scholarly journals A Signal Complexity-Based Approach for AM–FM Signal Modes Counting

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2170
Author(s):  
Vittoria Bruni ◽  
Michela Tartaglione ◽  
Domenico Vitulano
Keyword(s):  
Instantaneous Frequency ◽  
Individual Component ◽  
Stationary Process ◽  
Practical Applications ◽  
Time Frequency ◽  
Number Of Components ◽  
Multicomponent Signal ◽  
Multicomponent Signals ◽  
Robustness To Noise ◽  
Signal Complexity

Frequency modulated signals appear in many applied disciplines, including geology, communication, biology and acoustics. They are naturally multicomponent, i.e., they consist of multiple waveforms, with specific time-dependent frequency (instantaneous frequency). In most practical applications, the number of modes—which is unknown—is needed for correctly analyzing a signal; for instance for separating each individual component and for estimating its instantaneous frequency. Detecting the number of components is a challenging problem, especially in the case of interfering modes. The Rényi Entropy-based approach has proven to be suitable for signal modes counting, but it is limited to well separated components. This paper addresses this issue by introducing a new notion of signal complexity. Specifically, the spectrogram of a multicomponent signal is seen as a non-stationary process where interference alternates with non-interference. Complexity concerning the transition between consecutive spectrogram sections is evaluated by means of a modified Run Length Encoding. Based on a spectrogram time-frequency evolution law, complexity variations are studied for accurately estimating the number of components. The presented method is suitable for multicomponent signals with non-separable modes, as well as time-varying amplitudes, showing robustness to noise.

scholarly journals A pde-Based Analysis of the Spectrogram Image for Instantaneous Frequency Estimation

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 247
Author(s):  
Vittoria Bruni ◽  
Michela Tartaglione ◽  
Domenico Vitulano
Keyword(s):  
Instantaneous Frequency ◽  
Numerical Study ◽  
Frequency Estimation ◽  
Estimation Error ◽  
Destructive Interference ◽  
Instantaneous Frequency Estimation ◽  
Practical Applications ◽  
Time Frequency ◽  
Multicomponent Signals ◽  
Non Parametric

Instantaneous frequency (IF) is a fundamental feature in multicomponent signals analysis and its estimation is required in many practical applications. This goal can be successfully reached for well separated components, while it still is an open problem in case of interfering modes. Most of the methods addressing this issue are parametric, that is, they apply to a specific IF class. Alternative approaches consist of non-parametric time filtering-based procedures, which do not show robustness to destructive interference—the most critical scenario in crossing modes. In this paper, a method for IF curves estimation is proposed. The case of amplitude and frequency modulated two-component signals is addressed by introducing a spectrogram time-frequency evolution law, whose coefficients depend on signal IFs time derivatives, that is, the chirp rates. The problem is then turned into the resolution of a two-dimensional linear system which provides signal chirp rates; IF curves are then obtained by a simple integration. The method is non-parametric and it results quite robust to destructive interference. An estimate of the estimation error, as well as a numerical study concerning method sensitivity and robustness to noise are also provided in the paper.

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

2005 ◽  
Vol 461 (2059) ◽  
pp. 2159-2179 ◽  
Author(s):  
S Olhede ◽  
A.T Walden
Keyword(s):  
Instantaneous Frequency ◽  
Additive Noise ◽  
Simulation Experiment ◽  
Wavelet Packet ◽  
Covariance Structure ◽  
Time Instant ◽  
Analytic Signal ◽  
Flexible Approach ◽  
Time Frequency ◽  
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.

scholarly journals Instantaneous Frequency Estimation Based on Modified Kalman Filter for Cone-Shaped Target

2020 ◽  
Vol 12 (17) ◽  
pp. 2766
Author(s):  
Ke Ren ◽  
Lan Du ◽  
Xiaofei Lu ◽  
Zhenyu Zhuo ◽  
Lu Li
Keyword(s):  
Kalman Filter ◽  
Survival Rate ◽  
Instantaneous Frequency ◽  
Estimation Method ◽  
Consensus Algorithm ◽  
Instantaneous Frequency Estimation ◽  
Time Frequency ◽  
Multicomponent Signals ◽  
Modified Kalman Filter ◽  
Trajectory Correction

