers concerned with the physics and detailed fluid dynamics of a flow excited resonance. The phenomenon has been examined by using a rather different approach from others to date, in which usually stability theory has been applied to small wave-like disturbances in an unstable shear layer with an equivalent source to describe the radiation of sound providing the feedback. The physics of the flow acoustic interaction is explained in terms of the detailed momentum and energy exchanges occurring in the fluid itself. Gross properties of the flow and resonance are described in terms of the parameters necessary to determine the behaviour of the self-oscillatory system. In this first paper a full experimental investigation of a flow excited Helmholtz resonator is described, in which the detailed fluid dynamical and acoustic data necessary to develop a mathematical model for the flow was obtained, and a new theory of the interaction process is presented in the companion paper (Part II). The investigation described involved the use of a two-component Laser-Doppler Velocimeter (L.D.V.) and probe microphones to specify completely the velocity and pressure fields and a flow visualization to give qualitative information of the vortex shedding process. The overall aim of the work described in the two papers was to increase fundamental understanding of flow/acoustic interactions.

The active minimization of harmonic enclosed sound fields, part II: A computer simulation

Abstract This paper is Part II in a series of three papers on the active minimization of harmonic enclosed sound fields. In Part I it was shown that in order to achieve appreciable reductions in the total time averaged acoustic potential energy, Ep, in an enclosed sound field of high modal density then the primary and secondary sources must be separated by less than one half wavelength, even when a relatively large number of secondary sources are used. In this report the same theoretical basis is used to investigate the application of active control to sound fields of low modal density. By the use of a computer model of a shallow rectangular enclosure it is demonstrated that whilst the reductions in Ep which can be achieved are still critically dependent on the source locations, the criteria governing the levels of reduction are somewhat different. In particular it is shown that for a lightly damped sound field of low modal density substantial reductions in Ep can be achieved by using a single secondary source placed greater than half a wavelength from the primary source, provided that the source is placed at a maximum of the primary sound field. The problems of applying this idealized form of active noise control are then discussed, and a more practical method is presented. This involves the sampling of the sound field at a number of discrete sensor locations, and then minimizing the sum of the squared pressures at these locations. Again by use of the computer model of a shallow rectangular enclosure, the effects of the number of sensors and of the locations of these sensors are investigated. It is demonstrated that when a single mode dominates the response near optimal reductions in Ep can be achieved by minimizing the pressure at a single sensor, provided the sensor is at a maximum of the primary sound field. When two or three modes dominate the response it is found that if only a limited number of sensors are available then minimizing the sum of the squared pressures in the corners of the enclosure gives the best reductions in Ep. The reasons for this behaviour are discussed.