Time Frequency Signal Analysis

Transient vibration component of mechanical systems, such as, amplitude of frequency modulation are not easily detected by using the conventional Fourier analysis. Therefore, it is necessary to use appropriate analysis techniques in order to extract the signal components in both time and frequency domains. Hence, the objective of this work is to apply time-frequency energy distributions, namely, the Wigner Distribution and the Choi-Williams Distribution in the processing of the mechanical systems response in the time domain. These time-frequency analysis techniques will be applied in the study of the vibration of the mechanical systems in two different situations. In the first case the objective is to extract amplitude modulation components of vibration signals generated during the metal machining, or turning process. In the second situation, the time-frequency distributions were applied in the analysis of the frequency modulation components caused by the acceleration of a rotating ...

In manufacturing industries, manual lifting is commonly practiced by workers in their routine to move or transport the objects to a desired place. Manual lifting with high repetition and loading on the arm will contribute the effects of soft tissues and muscle fatigue that will affect the performance of the worker to work with efficient. This paper presents the analysis of EMG signal from muscle activity to see the performance of muscle fatigue. Various researchers have proposed fast Fourier transforms (FFT) in analysing the EMG signal. However, this technique only gives spectral information but does not provide temporal information. Thus, the technique is not suitable for EMG analysis that consists of magnitude and frequency variation. To overcome the limitation, spectrogram is proposed to analyse the signal because it can represent the signal in jointly time-frequency representation (TFR). In fatigue muscle activities, ten volunteers in fresh condition and no previous of history injury are used as the subjects. Data is taken from right Biceps Branchii with lifting height of 140 cm and load mass of 5 kg. This research shows that the repeatability of manual lifting will contribute to the muscle fatigue for all the phases stated in this paper. This study concludes that phase 2 contribute highest effort by doing manual lifting task, compared to phase 1, 3 and 4, but all phases experienced the muscle fatigue.

We present a review of the diversity of concepts and motivations for improving the concentration and resolution of timefrequency distributions (TFDs) along the individual components of the multi-component signals. The central idea has been to obtain a distribution that represents the signal's energy concentration simultaneously in time and frequency without blur and crosscomponents so that closely spaced components can be easily distinguished. The objective is the precise description of spectral content of a signal with respect to time, so that first, necessary mathematical and physical principles may be developed, and second, accurate understanding of a time-varying spectrum may become possible. The fundamentals in this area of research have been found developing steadily, with significant advances in the recent past.

This paper studies possible utilization of fiber optic switches for more efficient utilization of expensive electronic components which are the core of long range fiber-based sensors systems. Complex architecture of such systems starting to be used for monitoring of events along various linear objects like railway lines, product lines or object defense perimeters, are based on rather expensive ultra narrow band laser source and interrogation electronics. Possible sharing of these expensive components for sensing on more fiber optic lines is discussed in this work.

This paper studies possible utilization of fiber optic switches for more efficient utilization of expensive electronic components which are the core of long range fiber-based sensors systems. Complex architecture of such systems starting to be used for monitoring of events along various linear objects like railway lines, product lines or object defense perimeters, are based on rather expensive ultra narrow band laser source and interrogation electronics. Possible sharing of these expensive components for sensing on more fiber optic lines is discussed in this work.

An efficient multicycle hardware design of a time-varying (TV) filtering system, based on time-frequency (TF) analysis, is developed by following the idea of a new method for filter's region of support (FRS) real-tame estimation, also proposed here. Quite general estimation method provides multiple detection of the local filter's regions of support (in observed time-instant) in the practically only important case of a known single noisy signal realization. In this way, a very efficient real-time filtering of mono-and multicomponent nonstationary signals is enabled. By taking different number of clock cycles per frequency point, the proposed design enables application of various (almost all commonly used) TF distributions (TFDs) in the TV filtering research area. Additionally, it allows the implemented filter to share functional kernels within the execution, implying the optimization of the critical design performances and the improvement of the execution time.

The diagnosis of induction motor problems is a crucial operation in industrial settings. Among the different problems that can occur in induction motors (IM), gear system faults account for almost 60 percent of all faults. At this paper, the detection of stator and rotor failures utilizing electrical signals from IM under various structural factors. The evaluation results indicate that both stator and rotor faults enhance the amplitude of the sidebands of the motor current signature in a Maxwell finite element 2D design. The Finite Element Method is used to examine the electromagnetic field of an induction motor with a faulty gear system that is fed by both the mains and a three-phase voltage source (FEM). Analyses are conducted on electromagnetic field parameters such as voltage distribution, load torque distribution, and coil pitch.

