基于快速傅里叶变换的正弦信号频率高精度估计算法

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.

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

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.