The instantaneous frequency (IF) is a vital parameter for the analysis of non-stationary multicomponent signals, and plays an important role in space cone-shaped target recognition. For a cone-shaped target, IF estimation is not a trivial issue due to the proximity of the energy of the IF components, the intersections among different IF components, and the existence of noise. Compared with the general parameterized time-frequency (GPTF), the traditional Kalman filter can perform better when the energy of different signal components is close. Nevertheless, the traditional Kalman filter usually makes association mistakes at the intersections of IF components and is sensitive to the noise. In this paper, a novel IF estimation method based on modified Kalman filter (MKF) is proposed, in which the MKF is used to associate the intersecting IF trajectories obtained by the synchroextracting transform (SET). The core of MKF is the introduction of trajectory correction strategy in which a trajectory survival rate is defined to judge the occurrence of association mistakes. When the trajectory survival rate is below the predetermined threshold, it means that an association mistakes occurs, and then the new trajectories generated by the random sample consensus algorithm are used to correct the wrong associations timely. The trajectory correction strategy can effectively obviate the association mistakes caused by the intersections of IF components and the noise. The windowing technique is also used in the trajectory correction strategy to improve computational speed. The experimental results based on the electromagnetic computation data show that the proposed method is more robust and precise than the traditional Kalman filter. Moreover, the proposed method has great performance advantages compared with other methods (i.e., the multiridge detection, the ant colony optimization, and the GPTF methods) especially in the case of low signal noise ratio (SNR).

Non-Stationary Signal Analysis of the von Ka´rma´n Vortex Shedding in the Wake of a Fluttering Airfoil

2010 ◽  
Author(s):  
Amin Fereidooni ◽  
Abhijit Sarkar ◽  
Dominique Poirel ◽  
Aze´mi Benaissa ◽  
Vincent Me´tivier ◽  
...  
Keyword(s):  
Hilbert Transform ◽  
Vortex Shedding ◽  
Instantaneous Frequency ◽  
Positive Energy ◽  
Pitching Airfoil ◽  
Time Frequency ◽  
Multicomponent Signals ◽  
Vortex Shedding Frequency ◽  
Shedding Frequency ◽  
Non Stationary Signal

Stationary data lend themselves well to the Fourier decomposition into harmonic components. Conversely, spectral characteristics of non-stationary data vary with time, and hence do not generally admit the application of Fourier transform. In order to investigate the localized time-frequency characteristics of non-stationary data, the notions of instantaneous frequency and amplitude are invoked. These concepts are applied to the von Ka´rma´n vortex shedding observed in the wake of a self-sustained pitching airfoil. For this range of Reynolds numbers (104 – 105), it has been reported that at any given airspeed the shedding frequency of the vortex street varies with angle of attack (AOA), ranging from the Strouhal number St ≈ 0.6 at zero AOA and tending to St ≈ 0.1 for high AOA. For the pitching motion, which originates from a positive energy transfer from the flow to the airfoil due to negative aerodynamic damping, the von Ka´rma´n vortex shedding frequency varies with pitch angle hence with time. Hilbert transform provides a robust estimate of instantaneous frequency through the definition of analytic signals. However, Hilbert transform provides meaningful instantaneous frequency for only monocomponent signals. To overcome this difficulty, the Hilbert-Huang transform is commonly exploited. In this paper, both the Hilbert and Hilbert-Huang transforms are applied in order to capture the instantaneous vortex shedding frequency. For multicomponent signals Empirical Mode Decomposition (EMD) splits the signal to monocomponent signals, namely Intrinsic Mode Functions, through a so-called sifting process. Application of Hilbert transform to these functions produces instantaneous frequencies and amplitudes. Therefore the time-frequency-amplitude representation of the signal appears to be a promising tool for obtaining more physical insight into the time-varying vortex shedding frequency in the wake of a pitching airfoil.

scholarly journals Novel Method for Vibration Sensor-Based Instantaneous Defect Frequency Estimation for Rolling Bearings Under Non-Stationary Conditions

Sensors ◽  
2020 ◽  
Vol 20 (18) ◽  
pp. 5201 ◽  
Author(s):  
Dezun Zhao ◽  
Len Gelman ◽  
Fulei Chu ◽  
Andrew Ball
Keyword(s):  
Instantaneous Frequency ◽  
Frequency Estimation ◽  
Vibration Sensor ◽  
Rolling Bearings ◽  
Instantaneous Frequency Estimation ◽  
Noise Interference ◽  
Time Frequency ◽  
Multicomponent Signals ◽  
Stationary Conditions ◽  
Defect Frequency

It is proposed a novel instantaneous frequency estimation technology, multi-generalized demodulation transform, for non-stationary signals, whose true time variations of instantaneous frequencies are unknown and difficult to extract from the time-frequency representation due to essentially noisy environment. Theoretical bases of the novel instantaneous frequency estimation technology are created. The main innovations are summarized as: (a) novel instantaneous frequency estimation technology, multi-generalized demodulation transform, is proposed, (b) novel instantaneous frequency estimation results, obtained by simulation, for four types of amplitude and frequency modulated non-stationary single and multicomponent signals under strong background noise (signal to noise ratio is −5 dB), and (c) novel experimental instantaneous frequency estimation results for defect frequency of rolling bearings for multiple defect frequency harmonics, using the proposed technology in non-stationary conditions and in conditions of different levels of noise interference, including a strong noise interference. Quantitative instantaneous frequency estimation errors are employed to evaluate performance of the proposed IF estimation technology. Simulation and experimental estimation results show high effectiveness of the proposed estimation technology.

