Multi-component instantaneous frequency estimation using signal decomposition and time-frequency filtering
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ORIGINAL PAPER
Multi-component instantaneous frequency estimation using signal decomposition and time-frequency filtering Jamal Akram1
· Nabeel Ali Khan2 · Sadiq Ali3 · Adeel Akram4
Received: 26 January 2020 / Revised: 12 May 2020 / Accepted: 14 May 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract A novel method is presented for the instantaneous frequency estimation of multi-component signals with crossing signatures in the time-frequency domain. The proposed method uses a combination of Eigen decomposition of time-frequency distributions and time-frequency filtering to recursively extract signal components from the original mixture and estimate their instantaneous frequencies. The proposed algorithm outperforms other algorithms of similar complexity in terms of mean square error accuracy. Keywords Time-frequency · Instantaneous frequency · Wigner–Ville distribution · Eigen-decomposition · Ridge tracking · Ridge path regrouping
1 Introduction Many real-life signals are non-stationary in nature, i.e., their spectra change with time. Conventional spectral analysis techniques that assume signal stationarity thus fail to give suitable representation for these signals. Joint timefrequency distributions (TFDs) and multi-rate signal processing methods are powerful tools for the analysis and processing of such signals [1–10]. TFDs concentrate the signal energy along the instantaneous frequency (IF) curves thus
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Jamal Akram [email protected] Nabeel Ali Khan [email protected] Sadiq Ali [email protected] Adeel Akram [email protected]
1
Computer Engineering, University of Engineering and Technology, Taxila, Pakistan
2
Electrical Engineering, Foundation University, Islamabad, Pakistan
3
Electrical Engineering, University of Engineering and Technology, Peshawar, Pakistan
4
Telecom Engineering, University of Engineering and Technology, Taxila, Pakistan
making it an important parameter for the non-stationary signal analysis. Its accurate estimation helps in a number of applications including blind source separation [11–13], Direction of Arrival Estimation [14,15], signal detection [16], feature extraction [17,18], sparse reconstruction [19], electroencephalogram (EEG) signal modeling and classification [8] and jammer excision [9]. IF estimation methods can be broadly classified into two categories: parametric methods and nonparametric methods. Parametric methods generally achieve better performance, but they require the IF to follow a particular mathematical model [20–22]. Nonparametric methods generally involve (a) computation of a reduced interference TFD and (b) detection and tracking of ridges to estimate the IF [23–25]. A number of IF estimation methods have been developed for mono-component signals or signals with non-overlapping time-frequency (TF) signatures [26]. However, for signals with intersecting TF signature the IF estimation becomes a challenging task as the IF estimation algorithm may follow a wrong path after intersection point. The prob
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