Lüke and power residue sequence diffusers

Dadiotis, K; Angus, JAS; Cox, TJ

Abstract

Conventional Schroeder diffusers have been successfully used for many years. However, their frequency range is limited by the flat plate effect that occurs when all the wells radiate in phase. This occurs at harmonics of p times the design frequency f(0), where p is the small prime that is used to generate the structure. A typical diffuser, using p=7 and f(0)=500 Hz, has an upper frequency limit of only 3.5 kHz. Achieving a first flat plate frequency above 20 kHz requires a prime equal to at least 41 and results in diffusers that are too big to be practical in most applications. This paper suggests an alternative approach using number theoretic sequences that, although short in length, are based on large integers. Two new sequences, Type-II Luke and power residue, have this desired characteristic. They are investigated using both simple models and the more exact boundary element method. The results show the flat plate effect is moved to much higher frequencies as expected. For Luke sequences at certain frequencies, redirection rather than dispersion is achieved. Modulation techniques can be used to mitigate these problems. Power residue sequences perform the best, providing good diffusion and a flat plate frequency outside the audible range.

Citation

Dadiotis, K., Angus, J., & Cox, T. (2008). Lüke and power residue sequence diffusers. ˜The œJournal of the Acoustical Society of America (Online), 123(4), 2035-2042. https://doi.org/10.1121/1.2885761

• Journal Article Type: Article
• Publication Date: Apr 1, 2008
• Deposit Date: Apr 13, 2011
• Publicly Available Date: Apr 5, 2016
• Journal: The Journal of the Acoustical Society of America (JASA)
• Print ISSN: 0001-4966
• Peer Reviewed: Peer Reviewed
• Volume: 123
• Issue: 4
• Pages: 2035-2042
• DOI: https://doi.org/10.1121/1.2885761
• Publisher URL: http://dx.doi.org/10.1121/1.2885761