Time-Frequency Analysis of Non-Stationary Ground Motions via Multivariate Empirical Mode Decomposition

2014 ◽  
Vol 580-583 ◽  
pp. 1734-1741
Author(s):  
Yan Wen Su ◽  
Guo Qing Huang ◽  
Liu Liu Peng
Keyword(s):  
Frequency Analysis ◽  
Instantaneous Frequency ◽  
Stationary Process ◽  
Ground Motions ◽  
Analysis Framework ◽  
Spectral Evolution ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Multivariate Empirical Mode Decomposition ◽  
Mode Decomposition

In this paper, MEMD-based scalogram and coscalogram, and instantaneous frequency spectral are proposed to characterize the data derived from the multivariate non-stationary process. The scalogram and instantaneous frequency spectral capture spectral evolution of each component while the coscalogram reveals embedded intermittent correlation between two components. Compared with scale-based scalogram and coscalogram, frequency-based instantaneous frequency spectral provides more detailed portrayal for multivariate data. The effectiveness of the proposed MEMD-based time-frequency analysis framework is validated by numerical examples of uniformly and generally modulated ground motions.

Optimization of multicomponent signals entered to the system using estimation of instantaneous frequency

2021 ◽  
pp. 107754632098638
Author(s):  
Milad Daneshvar ◽  
Pouria Salehi
Keyword(s):  
Instantaneous Frequency ◽  
Energy Concentration ◽  
Signal Frequency ◽  
Signal Phase ◽  
Frequency Distributions ◽  
Time Frequency ◽  
Multicomponent Signals ◽  
Frequency Changes ◽  
Changes Over Time ◽  
Zero Points

The frequency signal displays are not efficient for analyzing nonstationary signals because of their inability to represent frequency changes over time. In fact, because most of the signals are real, nonstationary, and time varying, analyzing the signals in the time–frequency domain to estimate the instantaneous frequency of a signal is inevitable. The methods of estimating the instantaneous frequency of the multicomponent signals are divided into three groups, which include the methods using signal phase derivatives that are sensitive to noise, methods that calculate the number of zero points of the signal and consider the signal frequency equal to half the frequency of the zero points and are suitable for signals that can be imagined as stationary, and methods based on time–frequency distributions and distributions such as Wigner for instantaneous frequency calculations and more for instantaneous frequency calculations on nonstationary noise signals that exhibit varied time–frequency distributions. In this article, a new hybrid algorithm is used to evaluate different distribution criteria and comparing their performance in investigating one or more features of time–frequency distributions, such as resolution and energy concentration.

scholarly journals Estimating the Instantaneous Frequency of Linear and Nonlinear Frequency Modulated Radar Signals—A Comparative Study

Sensors ◽  
2021 ◽  
Vol 21 (8) ◽  
pp. 2840
Author(s):  
Hubert Milczarek ◽  
Czesław Leśnik ◽  
Igor Djurović ◽  
Adam Kawalec
Keyword(s):  
Instantaneous Frequency ◽  
Early Warning Systems ◽  
Vital Role ◽  
Estimation Methods ◽  
Radar Signal ◽  
Nonlinear Frequency ◽  
Modulation Recognition ◽  
Electronic Warfare ◽  
Time Frequency ◽  
Radar Signals

Automatic modulation recognition plays a vital role in electronic warfare. Modern electronic intelligence and electronic support measures systems are able to automatically distinguish the modulation type of an intercepted radar signal by means of real-time intra-pulse analysis. This extra information can facilitate deinterleaving process as well as be utilized in early warning systems or give better insight into the performance of hostile radars. Existing modulation recognition algorithms usually extract signal features from one of the rudimentary waveform characteristics, namely instantaneous frequency (IF). Currently, there are a small number of studies concerning IF estimation methods, specifically for radar signals, whereas estimator accuracy may adversely affect the performance of the whole classification process. In this paper, five popular methods of evaluating the IF–law of frequency modulated radar signals are compared. The considered algorithms incorporate the two most prevalent estimation techniques, i.e., phase finite differences and time-frequency representations. The novel approach based on the generalized quasi-maximum likelihood (QML) method is also proposed. The results of simulation experiments show that the proposed QML estimator is significantly more accurate than the other considered techniques. Furthermore, for the first time in the publicly available literature, multipath influence on IF estimates has been investigated.

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