Investigations in digital signal processing and electroacoustics

数字信号处理和电声学研究

• 批准号: 910-2007
• 负责人: Lipshitz, Stanley
• 金额: $ 1.09万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=366119
• 关键词: Investigations; digital; signal; processing; electroacoustics

This research falls into three distinct areas:(a) Many modern analogue-to-digital and digital-to-analogue conversion systems use an architecture known as a sigma-delta modulator.  These nonlinear dynamical systems, which are closely related to noise shapers, display behaviour that can appear to be chaotic, but which is actually completely deterministic.  Nevertheless, only the 1st-order sigma-delta modulator has thus far proved amenable to detailed mathematical analysis.  It is believed that a new insight into their behaviour, resulting from a recent discovery known as the "integer noise-shaping theorem," will allow a mathematical understanding to be achieved for a larger class of such systems.(b) The mathematical theory of dithered quantization and noise shaping, which we have developed primarily for digital audio applications over the past 20 years, is also applicable to image and video processing.  The full extension of the 1-dimensional audio results to 2-dimensional image processing requires the development of new theorems in the theory of functions of two complex variables -- specifically, the extension of Jensen's theorem, and of the properties of minimum-phase noise shapers, to two dimensions.  This will be the focus of this aspect of our research.(c) Low-frequency acoustic transducers have diaphragms that undergo excursions large enough that the linearized acoustic wave equation is not sufficiently precise to predict their behaviour.  In particular, a high-frequency transducer in close proximity to such a low-frequency transducer suffers both amplitude- and frequency-modulation effects due to this nonlinearity.  We shall investigate improved models to predict these effects and to control them.

这项研究分为三个不同的领域：(a)许多现代模数和数模转换系统使用一种称为sigma-delta调制器的架构。这些非线性动力系统与噪声形成器密切相关，表现出看似混乱的行为，但实际上是完全确定的。然而，迄今为止，只有一阶σ - δ调制器被证明可以进行详细的数学分析。据信，最近一项被称为“整数噪声整形定理”的发现将对它们的行为产生新的见解，这将使人们能够对更大类此类系统进行数学理解。(b)我们在过去20年中主要为数字音频应用开发的抖动量化和噪声整形的数学理论也适用于图像和视频处理。将一维音频结果完全扩展到二维图像处理需要在两个复杂变量的函数理论中发展新的定理-特别是詹森定理的扩展，以及最小相位噪声整形器的特性，到二维。这将是我们这方面研究的重点。(c)低频声波换能器的膜片承受足够大的偏移，以致线性化声波方程不够精确，无法预测其行为。特别是，由于这种非线性，靠近这种低频换能器的高频换能器会受到幅度和频率调制的影响。我们将研究改进的模型来预测和控制这些影响。