The growing field of the Internet of Things relies at the bottom on components with very scarce computing resources that currently do not allow complex processing of sensed data. Any computation involving Fast Fourier Transforms (FFT), Wavelet Transforms (WT), or simple sines and cosines is considered impractical on low-end devices due to the lack of floating point and math libraries. This article presents new techniques that make it possible to use these functions also on severely constrained target platforms. Current literature abounds with schemes to compute sine and cosine functions, with focus on speed, hardware footprint, software size, target type, or precision. Even so, there is no practical exploration of the design space available for embedded devices with limited resources, in particular when only integer operations are possible. We select an efficient set of recursive sine and cosine generators and measure the frequency, amplitude, and phase error over a wide parameter range. We show that their simplicity allows them to be implemented on the most bare targets with good precision, reducing power consumption and size while being the fastest on integer-only processors. We also introduce specially tailored FFT and WT algorithms and show that they are usable in practice while having an extremely small code footprint, good precision, and high speed.

中文翻译：

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为低功耗定点处理器适配递归正弦软件振荡器

物联网不断发展的领域在底层依赖于计算资源非常稀缺的组件，这些组件目前不允许对感知数据进行复杂的处理。由于缺乏浮点和数学库，任何涉及快速傅立叶变换 (FFT)、小波变换 (WT) 或简单正弦和余弦的计算在低端设备上都被认为是不切实际的。本文介绍了使这些功能也可以在严重受限的目标平台上使用的新技术。当前的文献中充斥着计算正弦和余弦函数的方案，重点是速度、硬件占用空间、软件大小、目标类型或精度。即便如此，对于资源有限的嵌入式设备的可用设计空间也没有实际探索，特别是当只能进行整数运算时。我们选择了一组高效的递归正弦和余弦发生器，并在很宽的参数范围内测量频率、幅度和相位误差。我们表明，它们的简单性使它们能够以良好的精度在最裸露的目标上实现，降低功耗和尺寸，同时在纯整数处理器上是最快的。我们还介绍了专门定制的 FFT 和 WT 算法，并表明它们在实践中可用，同时具有极小的代码占用空间、良好的精度和高速。降低功耗和尺寸，同时在纯整数处理器上速度最快。我们还介绍了专门定制的 FFT 和 WT 算法，并表明它们在实践中可用，同时具有极小的代码占用空间、良好的精度和高速。降低功耗和尺寸，同时在纯整数处理器上速度最快。我们还介绍了专门定制的 FFT 和 WT 算法，并表明它们在实践中可用，同时具有极小的代码占用空间、良好的精度和高速。