最小二乘法分離頻率相近的正弦信號(hào)
The Separation of Similar Frequency Sinusoidal Signal Based on the Least Square Method
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摘要: 傳統(tǒng)的快速傅里葉變換(FFT)可以有效地對(duì)正弦信號(hào)進(jìn)行分析，但對(duì)于分析頻率相近的正弦信號(hào)卻存在很大的誤差。該文提出了采用最小二乘法來(lái)分析該問(wèn)題。該算法在觀測(cè)矩陣的基礎(chǔ)上，利用2范數(shù)最小的終止準(zhǔn)則，通過(guò)求解超定方程組，辨識(shí)頻率相近信號(hào)組成的特征參數(shù)。仿真結(jié)果表明，該方法可以精確地分析頻率相近信號(hào)各組成部分，有效地抑制噪聲的干擾，具有較好的噪聲穩(wěn)定性和頻域分析能力，從而提高信號(hào)處理的效率與精度。
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關(guān)鍵詞:
- 信號(hào)處理;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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