基于快速傅里叶变换的正弦信号频率高精度估计算法

doi:10.11772/j.issn.1001-9081.2015.11.3280

计算机应用 ›› 2015, Vol. 35 ›› Issue (11): 3280-3283.DOI: 10.11772/j.issn.1001-9081.2015.11.3280

基于快速傅里叶变换的正弦信号频率高精度估计算法

樊磊^1,2, 齐国清¹

1. 大连海事大学信息科学技术学院, 辽宁大连 116026;
2. 大连工业大学信息科学与工程学院, 辽宁大连 116034

收稿日期:2015-06-18 修回日期:2015-07-23 发布日期:2015-11-13
通讯作者: 樊磊(1980-),男,吉林长春人,讲师,博士研究生,主要研究方向:数字信号处理、信号检测与参数估计.
作者简介:齐国清(1960-),男,辽宁凌海人,教授,博士,主要研究方向:雷达、通信、图像信号处理.
基金资助:
国家863计划项目(2011AA110201).

High accuracy frequency estimation algorithm of sinusoidal signals based on fast Fourier transform

FAN Lei^1,2, QI Guoqing¹

1. College of Information Science and Technology, Dalian Maritime University, Dalian Liaoning 116026, China;
2. School of Information Science and Engineering, Dalian Polytechnic University, Dalian Liaoning 116034, China

Received:2015-06-18 Revised:2015-07-23 Online:2015-11-13

摘要/Abstract

摘要： 为了进一步提高加性高斯白噪声背景中正弦信号的频率估计精度,提出了一种新的基于插值快速傅里叶变换(FFT)的正弦信号频率估计算法.首先,对N点正弦采样序列进行等长度时域补零延长,再进行 2N 点FFT; 然后, 搜索幅度最大离散谱线位置得到频率粗估计值; 最后, 采用幅度最大谱线以及原信号的离散时间傅里叶变换(DTFT)在幅度最大谱线左右两侧的两点抽样值进行精估计.仿真结果表明,当信号实际频率位于FFT两条离散谱线之间任意位置时,所提算法的频率估计均方根误差均接近克拉美罗下限,具有较好的一致性,估计精度高于Candan算法、Fang算法、三谱线合理结合(RCTSL)算法和Aboutanios算法, 且信噪比阈值较低,估计性能优于现有频率估计算法.

关键词: 频率估计, 快速傅里叶变换, 正弦信号, 离散时间傅里叶变换, 数字信号处理

Abstract: In order to further improve the estimation precision of sinusoid frequency in additive white Gaussian noise background, a new frequency estimation algorithm of sinusoidal signals based on interpolated Fast Fourier Transform (FFT) was proposed. Firstly, zeros of length N were padded to the sinusoid sampled data of length N in the time domain. Next, 2N-point FFT was performed and the coarse estimation was made by searching the location of the discrete spectrum line with maximum amplitude. Finally, the fine estimation was made by utilizing the spectrum line with maximum amplitude and two sample values of Discrete-Time Fourier Transform (DTFT) of the original signal on the left and right side of the maximum spectrum line. Simulation results show that the root mean square error of the proposed estimator is close to the Cramer-Rao lower bound when the signal frequency locates anywhere between two neighboring FFT discrete spectral lines and the performance is stable. The estimation precision is higher than Candan estimator, Fang estimator, Rational Combination of Three Spectrum Lines (RCTSL) estimator and Aboutanios estimator. The proposed estimator also has lower signal-to-noise ratio threshold than the existing estimators.

Key words: frequency estimation, Fast Fourier Transform (FFT), sinusoid, Discrete-Time Fourier Transform (DTFT), Digital Signal Processing (DSP)

中图分类号:

TN911.72

樊磊, 齐国清. 基于快速傅里叶变换的正弦信号频率高精度估计算法[J]. 计算机应用, 2015, 35(11): 3280-3283.

FAN Lei, QI Guoqing. High accuracy frequency estimation algorithm of sinusoidal signals based on fast Fourier transform[J]. Journal of Computer Applications, 2015, 35(11): 3280-3283.

