A Finite State Space Model for Representing the Broadband Infinite Series for Acoustic Reverberation between Parallel Reflecting Planes
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-06-04
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Panza, Michael J.. 2018. A Finite State Space Model for Representing the Broadband Infinite Series for Acoustic Reverberation between Parallel Reflecting Planes. Mathematical Problems in Engineering،Vol. 2018, no. 2018, pp.1-16.
https://search.emarefa.net/detail/BIM-1206361
Modern Language Association (MLA)
Panza, Michael J.. A Finite State Space Model for Representing the Broadband Infinite Series for Acoustic Reverberation between Parallel Reflecting Planes. Mathematical Problems in Engineering No. 2018 (2018), pp.1-16.
https://search.emarefa.net/detail/BIM-1206361
American Medical Association (AMA)
Panza, Michael J.. A Finite State Space Model for Representing the Broadband Infinite Series for Acoustic Reverberation between Parallel Reflecting Planes. Mathematical Problems in Engineering. 2018. Vol. 2018, no. 2018, pp.1-16.
https://search.emarefa.net/detail/BIM-1206361
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1206361