FAST real time sine wave Locking And trackiNg devicEs (FASTSINE)

波是物质世界的基本组成部分。在自然界中，它们是由钟摆等振荡器发射的，人们故意产生和传输波来携带信息。在这两种情况下，波都不是完全静态的，但可能具有缓慢或快速变化的幅度、频率和相位。其中一些特征相对容易监控，例如波幅。其他的，特别是频率和相移，则更难测量。事实上，用于准确定位波中的频率和相移的方法是许多通信系统的核心使能技术。普通的调频广播电路就是这种解码算法的早期例子。如今，我们对用波传输数字数据很感兴趣，我们需要快速、简单的算法来确定嵌入在噪声背景中的数字化波列的频率和相位含量。在某些情况下，波列可能是自然的-当我们研究机械振荡器，如引力波探测器的悬挂镜时，相位或频率的移动可能是由于悬挂线中的温度波动或应变释放。我为研究这种振荡而开发的方法被证明对于监测具有其他目的的波列的相位和频率也特别有效，包括在通信行业中产生和传输的波列，以及进入示波器和其他高端测试和测量设备的波列。此外，大自然是我们可能会发现有用和有趣的其他波的来源，比如脑电图仪测量的脑电波，或者冲突期间用于通信的令人困惑的混合波列。在这些情况下，快速解释在波动的波的相位和频率中编码的信息的方法也可能是有用和重要的。拟议的项目采用了我开发的算法，并将它们应用于对商业公司和社会都具有实际重要性的现实世界情况。尽管我开发的算法在数学上相当复杂，但它们是在迭代方程中实现的，迭代方程只使用乘法和除法等简单的数学运算，从而使它们能够快速地以数字方式实现。这些算法的商业潜力相当令人兴奋，我们当然期待在接下来的几个月里继续探索这些可能性。

Waves are a fundamental part of the physical world. In nature, they are emitted by oscillators such as a pendulum, and people deliberately generate and transmit waves to carry information. In both of these cases, the waves are not entirely static, but may have an amplitude, frequency, and phase that exhibit slow or rapid changes. Some of these characteristics are relatively easy to monitor, such as the wave amplitude. Others, particularly frequency and phase shifts, are more difficult to measure. In fact, methods for accurately locating frequency and phase shifts in a wave are a central enabling technology for many communications systems. An ordinary FM radio circuit is an early example of such a decoding algorithm. Nowadays, we are interested in transmitting digital data using waves, and we need fast, simple algorithms for determining the frequency and phase content of a digitised wave train embedded in a noisy background. In some cases, the wave trains may be natural - when we are studying a mechanical oscillator such as the suspended mirror of a gravitational wave detector, and the shifts in phase or frequency may be due to temperature fluctuations or strain releases in the suspension wire.Methods I have developed for the purpose of studying such oscillations have proved also particularly effective for monitoring the phase and frequency of wave trains having other purposes, including those generated and transmitted in the communications industry, and those entering oscilloscopes and other high-end pieces of test and measurement equipment. Furthermore, nature is a source of other waves that we may find useful and interesting, like brain waves measured by electroencephelographs or the confusing mixture of wave trains used for communications during conflicts. In these cases too, methods for rapidly interpreting the information encoded in the fluctuating phase and frequency of the waves may be useful and important.The proposed project takes the algorithms I have developed and applies them to real-world situations of practical importance both to commercial companies and to society. The algorithms I have developed, though mathematically quite sophisticated, are realised in iteration equations that utilise only simple mathematical operations like multiplies and divides, making them fast to implement digitally. The commercial potential of these algorithms is quite exciting, and we are certainly looking forward to continuing our exploration of these possibilities in the coming months.