A Novel Ridge Detector for Nonstationary Multicomponent Signals: Development and Application to Robust Mode Retrieval

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.

Download Full-text

Analysis of multicomponent signals by multilinear time-frequency representations

Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing ◽

10.1109/icassp.1994.390029 ◽

2002 ◽

Cited By ~ 4

Author(s):

S. Barbarossa ◽

G. Schiappa

Keyword(s):

Time Frequency ◽

Multicomponent Signals

Download Full-text

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

Mathematics ◽

10.3390/math8122170 ◽

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.

Download Full-text

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

Remote Sensing ◽

10.3390/rs12172766 ◽

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).

Download Full-text