Signal In Time-frequency Plane Research Articles

Self-paced learning for instantaneous frequencies estimation in heavy noise environments

Estimating instantaneous frequencies (IFs) overlap in both time and frequency domains is desired in time-frequency (TF) analysis. In this paper, a simple method, called IFs estimation based on self-paced learning (IFsESPL) algorithm, is proposed to separate overlapped components of multi-component (MC) non-stationary signals in TF plane, and simultaneously estimate IFs. The proposed IFsESPL algorithm first detects TF ridge points from a TF representation, and then the TF ridge points are used to construct training dataset of self-paced learning (SPL). In the following, minimization of particular objective function of SPL yields iteratively selecting and classifying the samples in training dataset into clusters. Each cluster is corresponding to one component of a MC signal and hence component separation is achieved. In addition, together with the partitioning of the training dataset, the IF of each component is estimated by a predefined parameterized model. IFsESPL incorporates SPL regime into TF ridge points regrouping to sequentially include ridge points into IFs estimation from easy to hard, which not only can separate crossed components in TF plane, but also can prevent interference of noise and outliers. The effectiveness of the proposed method is verified through analytical results and numerical examples.

Parameterised time-frequency analysis methods and their engineering applications: A review of recent advances

Abstract It is well known that time-frequency analysis (TFA) characterises signals in time-frequency plane. Theoretically, traditional non-parameterised TFA can analyze any signal, but it is unable to provide the best representation for complex signals. On the other hand, parameterised TFAs provide a better representation of signal by parameterising kernel functions using additional parameters. Recently, parameterised TFAs have attracted widespread attention. In this paper, we first briefly revisit non-parameterised TFAs, then further discuss adaptive TFAs developed from non-parameterised TFAs, and then review four types of recent parameterised TFAs: Warped TFAs, Chirplet transforms, parameterised atomic decomposition, and parameterised TFA affine. From underlying principles and implementation point of view, we introduced the relationships, advantages and disadvantages of different types of parameterised TFAs. At the same time, we summarized the application of parameterised TFA in various fields and discussed research directions and trends in parameterised TFA study. This review focuses on a class of methods in TFA, parameterised TFA, summarizing its latest research progress and related engineering applications, so as to provide reference and guidance for researchers applying parametric TFA in different fields.

An Improvement in Representation of Audio Signal in Time-Frequency Plane using EMD-2TEMD Based Approach

This study proposed an enhanced time-frequency representation of audio signal using EMD-2TEMD based approach. To analyze non-stationary signal like audio, timefrequency representation is an important aspect. In case of representing or analyzing such kind of signal in time-frequency-energy distribution, hilbert spectrum is a recent approach and popular way which has several advantages over other methods like STFT, WT etc. Hilbert-Huang Transform (HHT) is a prominent method consists of Empirical Mode Decomposition (EMD) and Hilbert Spectral Analysis (HSA). An enhanced method called Turning Tangent empirical mode decomposition (2T-EMD) has recently developed to overcome some limitations of classical EMD like cubic spline problems, sifting stopping condition etc. 2T-EMD based hilbert spectrum of audio signal encountered some issues due to the generation of too many IMFs in the process where EMD produces less. To mitigate those problems, a mutual implementation of 2T-EMD & classical EMD is proposed in this paper which enhances the representation of hilbert spectrum along with significant improvements in source separation result using Independent Subspace Analysis (ISA) based clustering in case of audio signals. This refinement of hilbert spectrum not only contributes to the future work of source separation problem but also many other applications in audio signal processing.

Gearbox Fault Detection Using Synchro-squeezing Transform

This paper presents a novel fault-detection method for gearbox vibration signatures using synchro-squeezing transform (SST). Premised upon the concept of time-frequency (TF) reassignment, SST provides a sharp representation of signals in TF plane compared to many popular TF methods. Additionally, it can also extract the individual components, called intrinsic mode functions or IMFs, of a non-stationary multi-component signal, akin to empirical mode decomposition. The rich mathematical structure based on continuous wavelet transform makes SST a promising candidate for gearbox diagnosis. This work utilizes the decomposing power of SST to extract the IMFs from gearbox signals. For robust detection of faults in gear-motors, a fault detection technique based on time-varying autoregressive coefficients of IMFs as features is utilized. Sequential Karhunen-Loeve transform is employed on the condition indicators to select the appropriate window sizes on which SST can be applied. Laboratory experimental data obtained from drivetrain diagnostics simulator provides test bed to demonstrate the robustness of the proposed algorithm.

Spectrum Sensing and AM-FM Decomposition through Synchrosqueezing

In this paper we have accomplished one of the tasks of cognitive radio i.e. dynamic spectrum sensing by using wavelet based Synchrosqueezing transform [1], a novel technique, which was proposed to analyze a signal in time-frequency plane. The distinctive feature of this transform compared to other techniques is that it enables us to decompose amplitude and frequency modulated signals and allows individual reconstruction of these components. The objective is also to separate the occupied band into amplitude modulated and frequency modulated bands.

Recent Developments in FRFT, DFRFT with their Applications in Signal and Image Processing

As a tool for analyzing one- and two- dimensional signals in time-frequency plane, fractional Fourier transform (FRFT) has got sound acclamation in the recent past. In this article, the developments of FRFT are presented based on the recent patents and publications. The escalation of mathematical properties of FRFT is discussed extensively. Especially, convolution, correlation, sampling and uncertainty theorems for the FRFT are included. Subsequently, due to existence of many algorithms for evaluating the discrete FRFT, a comparative analysis is made to establish the best one amongst available. Lastly, the application of FRFT (by way of implementing the identified DFRFT) in filtering, beam-forming, encryption and watermarking is highlighted. Keywords: Beam-forming, DFRFT, encryption, filtering, FRFT, image processing, LCT, signal processing, time-frequency plane, watermarking, fractional Fourier transform, Gaussian signal, Cross-Correlation Theorem, Fresnel integral, Lagrange interpolation polynomial