In this paper, a novel method is presented to analyze the amplitude modulated and frequency modulated (AM–FM) multicomponent signals using a combination of the variational mode decomposition (VMD) and the discrete energy separation algorithm (DESA). In the presented method, firstly, a multicomponent signal is decomposed using VMD method applied in an iterative way. In order to separate the monocomponent signals from multicomponent signal, a suitable convergence criterion is developed based on the values of estimated center frequencies ( $$\overline{\text {CF}}$$ CF ¯ ) and standard deviations ( $$\sigma _{\text {CF}}$$ σ CF ) of the decomposed components. Further, the estimation of amplitude envelope and the instantaneous frequency functions of monocomponent AM–FM signals has been carried out by employing DESA. Moreover, the proposed method is also applied on the synthetic AM–FM signal and speech signals to evaluate its performance. Furthermore, its performance is also compared with the Fourier–Bessel series expansion-based DESA, empirical wavelet transform-based DESA, and iterative eigenvalue decomposition-based DESA methods. The performance of the proposed method is compared with the other methods in terms of mean square error between actual and estimated amplitude envelopes ( $${\text {MSE}_{\text {AE}}}$$ MSE AE ), mean square error between actual and estimated instantaneous frequencies ( $${\text {MSE}_{\text {IF}}}$$ MSE IF ) for synthetic signal. The COSH distance measure is used as a performance measure for speech signals. It is found that the proposed method gives better results in terms of performance measures in several cases.

中文翻译：

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多分量 AM-FM 信号分析的非参数方法

在本文中，提出了一种使用变分模式分解 (VMD) 和离散能量分离算法 (DESA) 的组合来分析调幅和调频 (AM-FM) 多分量信号的新方法。在所提出的方法中，首先，使用以迭代方式应用的VMD方法来分解多分量信号。为了将单分量信号与多分量信号分开，基于估计的中心频率值 ($$\overline{\text {CF}}$$CF¯ ) 和标准偏差 ($$\sigma _{\text {CF}}$$ σ CF ) 的分解成分。此外，单分量 AM-FM 信号的幅度包络和瞬时频率函数的估计已通过使用 DESA 进行。而且，所提出的方法还应用于合成 AM-FM 信号和语音信号以评估其性能。此外，还将其性能与基于傅立叶-贝塞尔级数展开的 DESA、基于经验小波变换的 DESA 和基于迭代特征值分解的 DESA 方法进行了比较。在实际和估计幅度包络之间的均方误差 ( $${\text {MSE}_{\text {AE}}}$$ MSE AE )、均方合成信号的实际和估计瞬时频率（ $${\text {MSE}_{\text {IF}}}$$ MSE IF ）之间的误差。COSH 距离度量用作语音信号的性能度量。发现所提出的方法在几种情况下在性能测量方面给出了更好的结果。