Adapting Recursive Sinusoidal Software Oscillators for Low-power Fixed-point Processors

Abstract

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.

The fast continuous wavelet transformation (fCWT) for real-time, high-quality, noise-resistant time–frequency analysis

“…Wavelib 21 was used as the benchmark's baseline algorithm as it is the reference CWT C/C++ library 9 , and most microcontrollers are programmed using C/C++. Wavelib 21 thus serves as a baseline for the reported speed-ups (Fig.…”

“…Consequently, the WT suffers from a high computational load. This prohibits its use with low-end hardware and for real-time applications 9 , as real-time computation requires an algorithmic computation time that is smaller than the signal's duration.…”

Design of a flight controller to achieve improved fault tolerance

“…The execution of the bank of observers, without considering interruptions, is performed in around 57000 clock cycles with the microcontroller running at 100 MHz, as the number of floating point operations remains constant. As the Cortex-M3 does not have an FPU, floating point operations are not efficient, and thus it takes a great toll on the processing time [22].…”