参考文献

[1] RIFE D C, BOORSTYN R R. Single-tone parameter estimation from discrete-time observations[J]. IEEE Transactions on Information Theory, 1974, 120(5): 591-598.
[2] RIFE D C, VINCENT G A. Use of the discrete Fourier transform in the measurement of frequencies and levels of tones[J]. Bell System Technical Journal, 1970, 49(2): 197-228.
[3] JAIN V K, COLLINS W L, DAVIS D C. High-accuracy analog measurements via interpolated FFT[J]. IEEE Transactions on Instrumentation and Measurement, 1979, 28(2): 113-122.
[4] QUINN B G. Estimating frequency by interpolation using Fourier coefficients[J]. IEEE Transactions on Signal Processing, 1994, 42(5): 1264-1268.
[5] QUINN B G. Estimation of frequency, amplitude and phase from the DFT of a time series [J]. IEEE Transactions on Signal Processing, 1997, 45(3): 814-817.
[6] QI G, JIA X. Accuracy analysis of frequency estimation of sinusoid based on interpolated FFT[J]. Acta Electronica Sinica, 2004,32(4): 625-629. (齐国清,贾欣乐. 插值FFT估计正弦信号频率的精度分析[J]. 电子学报,2004,32(4): 625-629.)
[7] JACOBSEN E, KOOTSOOKOS P. Fast, accurate frequency estimators [J]. IEEE Signal Processing Magazine, 2007, 24(3): 123-125.
[8] CANDAN C. A method for fine resolution frequency estimation from three DFT samples [J]. IEEE Signal Processing Letters, 2011, 18(6): 351-354.
[9] CANDAN C. Analysis and further improvement of fine resolution frequency estimation method from three DFT samples [J]. IEEE Signal Processing Letters, 2013, 20(9): 913-916.
[10] FANG L, DUAN D, YANG L. A new DFT-based frequency estimator for single-tone complex sinusoidal signals [C]// MILCOM 2012: Proceedings of the 2012 IEEE Military Communications Conference. Piscataway: IEEE, 2012:1-6.
[11] YANG C, WEI G. A noniterative frequency estimator with rational combination of three spectrum lines[J]. IEEE Transactions on Signal Processing, 2011, 59(10): 5065-5070.
[12] ABOUTANIOS E, MULGREW B. Iterative frequency estimation by interpolation on Fourier coefficients [J]. IEEE Transactions on Signal Processing, 2005, 53(4): 1237-1242.

[1]	孙鹏, 肖经, 赵海盟, 刘帆, 晏磊, 赵红颖. 基于DSP的无人机遥感影像SIFT算法设计与实现[J]. 计算机应用, 2020, 40(4): 1237-1242.
[2]	王爱珍, 胡姣, 韩航程. 基于级联随机共振的直接序列扩频信号的捕获方法[J]. 计算机应用, 2018, 38(7): 2020-2023.
[3]	唐国斐, 周海芳, 谭庆平. 基于多核DSP的星载并行遥感图像压缩系统设计与实现[J]. 计算机应用, 2017, 37(5): 1246-1250.
[4]	方建超, 毛雪松. 非等间隔采样信号傅里叶频谱分析方法[J]. 计算机应用, 2016, 36(2): 492-494.
[5]	黄胜兵, 郑启龙, 郭连伟. 分簇VLIW DSP上支持单双字模式选择的SIMD编译优化[J]. 计算机应用, 2015, 35(8): 2371-2374.
[6]	何婷婷, 彭元喜, 雷元武. 基于Goldschmidt算法的高性能双精度浮点除法器设计[J]. 计算机应用, 2015, 35(7): 1854-1857.
[7]	张毅刘钰然罗元. 基于视觉的手势识别方法及其在数字信号处理器上的实现[J]. 计算机应用, 2014, 34(3): 833-836.
[8]	索维毅赵荣彩姚远刘鹏. 面向DSP的超字并行指令分析和冗余优化算法[J]. 计算机应用, 2012, 32(12): 3303-3307.
[9]	黄一才郁滨. 基于蓝牙单芯片的复杂密码算法实现机制[J]. 计算机应用, 2012, 32(12): 3453-3455.
[10]	许杰麻军平何虎. 基于VLIW DSP 加密与认证算法的实现[J]. 计算机应用, 2012, 32(06): 1650-1653.
[11]	陶巍刘建平张一闻. 基于麦克风阵列的声源定位系统[J]. 计算机应用, 2012, 32(05): 1457-1459.
[12]	黎山易清明陈庆石敏. 适用于GPS软件接收机的弱信号捕获方法[J]. 计算机应用, 2012, 32(03): 816-818.
[13]	田克纯魏丽丁萌. 改进线性拟合的调制信号载波频率估计算法[J]. 计算机应用, 2012, 32(02): 374-380.
[14]	陈明宋宝唐小琦. 基于DSP和FPGA的网络转换网关[J]. 计算机应用, 2011, 31(10): 2617-2620.
[15]	陈海燕黄虹. 基于E-Bus的YHFT-DSP仿真测试平台的设计与实现[J]. 计算机应用, 2011, 31(04): 1129-1132.

基于快速傅里叶变换的正弦信号频率高精度估计算法

High accuracy frequency estimation algorithm of sinusoidal signals based on fast Fourier transform

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics