Figure - available from: Signal Image and Video Processing
This content is subject to copyright. Terms and conditions apply.
![a Ideal TF representation of the signal. The estimated (circle mark) versus original IF using the b proposed method employing the LO-ADTFD, P=(2,8),(2,50)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P={(2, 8), (2, 50)}$$\end{document}; c RPRG employing the LO-ADTFD P=(2,8),(2,50)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P={(2, 8), (2, 50)}$$\end{document}; d RPRG using the AOKTFD as the underlying TFD [15]; e RPRG based on the Spectrogram (hamming, L=45,N=256\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L=45, N=256$$\end{document}) [6]; and f RPRG based on the MBD (α=0.5,N=256\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =0.5, N=256$$\end{document})](publication/328349342/figure/fig7/AS:962661818826752@1606527871118/a-Ideal-TF-representation-of-the-signal-The-estimated-circle-mark-versus-original-IF.png)
a Ideal TF representation of the signal. The estimated (circle mark) versus original IF using the b proposed method employing the LO-ADTFD, P=(2,8),(2,50)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P={(2, 8), (2, 50)}$$\end{document}; c RPRG employing the LO-ADTFD P=(2,8),(2,50)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P={(2, 8), (2, 50)}$$\end{document}; d RPRG using the AOKTFD as the underlying TFD [15]; e RPRG based on the Spectrogram (hamming, L=45,N=256\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L=45, N=256$$\end{document}) [6]; and f RPRG based on the MBD (α=0.5,N=256\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha =0.5, N=256$$\end{document})
Source publication
Instantaneous frequency (IF) estimation of multi-component signals with closely spaced and intersecting signal components of varying amplitudes is a challenging task. This paper presents a novel iterative time–frequency (TF) filtering approach to address this problem. The proposed algorithm first adopts a high-resolution time–frequency distribution...
Similar publications
In this note we exhibit recent advances in signal analysis via time-frequency distributions. New members of the Cohen class, generalizing the Wigner distribution, reveal to be effective in damping artefacts of some signals. We will survey their main properties and drawbacks and present open problems related to such phenomena.
To detect and recognize any type of events over the perimeter security system, this article proposes a fiber-optic vibration pattern recognition method based on the combination of time-domain features and time-frequency domain features. The performance parameters (event recognition, event location, and event classification) are very important and d...
Abstract The separation of overlapping components is a well-known and difficult problem in multicomponent signals analysis and it is shared by applications dealing with radar, biosonar, seismic, and audio signals. In order to estimate the instantaneous frequencies of a multicomponent signal, it is necessary to disentangle signal modes in a proper d...
Electromyography signal analysis and classification method for Health Screening Program for Social Security Organisation (SOCSO) Malaysia is the first time applied using time-frequency distribution (TFD). This paper presents the classification of EMG signals for health screening task for musculoskeletal disorder. A time-frequency method, i.e spectr...
Citations
... Besides, these two approaches are noise-sensitive, which will further cause distorted natural frequency estimation [34]. Recently, time-frequency representation (TFR) techniques have drawn increasing attention in field measurements of civil structures due to their advantage in concentrating signal energy along the instantaneous frequency curve while spreading the noise in the time-frequency plane [13,19,20]. Several time-frequency representation methods, including the short-time Fourier transform (STFT) [24,31], the wavelet transform (WT) [15], and the Wigner Ville distribution (WVD) [26], have been applied to analyze measured signals to obtain the instantaneous description of dynamic properties of civil structures. ...
Nowadays, some innovative spatial structural typologies among others rely on timber-concrete hybrid solutions for designing modern buildings. However, the dynamic identification analysis may be more elaborate, and sometimes troublesome, due to the coupling effects of the different dynamic nature of cross-laminated timber and reinforced concrete members. In the current manuscript, the authors explore some preliminary results of the dynamic analysis of a hybrid timber concrete building case study. The operational modal analysis (OMA) based on output-only techniques has been employed, referring specifically to enhanced frequency-domain decomposition (EFDD) and the stochastic subspace identification (SSI) methods. The authors compared several ambient vibration OMA results with forced shaker-induced vibration responses highlighting the absence of nonlinearities during in-service operational conditions in two different moments.
... The simplicity of these approaches is often accompanied by a not negligible computational effort, sensitivity to noise and incorrect ridge assignment in the case of interference or close chirps (switch problem). Some approaches designed to minimize this aspect are in [62][63][64], that mainly aim at estimating IF direction, and [65], that assumes local monotonicity. Alternative to Viterbi method but similar in spirit approaches are the Ridge Path Regrouping Method (RPRM) [66,67] (showing a certain sensitivity to noise), optimization techniques [66,38], properly designed to mitigate interference effects, and adaptive strategies, including those oriented to define adaptive or optimal support for the analysis windows [68]. ...
... In this Section performance of the proposed multi sensor RANSAC based IF estimator is compared with state of art methods including the robust and efficient ridge tracking IF estimation method [35], IF estimation method that exploits both orientation of ridges and spatial frequency [37], and ADTFD-based ridge tracking method [41]. For the RANSAC algorithm, we use 12.5% samples for model fitting and the number of simulations performed for IF estimation is 200 per component. ...
... Just like in the previous experiments the phases and amplitudes are randomly varied from 0 to 2π and 1 to 2 respectively. Experimental results, shown in Fig. 5, indicate that the proposed method achieves better performance than the existing methods [37], and [41]. ...
... Experimental results have been presented that clearly indicate that the proposed method achieves better performance than the stateof-the-art methods that track ridges in the TF domain. The main reason that RANSAC based method achieves better performance as compared to ridge tracking methods, e.g., [35], [37], [41], is that it computes a number of IF curves through random selection of TF peaks and selects the one that maximizes the objective function. On the other hand, the common tracking methods are prone to switching the wrong path as they only perform optimization at the local level. ...
... In many real-life applications (such as radar, sonar, and underwater acous- Recently, several methods have been developed to address this problem, such as random sample consensus algorithm [1], intrinsic mode chirp decomposition [2], intrinsic chirp component decomposition [3] and fast IF tracking algorithm (FAST-IF) [4,5]. However, in all those aforementioned methods, the number of components P is assumed to be known and larger than or equal to the true number of components M , P ≥ M , which enables recovering the IF of each component iteratively. ...
... However, when two IFs are intersecting in the TF plane, that procedure becomes invalid. Therefore, to address that issue, some methods [4,8,5] are taken into account for getting both amplitude and direction of the detected peak ...
... In (4) 3) Using the estimated IF, i.e.ω m (t), the corresponding component is removed from mixture signal based on TF filtering method [4,5]. This process is iterated until no new ridges are extracted in the TF plane. ...
... To further demonstrate the effectiveness of the proposed method, we compared it with several commonly used component extraction methods: RPRG [12], VA [11] and ADTFD-RT [13]. The F1 score, accuracy and running time on the test dataset mentioned above are listed in Table 4. ...
The fine state of targets can be represented by the extracted micro-Doppler (m-D) components from the radar echo. However, current methods do not consider the specialty of the m-D components, and their performance with non-sinusoidal components is poor. In this paper, a neural network is applied to signal extraction for the first time. Inspired by the semantic line detection in computer vision, the extraction of the m-D components is transformed into the network-based time–frequency curves detection problem. Specifically, a novel dual-branch network-based m-D components extraction method is proposed. According to the property of intersected multiple m-D components, the dual-branch network consisting of a continuous m-D components extraction branch, and a crossing point detection branch is designed to obtain components and cross points at the same time. In addition, a shuffle attention-fast Fourier convolution (SA-FFC) module is proposed to fuse local and global contexts and focus on key features. To solve the error correlation problem of multi-component signals, the first-order parametric continuous condition and cubic spline interpolation are employed to obtain complete and smooth components curves. Simulation and measurement results show that this method of good robustness is a good candidate for separating the non-sinusoidal m-D components with intersections.
... The extracted TF points are then used to obtain a robust estimate of a covariance matrix that results in improved estimation accuracy as compared to the original time-domain MUSIC and timedomain estimation of signal parameters via rational invariance techniques (ESPIRIT) algorithms [5,7,9,18,21]. The second category employs instantaneous frequency (IF) estimation algorithms in conjunction with TF representations to extract TF signature of sources [11,12,14,20,25]. Once the TF signature of the sources is estimated, the sources are separated through TF filtering and the MUSIC algorithm is applied separately for each source. ...
This paper presents a novel and robust algorithm to estimate the direction of arrival of sources by combining spatial time–frequency distributions and spatial filtering. The proposed algorithm first analyzes a given signal using robust spatial time–frequency distribution. Then, the strongest time–frequency points are selected and clustered to find out the direction of the strongest source. The signal corresponding to the strongest source is then removed through spatial filtering, and this process is iterated till the directions of all the sources are estimated. Numerical results indicate that the proposed method achieves better performance compared to other state-of-the-art methods for both complete signals and sparsely sampled signals. For example, in direction of arrival estimation, the proposed method achieves a mean square error of -\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-$$\end{document}37 dB which is 2 dB lower than the mean square error achieved by the next best method.
... For such signals, the adaptive directional TFD (ADTFD) achieves better performance as it adapts the shape of the smoothing kernel locally at each point in the TF plane [22]. The ADTFD has found applications in sparse signal reconstruction [24], source localization [21], feature extraction [18], and accurate IF estimation [23]. Moreover, the ADTFD has inspired convolutional neural networks-based TF signal analysis methods [16]. ...
