An analysis of instantaneous frequency representation using time-frequency distributions-generalized Wigner distribution

1995 ◽  
Vol 43 (2) ◽  
pp. 549-552 ◽  
Author(s):  
L.J. Stankovic ◽  
S. Stankovic
Keyword(s):  
Instantaneous Frequency ◽  
Wigner Distribution ◽  
Frequency Distributions ◽  
Time Frequency ◽  
Frequency Representation

Instantaneous Frequency Estimation of Ultrasonic Testing Signal Based on Matching Pursuits

2013 ◽  
Vol 631-632 ◽  
pp. 1367-1372 ◽  
Author(s):  
Xiu Li Du
Keyword(s):  
Instantaneous Frequency ◽  
Ultrasonic Testing ◽  
Frequency Estimation ◽  
Signal To Noise Ratio ◽  
Instantaneous Frequency Estimation ◽  
Time Frequency ◽  
Frequency Representation ◽  
Matching Pursuits ◽  
Testing Signal ◽  
Suppress Noise

The differences of instantaneous frequency (IF) characteristics between the defect echo and the noise can be used to detect defect and suppress noise for ultrasonic testing signal. Therefore, the IF is one of the important instantaneous parameters of ultrasonic testing signal. To estimate the IF of ultrasonic testing signals more effectively, the peak of time-frequency representation (TFR) from matching pursuits (MP) decomposition is proposed. The performances of IF estimators are compared on the simulated signals at different signal-to-noise ratio (SNR) and the real ultrasonic testing signal. The simulation results present that the proposed method can estimate accurate IF at different SNR.

scholarly journals COHEN’S CLASS TIME-FREQUENCY DISTRIBUTIONS FOR MEASUREMENT SIGNALS AS A MEANS OF MONITORING TECHNOLOGICAL PROCESSES

2019 ◽  
Vol 62 (4) ◽  
pp. 324-329
Author(s):  
D. B. Fedosenkov ◽  
A. A. Simikova ◽  
S. M. Kulakov ◽  
B. A. Fedosenkov
Keyword(s):  
Wigner Distribution ◽  
Bulk Material ◽  
Mathematical Tool ◽  
Distribution Map ◽  
Frequency Distributions ◽  
One Dimensional ◽  
Time Frequency ◽  
Technological Processes ◽  
Class Time ◽  
Cohen's Class

The article presents and describes Cohen’s class time-frequency distributions which are expedient to use as a mathematical tool that allows to create a convenient – in terms of information content and semantic clarity – visual-graphical representation of the opera ting modes of various technological processes including processes of ferrous metallurgy. It was noted that a controlling process is usually implemented without simultaneous visual monitoring of each scalar (one-dimensional) coordinate that is under control, but the presence of such monitoring is an important condition for the computer-aided controlling of the dynamics of non-stationary technological processes. To eliminate this drawback, it was proposed to perform synchronous monitoring using the multidimensional Cohen’s class time-frequency distributions, when each measurement scalar signal is specifically represented through one of these distributions, for example, the Wigner-Ville distribution. An expression is given for the generalized distribution of Cohen’s class with a distribution kernel and an ambiguity function. This function allows receiving distributions of various types from the maternal function. The most typical representatives of time-frequency distributions forming this class are given with their available  kernels. The possibility of appearance of interference elements, which make it difficult to identify the controlled modes, on a signal distribution map is proved. Case of the formation of virtual elements within the Wigner-Ville distribution representing a two-component one-dimensional signal is considered. Te conditions are explained for the emergence of parasitic elements on the distribution map, obtained, for example, during realizing the process of multi-component feeding the bulk blast furnace charge materials in the production of sintering mixture. An analytical expression is obtained for the Wigner distribution, which displays a multi-component scalar signal and contains the information (useful) and virtual (parasitic) parts of the time-frequency distribution. A link between the number of bulk material feeders available in the feeding devices unit and the number of parasitic (virtual) elements in the Wigner distribution was determined. Using the dosing process as an example, the effect of the noise components propagation in the Wigner distribution is demonstrated. An example is given to illustrate the penetration of noise into the Wigner distribution and appearance of the virtual concentration in it when displaying a signal waveform with a noisy pause and two sections with different frequencies. An expression for the Wigner distribution in the form of a comb function is obtained. The conclusion was made about the parameters of the distribution periodicity and the required sampling frequency of measurement signals.

scholarly journals NOISE CORRUPTION OF EMPIRICAL MODE DECOMPOSITION AND ITS EFFECT ON INSTANTANEOUS FREQUENCY

2010 ◽  
Vol 02 (03) ◽  
pp. 373-396 ◽  
Author(s):  
DANIEL N. KASLOVSKY ◽  
FRANÇOIS G. MEYER
Keyword(s):  
Empirical Mode Decomposition ◽  
Instantaneous Frequency ◽  
Poor Performance ◽  
Specific Mechanism ◽  
Time Frequency ◽  
Seismic Waveform ◽  
Mode Decomposition ◽  
Frequency Representation ◽  
Transition Modes ◽  
Nonstationary Data

Huang's Empirical Mode Decomposition (EMD) is an algorithm for analyzing nonstationary data that provides a localized time-frequency representation by decomposing the data into adaptively defined modes. EMD can be used to estimate a signal's instantaneous frequency (IF) but suffers from poor performance in the presence of noise. To produce a meaningful IF, each mode of the decomposition must be nearly monochromatic, a condition that is not guaranteed by the algorithm and fails to be met when the signal is corrupted by noise. In this work, the extraction of modes containing both signal and noise is identified as the cause of poor IF estimation. The specific mechanism by which such "transition" modes are extracted is detailed and builds on the observation of Flandrin and Goncalves that EMD acts in a filter bank manner when analyzing pure noise. The mechanism is shown to be dependent on spectral leak between modes and the phase of the underlying signal. These ideas are developed through the use of simple signals and are tested on a synthetic seismic waveform.

TRANSIENT TIME-FREQUENCY DISTRIBUTION BASED ON MONO-COMPONENT DECOMPOSITIONS

2013 ◽  
Vol 11 (03) ◽  
pp. 1350022 ◽  
Author(s):  
PEI DANG ◽  
TAO QIAN ◽  
YUAN YUAN GUO
Keyword(s):  
Frequency Distribution ◽  
Instantaneous Frequency ◽  
Characteristic Property ◽  
Transient Time ◽  
Frequency Distributions ◽  
Time Frequency ◽  
Fourier Frequency ◽  
New Type ◽  
Negative Time ◽  
Time Frequency Distribution

In this paper we propose a new type of non-negative time-frequency distribution associated with mono-components in both the non-periodic and periodic cases, called transient time-frequency distribution (TTFD), and study its properties. The TTFD of a mono-component signal can be obtained directly through its analytic instantaneous frequency. The characteristic property of TTFD is its complete concentration along the analytic instantaneous frequency graph. For multi-components there are induced time-frequency distributions called composing transient time-frequency distribution (CTTFD). Each CTTFD is defined as the superposition of the TTFDs of the composing intrinsic mono-components in a suitable mono-components decomposition of the targeted multi-component. In studying the properties of TTFD and CTTFD the relations between the Fourier frequency and analytic instantaneous frequency are examined.

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