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小波变换具有很强的信号分离能力，很容易把随机噪音从信号中分离出来，从而提高信号的信噪比。本文把小波变换引入到因子分析中，提出了基于小波变换平滑主成分分析，该算法既保留普通主成分分析的正交分解，又具备了小波变换的信号分离能力。模拟数据和实验数据的结果表明，该算法具有从低信噪比的数据中提取出有用信息，并提高信号的信噪比。迭代目标变换因子分析处理实验数据的结果表明，基于小波变换平滑主成分分析的处理结果优于普通主成分分析。
Wavelet transform has a strong signal separation capability, it is easy to separate random noise from the signal, thereby enhancing the signal to noise ratio. In this paper, the wavelet transform is introduced into factor analysis, and the principal component analysis based on wavelet transform smoothing is proposed. The algorithm not only preserves the orthogonal decomposition of common principal component analysis, but also possesses the signal separation ability of wavelet transform. The results of simulation data and experimental data show that this algorithm can extract useful information from low signal-to-noise ratio data and improve signal-to-noise ratio. The results of iterative target transform factor analysis and processing of experimental data show that the result of smoothing principal component analysis based on wavelet transform is better than that of ordinary principal component analysis.