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

Attenuation Analysis of Lamb Waves Using the Chirplet Transform

Guided Lamb waves are commonly used in nondestructive evaluation to monitor plate-like structures or to characterize properties of composite or layered materials. However, the dispersive propagation and multimode excitability of Lamb waves complicate their analysis. Advanced signal processing techniques are therefore required to resolve both the time and frequency content of the time-domain wave signals. The chirplet transform (CT) has been introduced as a generalized time-frequency representation (TFR) incorporating more flexibility to adjust the window function to the group delay of the signal when compared to the more classical short-time Fourier transform (STFT). Exploiting this additional degree of freedom, this paper applies an adaptive algorithm based on the CT to calculate mode displacement ratios and attenuation of Lamb waves in elastic plate structures. The CT-based algorithm has a clear performance advantage when calculating mode displacement ratios and attenuation for numerically-simulated Lamb wave signals. For experimental data, the CT retains an advantage over the STFT although measurement noise and parameter uncertainties lead to larger overall deviations from the theoretically expected solutions

Time-frequency representation of earthquake accelerograms and inelastic structural response records using the adaptive chirplet decomposition and empirical mode decomposition

In this paper, the adaptive chirplet decomposition combined with the Wigner-Ville transform and the empirical mode decomposition combined with the Hilbert transform are employed to process various non-stationary signals (strong ground motions and structural responses). The efficacy of these two adaptive techniques for capturing the temporal evolution of the frequency content of specific seismic signals is assessed. In this respect, two near-field and two far-field seismic accelerograms are analyzed. Further, a similar analysis is performed for records pertaining to the response of a 20-story steel frame benchmark building excited by one of the four accelerograms scaled by appropriate factors to simulate undamaged and severely damaged conditions for the structure. It is shown that the derived joint time–frequency representations of the response time histories capture quite effectively the influence of non-linearity on the variation of the effective natural frequencies of a structural system during the evolution of a seismic event; in this context, tracing the mean instantaneous frequency of records of critical structural responses is adopted. The study suggests, overall, that the aforementioned techniques are quite viable tools for detecting and monitoring damage to constructed facilities exposed to seismic excitations

Superposition frames for adaptive time-frequency analysis and fast reconstruction

In this article we introduce a broad family of adaptive, linear time-frequency representations termed superposition frames, and show that they admit desirable fast overlap-add reconstruction properties akin to standard short-time Fourier techniques. This approach stands in contrast to many adaptive time-frequency representations in the extant literature, which, while more flexible than standard fixed-resolution approaches, typically fail to provide efficient reconstruction and often lack the regular structure necessary for precise frame-theoretic analysis. Our main technical contributions come through the development of properties which ensure that this construction provides for a numerically stable, invertible signal representation. Our primary algorithmic contributions come via the introduction and discussion of specific signal adaptation criteria in deterministic and stochastic settings, based respectively on time-frequency concentration and nonstationarity detection. We conclude with a short speech enhancement example that serves to highlight potential applications of our approach.Comment: 16 pages, 6 figures; revised versio

End-to-end Source Separation with Adaptive Front-Ends

Source separation and other audio applications have traditionally relied on the use of short-time Fourier transforms as a front-end frequency domain representation step. The unavailability of a neural network equivalent to forward and inverse transforms hinders the implementation of end-to-end learning systems for these applications. We present an auto-encoder neural network that can act as an equivalent to short-time front-end transforms. We demonstrate the ability of the network to learn optimal, real-valued basis functions directly from the raw waveform of a signal and further show how it can be used as an adaptive front-end for supervised source separation. In terms of separation performance, these transforms significantly outperform their Fourier counterparts. Finally, we also propose a novel source to distortion ratio based cost function for end-to-end source separation.Comment: 4 figures, 4 page