声表面波式叉指单侧倾斜加权的Morlet小波处理器研究

Morlet wavelet analysis has good localization properties both in time domain and frequency domain. However, Morlet wavelet transform algorithm needs a lot of mathematical operations and complex programmings, which has a large time complexity and space complexity, so its execution efficiency is low. Therefore, scientists hope to implement Morlet wavelet transform by making various wavelet transform devices. The applicant found that: If lengths of the electrodes hypotenuses of input interdigital transducer (IDT) for surface acoustic wave (SAW) wavelet transform device are designed according to the envelopes arc lengths of Morlet wavelet function, the aperture width is large and uniform, and the IDT is divided into 180° phases and two parts, the electrodes unilateral incline weighted Morlet wavelet transform processors using SAW devices can be fabricated. The purpose of this project is to explore the implementation of Morlet wavelet transform using SAW devices, relationship between impulse response function and Morlet wavelet function of SAW devices, the corresponding mathematic models are established. The samples of electrodes unilateral incline weighted Morlet wavelet transform processors using SAW devices are developed. This project will lay the theoretical and technical basis of this processor. The wavelet processor will be widely used in many fields such as communications, radar, satellite, sensor and so on. So this project has important theoretical and practical value.

Morlet小波分析在时域和频域同时具有良好的局部化性质，但Morlet小波变换算法需要大量的数学运算和复杂的编程，具有较大的时间复杂度和空间复杂度，执行效率低。因此，科学家们希望通过制作各种小波变换器件实现Morlet小波变换。申请者发现：声表面波器件换能器的叉指倾斜边长按照Morlet小波函数包络弧长加权，且采用大宽均匀孔径，同时叉指换能器分成反相180°两部分时，能够制作出声表面波式叉指单侧倾斜加权的Morlet小波处理器。本项目旨在探讨用声表面波器件实现Morlet小波变换的方法；声表面波器件的脉冲响应函数与Morlet小波函数之间的关系；建立相应的数学模型以及研制出叉指单侧倾斜Morlet小波处理器样品。此项目将奠定该处理器的理论和技术基础。该小波处理器将广泛应用于通信、雷达、卫星、传感器等诸多领域。因此该项目具有重要的理论意义和实用价值。

Morlet小波变换是时间频率的局部化分析，可以高效地从大量信号中提取有效信息，但需要大量的数学运算。因此，科学家们希望通过制作各种小波变换器件实现Morlet小波变换。本项目通过声表面波器件输入换能器的叉指按照Morlet小波函数包络弧长加权，且采用大宽均匀孔径，同时叉指换能器分成反相180°两部分时，能够制作出了声表面波式叉指单侧倾斜加权的Morlet小波处理器。研究了声表面波式叉指单侧倾斜加权的Morlet小波处理器的新理论，建立了用声表面波器件阵列实现Morlet小波变换的数学模型；研究了该处理器的物理参数与其性能的关系，找出了最佳结构；最后研制出了该处理器的样品。本项目奠定了该处理器的理论和技术基础。该处理器将广泛应用于通信、雷达、卫星、传感器等诸多领域。.研究结论如下：.（1）研究了下列几个关键问题：其一，波束偏离；其二，衍射问题；其三，体波问题；其四，通带波纹和旁瓣问题；其五，耦合模理论，其六，声表面波式器件重构问题。对这些问题提出了解决的方法。.（2）当声表面波器件输入换能器的叉指按照Morlet小波函数包络弧长加权，且采用大宽均匀孔径，同时叉指换能器分成反相180°两部分设计，输出换能器是指条相等重叠、均匀周期叉指换能器时，能够制作出声表面波式叉指单侧倾斜加权的Morlet小波处理器。