最小二乘法分离频率相近的正弦信号
The Separation of Similar Frequency Sinusoidal Signal Based on the Least Square Method
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摘要: 传统的快速傅里叶变换(FFT)可以有效地对正弦信号进行分析，但对于分析频率相近的正弦信号却存在很大的误差。该文提出了采用最小二乘法来分析该问题。该算法在观测矩阵的基础上，利用2范数最小的终止准则，通过求解超定方程组，辨识频率相近信号组成的特征参数。仿真结果表明，该方法可以精确地分析频率相近信号各组成部分，有效地抑制噪声的干扰，具有较好的噪声稳定性和频域分析能力，从而提高信号处理的效率与精度。
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关键词:
- 信号处理;FFT;最小二乘法
Abstract: Traditional FFT can effectively analyze the sinusoidal signal, but the very big error exists for analyzing the similar frequency sinusoidal signal. In this article, adopting Least Square (LS) method which can separate similar frequency sinusoidal signal is put forward. Characteristic parameters of separating similar frequency sinusoidal signal can be identified by satisfying termination criterion of 2-norm minimum and solving overdetermined equations on observation matrix. The simulation result shows that each component of similar frequency signal such as amplitude, phase angle can be separated from original signal, the interference of noise can effectively be restrained, noise stability and the frequency domain analysis ability become better, so the efficiency and precision of signal processing can be raised. -
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