Time-frequency represetation of radar signals using Doppler-Lag block searching Wigner-Ville distribution

Radar signals are time-varying signals where the signal parameters change over time. For these signals, Quadratic Time-Frequency Distribution (QTFD) offers advantages over classical spectrum estimation in terms of frequency and time resolution but it suffers heavily from cross-terms. In generating accurate Time-Frequency Representation (TFR), a kernel function must be able to suppress cross-terms while maintaining auto-terms energy especially in a non-cooperative environment where the parameters of the actual signal are unknown. Thus, a new signal-dependent QTFD is proposed that adaptively estimates the kernel parameters for a wide class of radar signals. The adaptive procedure, Doppler-Lag Block Searching (DLBS) kernel estimation was developed to serve this purpose. Accurate TFRs produced for all simulated radar signals with Instantaneous Frequency (IF) estimation performance are verified using Monte Carlo simulation meeting the requirements of the Cramer-Rao Lower Bound (CRLB) at SNR > 6 dB

Instantaneous Frequency Estimation and Signal Separation Using Fractional Continuous Wavelet Transform

In the signal processing field, time-frequency representations (TFR\u27s) have intensively been improved to provide effective and powerful tools for reliable signal analysis. One of the most valuable and frequently used tools is Fourier transform (FT) which has been used to study the frequency content of stationary signals in the Fourier domain (FD). However, FT is not sufficient to study the frequency of non-stationary signals. For this particular type of signals to be best analyzed, some transforms such as the short time Fourier transform (STFT) and the continuous wavelet transform (CWT) have been introduced to provide us with a signal representation in the time-frequency plane. Another transform based on STFT and CWT; namely, the synchrosqueezing transform (SST), was introduced to improve the sharpness of the TFR\u27s by assigning the coefficient value to a different point in the TF plane. Also, TFR\u27s with satisfactory energy concentration and the corresponding SST’s involving both time and frequency variables were introduced; namely, the instantaneous frequency-embedded STFT (CWT) (IFE-STFT/IFE-CWT), where a rough estimation of the IF of a targeted component was used to achieve an accurate IF estimation. Recently, the STFT, the CWT and the corresponding SST’s with a time-varying window width are proposed and studied. These transforms have shown the confidence in the accuracy of both sharpening the TFR and separating the components of a multicomponent non-stationary signal, which then led to obtain a more accurate component retrieval formula at any local time. In order to improve the time-frequency resolutions, the concept of fractional Fourier transform (FrFT) was introduced as a potent tool to analyze time-varying signals; however, it fails in locating the frequency content in the fractional Fourier domain (FrFD). To this regard, the short time fractional FT (STFrFT) and the fractional CWT (FrCWT) were proposed to solve this issue by displaying the time and FrFD-frequency contents jointly in the time-FrFD-frequency plane. In this dissertation, we provide a component retrieval formula for a multicomponent signal from its FrCWT with integral involving only the scale variable and then introducing the corresponding SST (FrWSST). We also introduce the first and second order SST based on the IFE-CWT (IFE-WSST) and then propose time-FrFD-frequency representations with satisfactory energy concentration; namely, IFE-FrCWT and the corresponding SST (IFE-FrWSST). Lastly, we consider the FrCWT with a time-varying window width; namely, the adaptive FrCWT (AFrCWT) and the corresponding SST (AFrWSST). We propose these TFR\u27s in the FrFD for the purpose of not only improving the accuracy of the IF estimation and the energy concentration of these transforms, but also enhancing the separation conditions for the components of a multicomponent signal to be retrieved more accurately

Radon spectrogram-based approach for automatic IFs separation

The separation of overlapping components is a well-known and difficult problem in multicomponent signals analysis and it is shared by applications dealing with radar, biosonar, seismic, and audio signals. In order to estimate the instantaneous frequencies of a multicomponent signal, it is necessary to disentangle signal modes in a proper domain. Unfortunately, if signal modes supports overlap both in time and frequency, separation is only possible through a parametric approach whenever the signal class is a priori fixed. In this work, time-frequency analysis and Radon transform are jointly used for the unsupervised separation of modes of a generic frequency modulated signal in noisy environment. The proposed method takes advantage of the ability of the Radon transform of a proper time-frequency distribution in separating overlapping modes. It consists of a blind segmentation of signal components in Radon domain by means of a near-to-optimal threshold operation. The inversion of the Radon transform on each detected region allows us to isolate the instantaneous frequency curves of each single mode in the time-frequency domain. Experimental results performed on constant amplitudes chirp signals confirm the effectiveness of the proposed method, opening the way for its extension to more complex frequency modulated signals

