ï~~sequently, if a realistic mode distribution is found, it
can be used with a wide variety of input and output
ports.
* Picking ni in the branch loss factors gi = 1 - 2-"'
as a function of Too appears hard to do exactly. An
approximate formula is to choose ni so that gTo/DI
close to 0.001, where Di is the delay of the ith waveguide in seconds.
* Reverberation is realistically diffuse if the steadystate reverberator response to a sinusoidal input signal has a Rayleigh distributed amplitude throughout
the delay elements of the reverberator [20]. Equivalently, the intensity is exponentially distributed,
phase is uniformly distributed, and the real and imaginary parts of the sinusoidal response phasor are
Gaussian distributed [20]. These distributions correspond physically to the excitation of many modes
of vibration in the hall, yielding plane waves traveling in "all directions" with independent random phases.
See also [1,7].
* Assuming a Rayleigh amplitude distribution allows
calculation of probability of overflow as a function
of the number of guard bits provided.
References
Reverberation and Architectural Acoustics
[1] P. M. Morse, Vibration and Sound, published by
the American Institute of Physics for the Acoustical
Society of America, 1976 (1st ed. 1936, 2nd ed. 1948).
[2] L. L. Beranek, Acoustics, McGraw-Hill, New York,
1954, 1960.
[3] B. B. Bauer, "Stereophonic earphones and binaural
loudspeakers," J. Audio Eng. Soc., vol. 9, no. 2, pp.
148-151, April 1961.
[4] M. R. Schroeder and B. F. Logan, "Colorless Artificial
Reverberation," J. Audio Eng. Soc., vol. 9, no. 3, pp.
192-, July 1961.
[5] L. L. Beranek, Music, Acoustics, and Architecture,
John Wiley and Sons, Inc., New York, 1962.
[6] M. R. Schroeder, "Natural Sounding Artificial Reverberation," J. Audio Eng. Soc., vol. 10, no. 3, pp.
219-223, July 1962.
[7] P. M. Morse and U. Ingard, Theoretical Acoustics,
McGraw-Hill, New York, 1968.
[8] M. R. Schroeder, "Digital Simulation of Sound Transmission in Reverberant Spaces," J. Acoust. Soc. Amer.,
vol. 47, no. 2, pp. 424--431 (part 1), Feb. 1970.
[9] M. R. Schroeder, "Improved Quasi-Stereophony and
Colorless Artificial Reverberation," J. Acoust. Soc.
Amer., vol. 33, pp. 1061- (part 1), Feb. 1970.
[10] B. M. Gibbs and D. K. Jones, "A Simple Image Method
for Calculating the Distribution of Sound Pressure
Levels within an Enclosure," Acustica, vol. 26, pp.
24-32, 1972.
[11] H. Kutruff, Room Acoustics, Applied Science Publishers,
London, 1973.
[12] M. R. Schroeder, "Computer Models for Concert Hall
Acoustics," A. J. P., vol. 41, pp. 461-471, April 1973.
[13] J. M. Chowning, J. M. Grey, L. Rush, and J. A.
Moorer, "Computer Simulation of Music Instrument
Tones in Reverberant Environments," Music Dept.
Tech. Rep. STAN-M-1, Stanford University, 1974.
[14] W. Jesteadt, C.C. Wier, and D.M. Green, "Intensity
Discrimination as a Function of Frequency and Sensation
Level," J. Acoust. Soc. Amer., vol. 61, no. 1, pp. 169 -177, Jan. 1977.
[15] J. M. Chowning, J. M. Grey, L. Rush, J. A. Moorer,
and L. Smith, "Simulation of Music Instrument Tones
in Reverberant Environments: Final Report," Music
Dept. Tech. Rep. STAN-M-8, Stanford University,
1978.
[16] J. A. Moorer, "About this Reverberation Business,"
Computer Music J., vol. 3, no. 2, pp. 13-28, 1979.
Reprinted in [24].
[17] J. B. Allen and D. A. Berkeley, "Image Method for
Efficiently Simulating Small-Room Acoustics," J. Acoust.
Soc. Amer., vol. 65, no. 4, pp. 943-950, April 1979.
[18] M. Barron and A. H. Marshall, "Spatial Impression
due to Early Lateral Reflections in Concert Halls: the
Derivation of a Physical Measure," J. Sound Vib., vol.
77, no. 2, pp. 211-232, Feb. 1981.
[19] M. R. Schroeder, "Modulation Transfer Function:
Definition and Measurement," Acustica, vol. 49, pp.
179-182, 1981.
[20] K. J. Ebeling, K. Freudenstein, and H. Alrutz, "Experimental Investigations of Statistical Properties of
Diffuse Sound Fields in Reverberation Rooms," Acustica,
vol. 51, no. 3, pp. 145-153, 1982.
[21] C. Sheeline, "An Investigation of the Effects of Direct
and Reverberant Signal Interactions on Auditory Distance Perception," Ph.D. Dissertation, Hearing and
Speech Sc. Dept., Stanford University, Nov. 1982. Music
Dept. Tech. Rep. STAN-M-13.
52
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