This study proposes a novel high-resolution time–frequency distribution (TFD) that is based on the iterative application of the locally adaptive directional kernel for both mono-sensor and multi-sensor recordings. In each iteration, the adaptive directional kernel suppresses cross-terms, whereas the resolution of the auto-terms remains unaffected. The mono-sensor variant of the proposed TFD outperforms existing TFDs not only in terms of high resolution and cross-term suppression properties but also in robustness to noise and missing samples. The multi-sensor variant improves the resolution performance of the existing direction of arrival estimation algorithms, i.e. time–frequency MUSIC algorithm.
... In addition, later development on SET and SEWT includes [47][48][49][50][51][52]. Most of these methods are applicable only to signals with well separated components in the TF plane, but for crossing components there are also many approaches like those from Khan et al. [53], [54], Djurović [55], Zhu et al. [49], Chui et al. [56], [57], etc. ...
Time-frequency (TF) analysis method provides a powerful tool to analyze non-stationary signals. However, for strongly time-varying signals, how to characterize the time-varying features of signals accurately, how to achieve a highly concentrated TF representation, and how to reconstruct signals with high accuracy are still challenging tasks. In this paper, in order to analyze strongly amplitude-modulated and frequency-modulated signals, we introduce an accurate instantaneous frequency (IF) estimator, further propose a high-resolution TF analysis method and three high-accuracy reconstruction methods. Firstly, we present signal parameter, chirp rate and IF estimation from the wavelet transform of Gaussian amplitude-modulated linear chirp model. Based on this, we introduce the self-matched extracting wavelet transform (SMEWT), which improves the energy concentration of TF representation, by only retaining TF information related to the IF of the signal. Furthermore, the signal parameter, chirp rate and IF estimation lead to accurate signal reconstruction formulas. In this regard, we provide a theoretical analysis and comparison of SMEWT reconstruction, and present two hybrid reconstruction methods of signal. It is well known that the reassignment method can improve the readability of the TF representation, but it cannot reconstruct the signal. It is worth mentioning that one of the proposed hybrid reconstruction methods is a combination of the reassignment method and deduced reconstruction formula, which not only captures the flavor and philosophy of the reassignment method, but also uses a hybrid way in signal reconstruction. Finally, simulated and real signals are employed to confirm the effectiveness of the proposed methods by comparing with some classical TF analysis methods.
... IF estimation for signals with multiple components is especially challenging and many approaches have been made [10] , including estimations relying on the first derivative of the IF [11,12] , eigenvector decomposition [13] , image analysis [14] , parametric estimation [15] , and the chirplet transform [16] . There have also been improvements made on the Viterbi algorithm that can resolve intersecting components [17,18] , as well as a similar ridge tracking approach [19] . Another approach combines the quasi-maximum likelihood and the random sample consensus [20] . ...
Joint time-frequency representations are important tools when estimating the instantaneous frequency. The widely used spectrogram is known to have poor energy localisation, which the reassignment method improves. However, the reassignment method is sensitive to noise. In this paper we present a multitaper reassigned spectrogram (MTRS) that is robust to noise and tailored to short duration transient signals. The MTRS is designed for oscillating transients with Gaussian envelopes and uses the Hermite functions as windows. The novel reassignment coordinates needed for the MTRS are derived in this paper. The MTRS localises energy at the instantaneous frequencies of transients, while white Gaussian noise is made flatter by the use of multiple windows. It is shown that the MTRS is more noise robust compared to reassignment with just one window, and that it improves on the energy localisation of the spectrogram. Thus, our MTRS is sparse, easy to interpret, and well suited for instantaneous frequency estimation, even for signals with overlapping transients and low signal-to-noise ratios.
... A number of instantaneous frequency estimation has been developed for monosensor recordings that include RANSAC-based methods [8][9][10][11], Hough transform-based methods [12,13], Viterbi-based methods [14][15][16][17], image-processing techniques [3,18], ridge detection, and tracking approaches [19][20][21][22]. Most of the above-mentioned methods first transform a given signal to a joint TF domain using time-frequency distributions (TFDs) and then estimate the IF curve by detecting and linking peaks. ...
Instantaneous frequency in multi-sensor recordings is an important parameter for estimation of direction of arrival estimation, source separation, and sparse reconstruction. The instantaneous frequency estimation problem becomes challenging when signal components have close or overlapping signatures and the number of sensors is less than the number of sources. In this study, we develop a computationally efficient method that exploits the direction of the IF curve in addition to the angle of arrival as additional features for the accurate tracking of IF curves. Experimental results show that the proposed scheme achieves better accuracy compared to the-state-of-art method in terms of mean square error (MSE) with a slight increase in the computational cost, i.e., the proposed method achieves MSE of −50 dB at the signal to noise ratio of 0 dB whereas the existing method achieves the MSE of −38 dB.
