A Linear System Approach to Room Acoustics

Taking the variables that effect the propagation of sound in a room, such as properties of the room confines, objects in the room, air absorption, etc., and assuming they are linear operators, we can formulate a linear system approach to room acoustics. Given the impulse response of a linear system, it is possible to find by analysis all the properties of the system, whether in the time domain or frequency domain. In relation to any two fixed points in a room, one for source input and the other for received signal pickup, by use of the principles of correlation, a method is available to derive the impulse response of the room. (This is one of several methods, but it is straightforward and successful in practical applications.) It follows that by experimentally determining the impulse response function of the system considered one can obtain in situ values of transmission and reflection coefficients, energy decay rates, and parameters required for prediction of sound levels from multiple coherent sound sources. Use is made of the correlation function a second time to generate standard acoustic quantities from the available impulse response function. [Supported in part by two grants from NASA.]