Time-frequency Representation Of Non-stationary Signals Research Articles

New theoretical insights in the decomposition and time-frequency representation of nonstationary signals: The IMFogram algorithm

The analysis of the time–frequency content of a signal is a classical problem in signal processing, with a broad number of applications in real life. Many different approaches have been developed over the decades, which provide alternative time–frequency representations of a signal each with its advantages and limitations. In this work, following the success of nonlinear methods for the decomposition of signals into intrinsic mode functions (IMFs), we first provide more theoretical insights into the so–called Iterative Filtering decomposition algorithm, proving an energy conservation result for the derived decompositions. Furthermore, we present a new time–frequency representation method based on the IMF decomposition of a signal, which is called IMFogram. We prove theoretical results regarding this method, including its convergence to the spectrogram representation for a certain class of signals, and we present a few examples of applications, comparing results with some of the most well-known approaches available in the literature.

Fourier–Bessel series expansion based empirical wavelet transform for analysis of non-stationary signals

In this paper, a new method has been presented for the time–frequency (TF) representation of non-stationary signals. The existing empirical wavelet transform (EWT) has been enhanced using Fourier–Bessel series expansion (FBSE) in order to obtain improved TF representation of non-stationary signals. We have used the FBSE method for the spectral representation of the analyzed multi-component signals with good frequency resolution. The scale-space based boundary detection method has been applied for the accurate estimation of boundary frequencies in the FBSE based spectrum of the signal. After that, wavelet based filter banks have been generated in order to decompose non-stationary multi-component signals into narrow-band components. Finally, the normalized Hilbert transform has been applied for the estimation of amplitude envelope and instantaneous frequency functions from the narrow-band components and obtained the TF representation of the analyzed non-stationary signal. We have applied our proposed method for the TF representation of multi-component synthetic signals and real electroencephalogram (EEG) signals. The proposed method has provided better TF representation as compared to existing EWT method and Hilbert–Huang transform (HHT) method, especially when analyzed signal possesses closed frequency components and of short time duration.

An effective approach for structural damage localization in flexural members based on generalized S-transform

This paper presents a method for structural damage localization based on signal processing using generalized S-transform (SGS). The S-transform is the combinations of the properties of the short-time Fourier transform (STFT) and wavelet transform (WT) that has been developed over the last few years in an attempt to overcome inherent limitations of the wavelet and short time Fourier transform in Time-Frequency representation of non-stationary signals. The generalized type of this transform is the SGS-transform that has adjustable Gaussian window width in the time-frequency representation of signals. In this research, the SGS-transform has been employed due to its favorable performance in detection of the structural damages. The performance of the proposed method has been verified by means of three numerical examples and also the experimental data obtained from the vibration test of 8-DOFs mass–stiffness system. By way of the comparison between damage location obtained from the proposed method and simulation model, it was concluded that the method is sensitive to the damage existence and clearly demonstrates the damage location.

Signal Reconstruction from Nonuniformly Spaced Samples Using Evolutionary Slepian Transform-Based POCS

We consider the reconstruction of signals from nonuniformly spaced samples using a projection onto convex sets (POCSs) implemented with the evolutionary time-frequency transform. Signals of practical interest have finite time support and are nearly band-limited, and as such can be better represented by Slepian functions than by sinc functions. The evolutionary spectral theory provides a time-frequency representation of nonstationary signals, and for deterministic signals the kernel of the evolutionary representation can be derived from a Slepian projection of the signal. The representation of low pass and band pass signals is thus efficiently done by means of the Slepian functions. Assuming the given nonuniformly spaced samples are from a signal satisfying the finite time support and the essential band-limitedness conditions with a known center frequency, imposing time and frequency limitations in the evolutionary transformation permit us to reconstruct the signal iteratively. Restricting the signal to a known finite time and frequency support, a closed convex set, the projection generated by the time-frequency transformation converges into a close approximation to the original signal. Simulation results illustrate the evolutionary Slepian-based transform in the representation and reconstruction of signals from irregularly-spaced and contiguous lost samples.

Time–Frequency Analysis of Complex Space Phasor in Power Electronics

This paper considers applying nonparametric and parametric methods for the calculation of the time-frequency representation of nonstationary signals in power electronics. A space phasor is proposed as a complex representation of a three-phase signal to calculate the spectrum of positive-and negative-sequence components. The developed methods are tested with nonstationary multiple-component signals occurring during the fault operation of inverter-fed drives. First, the main differences between parametric and nonparametric methods are underlined. Then, some aspects of additional kernel functions are introduced on the basis of Wigner and Choi-Williams distributions. An additional comparison of uncertainty of measurements using the described methods, as well as a widely used Fourier technique, can be useful for practitioners. The proposed methods allow tracking instantaneous frequency as well as magnitude that can lead to applications in the diagnosis and power quality areas.

Feature extraction and gating techniques for ultrasonic shaft signal classification

Discrete wavelet transform (DWT) coefficients of ultrasonic test signals are considered useful features for input into classifiers due to their effective time-frequency representation of non-stationary signals. However, DWT exhibits a time-variance problem that has resulted in reservations for its wide acceptance. In this paper, a new technique to derive a preprocessing method for time-domain A-scans signal is presented. This technique offers consistent extraction of a segment of the signal from long signals that occur in the non-destructive testing of shafts. Two different classifiers using artificial neural networks and support vector machines are supplied with features generated by our new preprocessing method and their classification performance are compared and evaluated. Their performances are also compared with other alternatives and report the results here. This investigation establishes experimentally that DWT coefficients can be used as a feature extraction scheme more reliably by using our new preprocessing technique.