This paper proposes an active fault tolerant control scheme to cope with faults or failures affecting the flywheel spin rate sensors or satellite reaction wheel motors. The active fault tolerant control system consists of a fault detection and diagnosis module along with a control allocation and fault accommodation module directly exploiting the on-line fault estimates. The use of the nonlinear geometric approach and radial basis function neural networks allows to obtain a precise fault isolation, independently from the knowledge of aerodynamic disturbance parameters, and to design generalised estimation filters, which do not need a priori information about the internal model of the signal to be estimated. The adaptive control allocation and sensor fault accommodation can handle both temporal faults and failures. Simulation results illustrate the convincing fault correction and attitude control performances of the proposed system.

In this paper, we introduce the discrete evolutionary transform (DET) capable of representing deterministic non-stationary signals. Besides the signal representation, the DET permits the computation of a kernel from which the evolutionary spectrum of the signal is obtained. The signal representation is modeled after the Wold}Cramer representation used for random non-stationary signals in Priestley's evolutionary spectral theory. The proposed transform generalizes the short-time Fourier transform and the spectrogram. To illustrate how to de"ne the windows used in the DET we consider the Gabor and the Malvar cases. The Gabor-based window is time dependent and uses the bi-orthogonal analysis and synthesis windows of the expansion. The Malvar-based window is a function of time and of frequency, and depends on the orthogonal functions used in the expansion. Two types of transforms are shown: sinusoidal and chirp DETs. The sinusoidal DET represents well signals with narrow-band components, while the chirp transformation is capable of representing well signals with wide-band components provided that the instantaneous frequency information of the signal components is estimated. Examples are used to illustrate the implementation of the DET. The examples show the capability of the transform in providing excellent representation for a signal and a spectrum with very good time}frequency resolution.

In this paper, we examine the time-frequency representation (TFR) and sparse reconstruction of non-stationary signals in the presence of missing data samples. These samples lend themselves to missing entries in the instantaneous auto-correlation function (IAF) which, in turn, induce artifacts in the time-frequency distribution and ambiguity function. The artifacts are additive noise-like and, as such, can be mitigated by using proper time-frequency kernels. We show that the sparse signal reconstruction methods applied to the time-lag domain improve the TFR over the direct application of Fourier transform to the IAF. Additionally, the paper demonstrates that the use of signal-adaptive kernels provides superior performance compared to data-independent kernels when missing data are present.

Scalogram is widely used to measure instantaneous frequencies of non-stationary signals. However, the basic property of the scalogram is observed only for stationary sinusoidal functions. A property of the scalogram for non-stationary signal is analytically derived in this paper. Based on the property, a new frequency measurement algorithm is proposed. In addition, a filter that can separate two similar frequency signals is developed based on the wavelet transform.

The bearing reliability plays major role in obtaining the desired performance of any machine. A continuous condition monitoring of machine is required in certain applications where failure of machine leads to loss of production, human safety and precision. Machine faults are often linked to the bearing faults. Condition monitoring of machine involves continuous watch on the performance of bearings and predicting the faults of bearing before it cause any adversity. This paper investigates an experimental study to diagnose the fault while bearing is in operation. An acoustic emission technique is used in the experimentation. An algorithm is developed to process various types of signals generated from different bearing defects. The algorithm uses time domain analysis along with combination low frequency analysis technique such as fast Fourier transform and high frequency envelope detection. Two methods have adopted for envelope detection which are Hilbert transform and order analysis. ...

Wavelet transforms introduce new classes of basis functions for time-frequency signal analysis and have inherent properties that are particularly useful for the compression of analogue point on wave transient and disturbance power system signals. This paper examines the compression properties of the discrete wavelet and evaluates the transform using actual power system data. The results presented in the paper indicate that compression ratios up to 10:1 with acceptable distortion are achievable. The paper discusses the application of wavelet compression for rapid information access and exchange in network operation and control.

Protection of Direct Current (DC) microgrids is a challenging task because of large currents within a few milliseconds after the occurrence of a DC fault, which causes serious damage to converters. The present study introduces a protection algorithm based on Traveling Waves (TWs) to detect and locate faults. The proposed method implements the High-order Synchrosqueezing Transform (HOSST) to capture TWs using local measurements. Unlike conventional methods, HOSST can analyze signals in both time and frequency domains by creating a concentrated energy in the time–frequency representation. By extracting impulse features, HOSST detects TWs with high accuracy even in a noisy environment for different types of DC faults with various fault resistances. The proposed method can identify external and internal faults by determining the polarity of TWs, which makes the relays operate properly within their protection zone and prevents mal-operation. To demonstrate the efficiency of the proposed method, it is applied to a DC microgrid. The results show the high accuracy of the presented approach in the fault location with a slight error with selectivity, reliability, sensitivity, and high speed, which is independent of the voltage level and configuration. In addition, the certainty of the proposed method is higher than the previous studies due to the simultaneous use of current and voltage.

