Analysis of multicomponent signals by multilinear time-frequency representations

2002 ◽  
Author(s):  
S. Barbarossa ◽  
G. Schiappa
Keyword(s):  
Time Frequency ◽  
Multicomponent Signals

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 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 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 Design and implementation of the subsystem subject to emission of multicomponent high-frequency signals to ensure its reliability

2019 ◽  
Vol 9 (5) ◽  
pp. 4204
Author(s):  
Milad Daneshvar ◽  
Naser Parhizgar ◽  
Homayoon Oraizi
Keyword(s):  
High Frequency ◽  
Detection Methods ◽  
System Behavior ◽  
Time Frequency ◽  
Telecommunication Systems ◽  
Multicomponent Signals ◽  
Extensive Range ◽  
Interference Signals ◽  
Analytic Signals ◽  
Phase Differences

Telecommunication systems, especially digital ones, are mostly known to be immune to noise given their extensive range of applications. This study aimed to investigate the methods and tools used for the analysis of multicomponent signals input to high-frequency digital subsystems, including the analysis of changes in its electrical behavior. This research mainly focuses on analyzing a high-frequency telecommunication subsystem, recording the results, investigating the system behavior against signals with different amplitudes and phases, detecting the received signals, and measuring the phase differences. The study extended the mono-component signals to multi-component signals and accurately extracted the statistical signal specifications using analytic signals in the time-frequency domain. To this end, a method was proposed based on the switch matrix to relate the different components and parameters, and also a mathematical model based on the state-space equations was employed to evaluate the nonlinear system modes. Given that the decoupling of measurement parameters is a problem to be tackled from multiple aspects, the costs and test durations were also taken into calculations in addition to considering all the detection methods for interference signals, reliability and time under test.

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