Analysis Of Multicomponent Signals Research Articles

Second-Order Synchrosqueezing Transform or Invertible Reassignment? Towards Ideal Time-Frequency Representations

This paper considers the analysis of multicomponent signals, defined as superpositions of real or complex modulated waves. It introduces two new post-transformations for the short-time Fourier transform that achieve a compact time-frequency representation while allowing for the separation and the reconstruction of the modes. These two new transformations thus benefit from both the synchrosqueezing transform (which allows for reconstruction) and the reassignment method (which achieves a compact time-frequency representation). Numerical experiments on real and synthetic signals demonstrate the efficiency of these new transformations, and illustrate their differences.

Analysis of multicomponent LFM signals by Teager Huang-Hough transform

A novel detection approach of linear FM (LFM) signals, with single or multiple components, in the time-frequency plane of Teager-Huang (TH) transform is presented. The detection scheme that combines TH transform and Hough transform is referred to as Teager-Huang-Hough (THH) transform. The input signal is mapped into the time-frequency plane by using TH transform followed by the application of Hough transform to recognize time-frequency components. LFM components are detected and their parameters are estimated from peaks and their locations in the Hough space. Advantages of THH transform over Hough transform of Wigner-Ville distribution (WVD) are: 1) cross-terms free detection and estimation, and 2) good time and frequency resolutions. No assumptions are made about the number of components of the LFM signals and their models. THH transform is illustrated on multicomponent LFM signals in free and noisy environments and the results compared with WVD-Hough and pseudo-WVD-Hough transforms.

Filtering in Time-Frequency Domain using STFrFT

The Fractional Fourier Transform is a generalized form of Fourier Transform, which can be interpreted as a rotation by angle α in time-frequency plane or decomposition of signals in terms of chirps. However it fails in locating Fractional Fourier Domain Frequency contents. Short-time FRFT variants are suitable for analysis of multicomponent and nonlinear chirp signals with improved time-frequency resolution. Short-Time FRFT is the simultaneous representation of, combination of the time and FRFD-frequency information. Filtering in the fractional domain separates the noise and the highly concentrated signal. Filtering results depict that the results in fractional domain give better results. The timefrequency representation in fractional domain is useful tool for various applications like filtering of chirp signals. Simulations are performed on MATLAB platform.

The role of functional data analysis for instantaneous frequency estimation

This paper proposes a method for estimating the instantaneous frequency of a nonstationary signal; this method is based on a combination of empirical mode decomposition and functional data analysis. The proposed method incorporates a basis expansion technique for a functional data into time-varying phase derived by empirical mode decomposition and Hilbert transform, which provides a stable instantaneous frequency function. The superiority of the proposed method for instantaneous frequency estimation is demonstrated by various simulation studies. The analysis of multicomponent signals by the proposed method is also discussed. Furthermore, it is shown that the proposed method is highly effective for identifying groups (clusters) of nonstationary signals on the basis of the instantaneous frequency information.

A New Algorithm for Multicomponent Signals Analysis Based on SynchroSqueezing: With an Application to Signal Sampling and Denoising

In this paper, we address the problem of the retrieval of the components from a multicomponent signal using ideas from the synchrosqueezing framework. The emphasis is on the wavelet choice and we propose a novel algorithm based first on the detection of components followed by their reconstruction. Simulations illustrate how the proposed procedure compares with the empirical mode decomposition and other related methods in terms of mode-mixing. We conclude the paper by studying the sensitivity of the proposed technique to sampling and an application to signal denoising.

Comparative analysis of variants of Gabor-Wigner transform for cross-term reduction

Abstract Gabor Wigner Transform (GWT) is a composition of two time-frequency planes (Gabor Transform (GT) and Wigner Distribution (WD)), and hence GWT takes the advantages of both transforms (high resolution of WD and cross-terms free GT). In multi-component signal analysis where GWT fails to extract auto-components, the marriage of signal processing and image processing techniques proved their potential to extract autocomponents. The proposed algorithm maintained the resolution of auto-components. This work also shows that the Fractional Fourier Transform (FRFT) domain is a powerful tool for signal analysis. Performance analysis of modified fractional GWT reveals that it provides a solution of cross-terms of WD and blurring of GT.

