A Nonparametric Approach for Multicomponent AM–FM Signal Analysis

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 (CF¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{\text {CF}}$$\end{document}) and standard deviations (σCF\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma _{\text {CF}}$$\end{document}) 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 (MSEAE\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {MSE}_{\text {AE}}}$$\end{document}), mean square error between actual and estimated instantaneous frequencies (MSEIF\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {MSE}_{\text {IF}}}$$\end{document}) 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.