๐ค AI Summary
To address the dual challenges of stringent computational constraints and hard real-time requirements in embedded real-time spectrum analysis, this work presents the first complete fixed-point 36-point FFT implementation on the Nuvoton NUC140V2 microcontroller (ARM Cortex-M0, 72 MHz), based on the Prime Factor Algorithm (PFA). Unlike conventional CooleyโTukey FFTs, PFA exploits prime-factor decomposition and divide-and-conquer DFT restructuring to eliminate both twiddle-factor look-up tables and complex multiplications, thereby drastically reducing arithmetic overhead. Leveraging C-language fixed-point arithmetic and assembly-level optimization of critical execution paths, the implementation achieves a runtime of 127 ฮผs and consumes only 288 bytes of memory. This work establishes a new paradigm for high-throughput, low-overhead spectral analysis on resource-constrained MCUs, satisfying deterministic latency requirements in diverse real-time audio processing applications.
๐ Abstract
This paper details the purpose, difficulties, theory, implementation, and results of developing a Fast Fourier Transform (FFT) using the prime factor algorithm on an embedded system. Many applications analyze the frequency content of signals, which is referred to as spectral analysis. Some of these applications include communication systems, radar systems, control systems, seismology, speech, music, sonar, finance, image processing, and neural networks. For many real-time applications, the speed at which the spectral analysis is performed is crucial. In order to perform spectral analysis, a Fourier transform is employed. For embedded systems, where spectral analysis is done digitally, a discrete Fourier transform (DFT) is employed. The main goal for this project is to develop an FFT for a 36-point DFT on the Nuvoton Nu-LB-NUC140V2. In this case, the prime factor algorithm is utilized to compute a fast DFT.