Application of multi-scale chirplet path pursuit and fractional Fourier transform for gear fault detection in speed up and speed-down processes

Demodulation is very important for gear fault detection. However, the demodulation is substantially complicated by the non-stationary nature of the signal during the speed-up and speed-down processes. As such, we propose a new technique to detect gear faults under such conditions based on the multi-scale chirplet path pursuit (MSCPP) algorithm and the fractional Fourier transform (FrFT) method. With the MSCPP algorithm, the instantaneous frequency of the signal component with the largest energy in the multi-components gear vibration signal can be estimated. Then according to the estimated instantaneous frequency, the vibration signal segment whose instantaneous frequency curve approximated as either an ascending or descending linear segment can be obtained from the original gear vibration signal. In other words, the vibration signal segment that can be regarded as a multi-component linear frequency modulated (LFM) signal is extracted. As the FrFT is suitable for multi-component LFM signal analysis, it is then applied to demodulating this vibration signal segment and hence detecting local gear faults based on the revealed modulation phenomenon. The effectiveness of the proposed method has been demonstrated by both simulation and experimental data.

Estimation of instantaneous frequencies using iterative empirical mode decomposition

A novel instantaneous frequency-based time–frequency representation is proposed for the analysis of multicomponent signals. The concept of frequency translation is innovatively combined with the empirical mode decomposition algorithm to formulate an iterative procedure, referred to as the iterative empirical mode decomposition, to separate the components present in a signal at a suitably selected frequency resolution. The instantaneous frequency and amplitude estimated on the separated components are used to form the new time–frequency representation. The iterative empirical mode decomposition is assessed for component resolvability, and the performance of the aforementioned time–frequency representation is compared with several other time–frequency representations based on visual inspection and using objective criteria. The Hilbert spectrum formed using the iterative empirical mode decomposition not only provides high concentration of energy about the components’ instantaneous frequencies at high signal-to-noise ratio, but also good resolution while keeping the interference terms at a minimum.

New Algorithm to Identify Inrush Current Based on Improved EMD

Empirical mode decomposition (EMD), which is the core mechanic of the Hilbert-Huang transform(HHT), is a local, fully data driven and self-adaptive analysis approach. It is a powerful tool for analyzing multi-component signals. Aiming at the reduction of scale mixing and artificial frequency components, an improved scheme was proposed for analysis and reconstruction of nonstationary and multicomponent signals. The improved EMD method uses the wavelet analysis method and normalized correlation coefficient to deal with the problems. Because the inrush current is a peaked wave with nonstationary component, a new algorithm based on improved EMD is presented for fast discrimination between inrush current and fault current of power transformers. Theoretical analysis and dynamic simulation results show that the method is effective and reliable under various fault conditions and simple to be applied.

MCRC software: A tool for chemometric analysis of two-way chromatographic data

This paper describes the development and implementation of MCRC software, chemometric software for Multivariate Curve Resolution of two-way Chromatographic data. MCRC software is developed for chemometric analysis of chromatographic data; however, it may also be used for other types of multivariate data. It consists of five groups of techniques for preprocessing, chemical rank determination, local rank analysis, multivariate resolution and peak integration. This software has the ability of the analysis of complex multi-component chromatographic signals of gas chromatography–mass spectrometry (GC–MS) and high performance liquid chromatography–diode array detection (HPLC–DAD). The software allows a user to apply the implemented methods in an easy way and it gives a straightforward possibility to visualize the obtained results. The main features of the presented software are providing a number of preprocessing techniques, implementation of different chemical rank determination methods, usage of iterative and non-iterative resolution techniques and a user-friendly environment with a variety of graphical outputs. The implementation of the MCRC software is demonstrated by the analysis of an overlapped peak cluster of simulated GC–MS data.

Analysis of multicomponent AM-FM signals using FB-DESA method

The discrete energy separation algorithm (DESA) together with the Gabor's filtering provides a standard approach to estimate the amplitude envelope (AE) and the instantaneous frequency (IF) functions of a multicomponent amplitude and frequency modulated (AM-FM) signal. The filtering operation introduces amplitude and phase modulations in the separated monocomponent signals, which may lead to an error in the final estimation of the modulation functions. In this paper, we have proposed a method called the Fourier-Bessel expansion-based discrete energy separation algorithm (FB-DESA) for component separation and estimation of the AE and IF functions of a multicomponent AM-FM signal. The FB-DESA method does not introduce any amplitude or phase modulation in the separated monocomponent signal leading to accurate estimations of the AE and IF functions. Simulation results with synthetic and natural signals are included to illustrate the effectiveness of the proposed method.