Analysis and decomposition of frequency modulated multicomponent signals

Frequency modulated (FM) signals are studied in many research fields, including seismology, astrophysics, biology, acoustics, animal echolocation, radar and sonar. They are referred as multicomponent signals (MCS), as they are generally composed of multiple waveforms, with specific time-dependent frequencies, known as instantaneous frequencies (IFs). Many applications require the extraction of signal characteristics (i.e. amplitudes and IFs). that is why MCS decomposition is an important topic in signal processing. It consists of the recovery of each individual mode and it is often performed by IFs separation. The task becomes very challenging if the signal modes overlap in the TF domain, i.e. they interfere with each other, at the so-called non-separability region. For this reason, a general solution to MCS decomposition is not available yet. As a matter of fact, the existing methods addressing overlapping modes share the same limitations: they are parametric, therefore they adapt only to the assumed signal class, or they rely on signal-dependent and parametric TF representations; otherwise, they are interpolation techniques, i.e. they almost ignore the information corrupted by interference and they recover IF curve by some fitting procedures, resulting in high computational cost and bad performances against noise. This thesis aims at overcoming these drawbacks, providing efficient tools for dealing with MCS with interfering modes. An extended state-of-the-art revision is provided, as well as the mathematical tools and the main definitions needed to introduce the topic. Then, the problem is addressed following two main strategies: the former is an iterative approach that aims at enhancing MCS' resolution in the TF domain; the latter is a transform-based approach, that combines TF analysis and Radon Transform for separating individual modes. As main advantage, the methods derived from both the iterative and the transform-based approaches are non-parametric, as they do not require specific assumptions on the signal class. As confirmed by the experimental results and the comparative studies, the proposed approach contributes to the current state of the-art improvement

Wigner-Ville Distribution Associated with the Linear Canonical Transform

The linear canonical transform is shown to be one of the most powerful tools for nonstationary signal processing. Based on the properties of the linear canonical transform and the classical Wigner-Ville transform, this paper investigates the Wigner-Ville distribution in the linear canonical transform domain. Firstly, unlike the classical Wigner-Ville transform, a new definition of Wigner-Ville distribution associated with the linear canonical transform is given. Then, the main properties of the newly defined Wigner-Ville transform are investigated in detail. Finally, the applications of the newly defined Wigner-Ville transform in the linear-frequency-modulated signal detection are proposed, and the simulation results are also given to verify the derived theory

Diagnosis of Induction Motor Faults in Time-Varying Conditions Using the Polynomial-Phase Transform of the Current

© 2011 IEEE. Personal use of this material is permitted. Permissíon from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertisíng or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.[EN] Transient motor current signature analysis is a recently developed technique for motor diagnostics using speed transients. The whole speed range is used to create a unique stamp of each fault harmonic in the time-frequency plane. This greatly increases diagnostic reliability when compared with non-transient analysis, which is based on the detection of fault harmonics at a single speed. But this added functionality comes at a price: well-established signal analysis tools used in the permanent regime, mainly the Fourier transform, cannot be applied to the nonstationary currents of a speed transient. In this paper, a new method is proposed to fill this gap. By applying a polynomial-phase transform to the transient current, a new, stationary signal is generated. This signal contains information regarding the fault components along the different regimes covered by the transient, and can be analyzed using the Fourier transform. The polynomial-phase transform is used in radar, sonar, communications, and power systems fields, but this is the first time, to the best knowledge of the authors, that it has been applied to the diagnosis of induction motor faults. Experimental results obtained with two different commercial motors with broken bars are presented to validate the proposed method.This work was supported by the Spanish "Ministerio de Educacion y Ciencia" in the framework of the "Programa Nacional de Proyectos de Investigacion Fundamental," project reference DPI2008-06583/DPI.Pineda-Sanchez, M.; Riera-Guasp, M.; Roger-Folch, J.; Antonino-Daviu, J.; Pérez-Cruz, J.; Puche-Panadero, R. (2011). Diagnosis of Induction Motor Faults in Time-Varying Conditions Using the Polynomial-Phase Transform of the Current. IEEE Transactions on Industrial Electronics. 58(4):1428-1439. https://doi.org/10.1109/TIE.2010.2050755S1428143958