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A Contour Integral Method for Time-Domain Response Calculations

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A fundamental aspect of loudspeaker modeling is the ability to calculate the time-domain response of a driver in free air or in a specified enclosure given prior calculation of the frequency response. This report presents a numerical method to compute the time-domain response of a loudspeaker or other transducer using contour integration of its frequency response. The approach is based on Weideman’s scheme for inversion of the Laplace transform along a parabolic contour, and it is applicable to analytic functions that contain isolated singularities (poles) and branch points in the left half-plane. The new approach is motivated by the need to implement viscoelastic and semi-inductance effects into linear and nonlinear, time-dependent transducer calculations. Because the response functions that describe these phenomena contain fractional power and logarithmic singularities, solution methods based on rational function decomposition cannot be used. The new method is simple to implement, requires few function evaluations, and is remarkably accurate. For analyzing the step response in box models, the proposed contour method based on Weideman can be universally applied with only a few additional lines of new code.

JAES Volume 66 Issue 5 pp. 360-368; May 2018
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