The paper is concerned with the analysis of instantaneous values and evaluation of certain power quality indices corresponding to phase currents and voltages acquired from the primary winding of a locomotive transformer. Representative data sets acquired during all operating regimes (acceleration, constant speed, normal and respectively regenerative braking) were analyzed. Firstly the background noise was estimated by using a wavelet thrashing tree considering a wavelet mother with a short filter. Specific computational aspects related to the use of the Stationary Wavelet Transform were presented and it was used to evaluate the instantaneous values of the fundamental harmonic, respectively the distorting residue. Discrete Wavelet Transform was used for 3 situations to deal with time-frequency localization of deviations from stationarity. A nodal analysis was also made with an original implementation of the Wavelet Packet Transform in a special situation, when the deviation from stat...

This paper presents a new three phase approach based on space vector discrete wavelet transform to detect and localize power quality disturbances (PQD). This approach provides high resolution time frequency representation used to detect and localize the disturbances. Supplementary information about detected disturbances (duration and frequency spectrum) extracted in order to characterize them. From the monitored three phase voltage signals a space vector is generated using Clarke Transformation. For normal system voltage the space vector is of constant magnitude signal of 1.5pu. If PQD occurs in any one or all phases of system, results in change of magnitude or frequency or both of the space vector. The space vector is decomposed using Discrete Wavelet Transform (DWT) and the magnitude of detail coefficients is used to detect and localize the PQ disturbances. The proposed technique monitors all three phase voltages simultaneously therefore can offer fast detection than existing sing...

DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

The paper deals with the non-destructive testing of structural elements by means of the acoustic response using the jointed time and frequency transforms. These methods make it possible to localise the beginning and the end of frequency components contained in the measured signal, and in this way, they enable us to analyse perfectly the spectrum of the non-stationary noise. In this way, this mathematical procedure enables us to distinguish a good specimen from a defective one.

Direction of arrival (DOA) estimation is a well studied topic and used in many different applications. Although it is usually based on time-difference-of-arrival (TDOA) of coherent signals, it is sometimes possible to also use frequency-difference-of-arrival (FDOA). By combining TDOA and FDOA a more reliable estimate of the DOA can be obtained. This can be useful in military applications such as reconnaissance and surveillance where the objective is to locate unknown transmitters. It is however not always possible to obtain accurate TDOA and FDOA estimates. In this study the conditions for this are examined for the airborne case when the receivers are on the same aerial vehicle. A method for simulating and estimating TDOAs and FDOAs is also presented. The results are based on simulations with three different signal types and conditions are found for which accurate TDOA and FDOA estimation can be achieved. These conditions are obtained from the Cramér-Rao bounds for TDOA and FDOA. It is shown that FDOA can in some cases yield a higher accuracy in the DOA estimate than what is possible with TDOA. Sammanfattning Riktning av ankomst (förkortat DOA)är ett väl studeratämne och används i många olika sammanhang.Även om det oftaär baserat på tidsskillnader i ankomst (förkortat TDOA) hos koherenta vågor,är det ibland möjligt attäven använda frekvensskillnader i ankomst (förkortat FDOA). Genom att kombinera TDOA och FDOA kan ett mer pålitligt estimat av DOA fås. Detta kan vara användbart i militära sammanhang så som spaning ochövervakning då måletär att lokalisera okända sändare. Detär dock inte alltid möjligt att uppnå noggranna TDOA och FDOA estimat. I denna studie undersöks villkoren för detta för fallet då mottagarnaär på samma luftburna farkost. En metod för att simulera och estimera TDOA och FDOA visas också. Resultaten baseras på simuleringar med tre olika signaltyper och villkor för vilka noggranna TDOA och FDOA estimat kan uppnås tas fram. Dessa villkorär tagna från Cramér-Raos sats för TDOA och FDOA. Det visas att FDOA kan i vissa sammanhang ge en högre noggrannhet i DOA estimatetän vad somär möjligt med TDOA.

The polynomial Wigner-Ville distribution (PWVD) is a time-frequency signal analysis tool for representing polynomial frequency modulated (FM) signals. In this correspondence, we present an optimization procedure to design PWVD's and discuss the need for higher order PWVD's.

One method of identifying defects is to directly solve the optimization problem to obtain a set of parameters for locating and quantifying damages in the structure. Numeric or digital simulation uses computerized modelling and analysis to test static or dynamic behaviour of components subjected to stress,under different operating conditions.This type of analysis involves, however, the assimilation of operating modes with a specialized assisted design program as well as finite element simulation and analysis programs.Method used in present paper for analysing defects on components such L-shaped platens assembly is one of finite element, by means of SolidWork software. The purpose is to obtain Eigen modes ofL-shaped platens assembly embedded on a surface in order to use the results for further analysis in technical applications.