Pitch- and Formant-Based Order Adaptation of the Fractional Fourier Transform and Its Application to Speech Recognition

Fractional Fourier transform(FrFT) has been proposed to improve the time-frequency resolution in signal analysis and processing. However, selecting the FrFT transform order for the proper analysis of multicomponent signals like speech is still debated. In this work, we investigated several order adaptation methods. Firstly, FFT- and FrFT- based spectrograms of an artificially-generated vowel are compared to demonstrate the methods. Secondly, an acoustic feature set combining MFCC and FrFT is proposed, and the transform orders for the FrFT are adaptively set according to various methods based on pitch and formants. A tonal vowel discrimination test is designed to compare the performance of these methods using the feature set. The results show that the FrFT-MFCC yields a better discriminability of tones and also of vowels, especially by using multitransform-order methods. Thirdly, speech recognition experiments were conducted on the clean intervocalic English consonants provided by the Consonant Challenge. Experimental results show that the proposed features with different order adaptation methods can obtain slightly higher recognition rates compared to the reference MFCC-based recognizer.

Keystone transformation of the Wigner–Ville distribution for analysis of multicomponent LFM signals

Signal detection and parameter estimation for mono- and multicomponent linear frequency modulation (LFM) signals are studied by using the keystone transform of the Wigner–Ville distribution (WVD). The keystone-Wigner transform (KWT) introduces a weight factor containing a range of chirp rate into the time-lag instantaneous autocorrelation function and uses a one-dimensional (1-D) interpolation of the phase which we call keystone formatting. The proposed processing eliminates the effects of linear frequency migration (i.e., the frequency linearly varies along the time axis) to all the signal components even if their chirp rates are unknown. The Fourier transform (FFT) over the time variable to results of the KWT make the power of multicomponent LFM signal concentrated as the locations corresponding to their parameters. Furthermore, the KWT can be efficiently implemented using only complex multiplications and FFT based on the scaling principle instead of interpolating. The computational complexity of KWT is O ( 4 N 2 log 2 N ) . Performance analysis is presented by using the perturbation method and verified by simulation results. Finally, the effectiveness of the KWT is validated by a real application example.

A proposed High-Resolution Time-Frequency Distribution for the Analysis of Multicomponent and Speech Signals

Abstract— In this paper, we propose a novel time-frequencydistribution (TFD) for the analysis of multi-component signals. In particular, we use synthetic as well as real-life speech signals toprove the superiority of the proposed TFD in comparison to someexisting ones. In the comparison, we consider the cross-termssuppression and the high energy concentration of the signal around its instantaneous frequency (IF). Keywords — Cohen’s Class, Multicomponent signal, Separable Kernel, Speech signal, Time- frequency resolution. I. I NTRODUCTION HE spectrogram, a smoothed version of the well-knownWigner-Ville distribution (WVD), has been widely usedin speech applications [1], [2], [3], [4]. The spectrogram,which is in general a cross-terms free time-frequencydistribution (TFD), suffers from the undesirable trade-offbetween the time concentration and the frequencyconcentration. To address the problem of cross-termssuppression, while keeping a high time-frequency resolution,other TFDs have been proposed. Among these, one can citethe smoothed pseudo WVD (SPWVD) [9], the Zhao-Atlas-Marks distribution (ZAMD) [5] and the B-distribution (BD)[6], just to name a few. In this paper, we present a new distribution for the analysis of multicomponent signals. This distribution, inspired from the Butterworth kernel quadraticTFD [8], has the ability of suppressing the cross-terms while keeping a high-resolution in the time-frequency plane. Toassess the performance of this proposed distribution, we alsopropose to compare it to some existing ones known for theircross-terms suppression property. In the comparisonexamples, we use synthetic as well as real-life data from aspeech application. The comparison results show the highperformance of the proposed TFD in dealing with non-stationary multicomponent signals.The paper is organized as follows: In Section 2, a theoretical aspect of some TFR interest is presented. A proposed hightime-frequency resolution quadratic TFD is introduced inSection 3. In Section 4, simulations and comparison examplesas well as a discussion are presented. Section 5 concludes thepaper.II. THEORETICAL BACKGROUND FOR QUADRATICTFD

Analysis of Multicomponent Polynomial Phase Signals

While the theory of estimation of monocomponent polynomial phase signals is well established, the theoretical and methodical treatment of multicomponent polynomial phase signals (mc-PPSs) is limited. In this paper, we investigate several aspects of parameter estimation for mc-PPSs and derive the Crameacuter-Rao bound. We show the limits of existing techniques and then propose a nonlinear least squares (NLS) approach. We also motivate the use the Nelder-Mead simplex algorithm for minimizing the nonlinear cost function. The slight increase in computational complexity is a tradeoff for improved mean square error performance, which is evidenced by simulation results

