基于FPGA和Sinc插值的分数阶傅里叶变换建模与设计
Modeling and Design of Fractional Fourier Transform Based on FPGA and Sinc Interpolation
摘要: 分数阶傅里叶变换(FrFT)在信号和图像处理领域受到了广泛的关注。在FrFT离散形式的演变过程中，低计算复杂度对实际应用至关重要。提出了一种高效的现场可编程门阵列(FPGA)实现FrFT算法的方法。本文将FrFT的计算过程分解为一次卷积和两次乘法的同时，为了提高插值精度，采用了sinc插值作为插值算法，并采用有限脉冲响应滤波器组成卷积模块，提高了信号卷积的鲁棒性。针对FPGA器件XC7VX690T，采用simulink和verilog硬件描述语言(HDL)对所提出的体系结构进行了综合。所得结果与仿真结果非常接近。最后，讨论了体系结构设计和硬件要求以及体系结构中的组成模块。
Abstract: Fractional Fourier transform (FrFT) has received much attention in the field of signal and image processing. In the evolution of discrete forms of FrFT, low computational complexity is essential for practical applications. An efficient method of implementing FrFT algorithm using field programma-ble gate array (FPGA) is presented. In this paper, the calculation process of FRFT is decomposed into one convolution and two multiplications. At the same time, in order to improve the interpolation accuracy, sinc interpolation is used as the interpolation algorithm, and the convolution module is composed of finite impulse response filter, which improves the robustness of signal convolution. For FPGA device (XC7VX690T), simulink and verilog hardware description language (HDL) were used to analyze the proposed architecture. The obtained results are very close to the simulation results. Fi-nally, the architecture design and hardware requirements as well as the components of the archi-tecture are discussed.
文章引用：李尚恒, 丁召, 周骅. 基于FPGA和Sinc插值的分数阶傅里叶变换建模与设计[J]. 建模与仿真, 2023, 12(5): 4415-4424. https://doi.org/10.12677/MOS.2023.125402

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