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首页> 外文期刊>Mathematical Problems in Engineering >A Finite State Space Model for Representing the Broadband Infinite Series for Acoustic Reverberation between Parallel Reflecting Planes
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A Finite State Space Model for Representing the Broadband Infinite Series for Acoustic Reverberation between Parallel Reflecting Planes

机译：表示平行反射平面之间声学混响的宽带无限级数的有限状态空间模型

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摘要

The acoustic reverberation between two parallel reflecting planes can be represented by an infinite series of the images caused by the planes. To provide a more useful model for analysis and control, the infinite series version of the Green's function is converted into a finite state space model that retains the high frequency character that enables broadband noise inputs to be examined. The infinite series is first summed into a very accurate, approximate closed form expression in the time domain in terms of a radical function. The radical is then transformed into an expression containing exponentials which have exact Laplace transforms that lead to an overall closed form transfer function for the system. The system transfer function is transformed into a third-order state space model that theoretically contains all of the frequency characteristics of the infinite series representation. The accuracy of the state space model is examined by comparing it to the infinite series solution for three typical types of acoustical inputs: exponential for impulse noise, single frequency sine for harmonic noise, and a multifrequency Schroeder phased harmonic sequence for random noise.
机译：两个平行反射平面之间的声音混响可以由平面引起的无穷系列图像表示。为了提供更有用的分析和控制模型，格林函数的无限级数版本被转换为有限状态空间模型，该模型保留了允许检查宽带噪声输入的高频特性。首先根据时基函数将无穷级数求和成一个非常精确的近似封闭形式的时域表达式。然后将部首转换为包含指数的表达式，这些指数具有精确的拉普拉斯变换，从而导致系统具有整体封闭式传递函数。将系统传递函数转换为一个三阶状态空间模型，该模型理论上包含无限级数表示形式的所有频率特性。通过将状态空间模型与三种典型声学输入的无穷级解进行比较，来检验状态空间模型的准确性：用于脉冲噪声的指数函数，用于谐波噪声的单频正弦函数和用于随机噪声的多频Schroeder相谐波序列。

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