A generalized demodulation approach to time-frequency projections for multicomponent signals

In this paper, we introduce a flexible approach for the time-frequency analysis of multicomponent signals involving the use of analytic vectors and demodulation. The demodulated analytic signal is projected onto the time-frequency plane so that, as closely as possible, each component contributes exclusively to a different ‘tile’ in a wavelet packet tiling of the time-frequency plane, and at each time instant, the contribution to each tile definitely comes from no more than one component. A single reverse demodulation is then applied to all projected components. The resulting instantaneous frequency of each component in each tile is not constrained to a set polynomial form in time, and is readily calculated, as is the corresponding Hilbert energy spectrum. Two examples illustrate the method. In order better to understand the effect of additive noise, the approximate variance of the estimated instantaneous frequency in any tile has been formulated by starting with pure noise and studying its evolving covariance structure through each step of the algorithm. The validity and practical utility of the resulting expression for the variance of the estimated instantaneous frequency is demonstrated via a simulation experiment.

Efficient Analysis of Time-Varying Multicomponent Signals with Modified LPTFT

This paper presents efficient algorithms for the analysis of nonstationary multicomponent signals based on modified local polynomial time-frequency transform. The signals to be analyzed are divided into a number of segments and the desired parameters for computing modified the local polynomial time-frequency transform in each segment are estimated from polynomial Fourier transform in the frequency domain. Compared to other reported algorithms, the length of overlap between consecutive segments is reduced to minimize the overall computational complexity. The concept of adaptive window lengths is also employed to achieve a better time-frequency resolution for each component. Numerical simulations with synthesized multicomponent signals show that the proposed ones achieve better performance on instantaneous frequency estimation with greatly reduced computational complexity.

Orthonormal-Basis Partitioning and Time-Frequency Representation of Cardiac Rhythm Dynamics

Although a number of time-frequency representations have been proposed for the estimation of time-dependent spectra, the time-frequency analysis of multicomponent physiological signals, such as beat-to-beat variations of cardiac rhythm or heart rate variability (HRV), is difficult. We thus propose a simple method for 1) detecting both abrupt and slow changes in the structure of the HRV signal, 2) segmenting the nonstationary signal into the less nonstationary portions, and 3) exposing characteristic patterns of the changes in the time-frequency plane. The method, referred to as orthonormal-basis partitioning and time-frequency representation (OPTR), is validated using simulated signals and actual HRV data. Here we show that OPTR can be applied to long multicomponent ambulatory signals to obtain the signal representation along with its time-varying spectrum.

Short-time fractional Fourier methods for the time-frequency representation of chirp signals.

The fractional Fourier transform (FrFT) provides a valuable tool for the analysis of linear chirp signals. This paper develops two short-time FrFT variants which are suited to the analysis of multicomponent and nonlinear chirp signals. Outputs have similar properties to the short-time Fourier transform (STFT) but show improved time-frequency resolution. The FrFT is a parameterized transform with parameter, a, related to chirp rate. The two short-time implementations differ in how the value of a is chosen. In the first, a global optimization procedure selects one value of a with reference to the entire signal. In the second, a values are selected independently for each windowed section. Comparative variance measures based on the Gaussian function are given and are shown to be consistent with the uncertainty principle in fractional domains. For appropriately chosen FrFT orders, the derived fractional domain uncertainty relationship is minimized for Gaussian windowed linear chirp signals. The two short-time FrFT algorithms have complementary strengths demonstrated by time-frequency representations for a multicomponent bat chirp, a highly nonlinear quadratic chirp, and an output pulse from a finite-difference sonar model with dispersive change. These representations illustrate the improvements obtained in using FrFT based algorithms compared to the STFT.

Resolution measure criteria for the objective assessment of the performance of quadratic time-frequency distributions

This paper presents the essential elements for developing objective methods of assessment of the performance of time-frequency signal analysis techniques. We define a measure for assessing the resolution performance of time-frequency distributions (TFDs) in separating closely spaced components in the time-frequency domain. The measure takes into account key attributes of TFDs, such as components mainlobes and sidelobes and cross-terms. The introduction of this measure allows to quantify the quality of TFDs instead of relying solely on visual inspection of their plots. The method of assessment of performance of TFDs also allows the improvement of methodologies for designing high-resolution quadratic TFDs for time-frequency analysis of multicomponent signals. Different TFDs, including the modified B distribution, are optimized using this methodology. Examples of a performance comparison of quadratic TFDs in resolving closely spaced components in the time-frequency domain, using the proposed resolution measure, are provided.