This study proposes a method for locating and evaluating plate damage based on the determination of natural frequencies and modal forms of defective plates using an optimization approach. For simulations finite element method is used, form SolidWorks software. The efficiency of the presented method is explored by a comparison of the results obtained for several case studies of L-shaped plates assemblies having different defects and positions on plates. The results obtained confirm the applicability and effectiveness of the suggested method for solving the problems of localizing and quantifying defects on plates.

In present paper we have conducted a study for locating and evaluating plate damage based on the determination of geometrical percentage deviation. Study of defects is of great importance because by a proper identification we are able to prevent loss part of component characteristics and endurance. We considered rectangular thin plates of various dimensions, under the influence of temperature. Impact of considered factor decreases with thickness of plate and in this scenario geometrical imperfections measured as deviations from ideal plate surface play a fundamental role in predicting the non-linear response.

A new signal-adaptive joint time-frequency distribution for the analysis of nonstationary signals is proposed. It is based on a fractional-Fourier-domain realization of the weighted Wigner distribution producing auto-terms close to the ones in the Wigner distribution itself, but with reduced cross-terms. Improvement over the standard time-frequency representations is achieved when the principal axes of a signal (defined as mutually orthogonal directions in the time-frequency plane for which the width of the signal's fractional power spectrum is minimum or maximum) do not correspond to time and frequency. The computational cost of this fractional-domain realization is the same as the computational cost of the realizations in the time or the frequency domain, since the windowed Fourier transform of the fractional Fourier transform of a signal corresponds to the short-time Fourier transform of the signal itself, with the window being the fractional Fourier transform of the initial one. The appropriate fractional domain is found from the knowledge of three second-order fractional Fourier transform moments. Numerical simulations confirm a qualitative advantage in the time-frequency representation, when the calculation is done in the optimal fractional domain. The approach can be generalized to the time-frequency distributions from the Cohen class.

Ultrasound shear wave elastography (SWE) is a noninvasive approach for evaluating mechanical properties of soft tissues. In SWE either group velocity measured in the time-domain or phase velocity measured in the frequency-domain can be reported. Frequency-domain methods have the advantage over time-domain methods in providing a response for a specific frequency, while timedomain methods average the wave velocity over the entire frequency band. Current frequency-domain approaches struggle to reconstruct SWE images over full frequency bandwidth. This is especially important in the case of viscoelastic tissues, where tissue viscoelasticity is often studied by analyzing the shear wave phase velocity dispersion. For characterizing cancerous lesions, it has been shown that considerable biases can occur with group velocity-based measurements. However, using phase velocities at higher frequencies can provide more accurate evaluations. In this paper, we propose a new method called Ultrasound Shear Elastography with Expanded Bandwidth (USEWEB) used for two-dimensional (2D) shear wave phase velocity imaging. We tested the USEWEB method on data from homogeneous tissue-mimicking liver fibrosis phantoms, custom-made viscoelastic phantom measurements, phantoms with cylindrical inclusions experiments, and in vivo renal transplants scanned with a clinical scanner. We compared results from the USEWEB method with a Local Phase Velocity Imaging (LPVI) approach over a wide frequency range, i.e., up to 200-2000 Hz. Tests carried out revealed that the USEWEB approach provides 2D phase velocity images with a coefficient of variation below 5% over a wider frequency band for smaller processing window size in comparison to LPVI, especially in viscoelastic materials. In addition, USEWEB can produce correct phase velocity images for much higher frequencies, up to 1800 Hz, compared to LPVI, which can be used to characterize viscoelastic materials and elastic inclusions.

Frequency domain analysis and Fourier transforms are a cornerstone of signal and system analysis. These ideas are also one of the conceptual pillars within electrical engineering. Among all of the mathematical tools utilized in electrical engineering, frequency domain analysis is arguably the most far-reaching. In fact, these ideas are so important that they are widely used in many fields-not just in electrical engineering, but in practically all branches of engineering and science, and several areas of mathematics.

A concise introduction to the concept of fractional Fourier transforms is followed by a discussion of their relation to chirp and wavelet transforms. The notion of fractional Fourier domains is developed in conjunction with the Wigner distribution of a signal. Convolution, filtering, and multiplexing of signals in fractional domains are discussed, revealing that under certain conditions one can improve on the special cases of these operations in the conventional space and frequency domains. Because of the ease of performing the fractional Fourier transform optically, these operations are relevant for optical information processing.