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.

SPARSE RECONSTRUCTION OF HARDY SIGNAL AND APPLICATIONS TO TIME-FREQUENCY DISTRIBUTION

2013 ◽  
Vol 11 (03) ◽  
pp. 1350031
Author(s):  
TAO QIAN ◽  
SHUANG LI ◽  
WEIXIONG MAI
Keyword(s):  
Frequency Distribution ◽  
Optimization Technique ◽  
Singular Values ◽  
Reproducing Kernels ◽  
Periodic Case ◽  
Time Frequency ◽  
New Type ◽  
First Time ◽  
Analytic Signals ◽  
Time Frequency Distribution

In this paper, we introduce a sparse recovery strategy for analytic signals in Hardy space H2(𝔻), where 𝔻 denotes the unit disk of the complex plane. The representation strategy is based on the optimization technique. We investigate the asymptotic singular values distribution of the dictionary matrix and give an estimation of the number of rows of the random matrix. To the best of our knowledge, this is the first time that such result is given. This result demonstrates that the dictionary of the normalized Szegö kernels (or reproducing kernels) is perfect for decompositions of analytic signals. A numerical example is presented exhibiting the theory. As applications, we still work on time-frequency analysis and propose a new type of non-negative time-frequency distribution associated with mono-components in the periodic case.

Time–Frequency Distribution Analyses of Ku-Band Radar Doppler Echo Signals

Frequenz ◽  
2015 ◽  
Vol 69 (3-4) ◽  
Author(s):  
Dimitrije Bujaković ◽  
Milenko Andrić ◽  
Boban Bondžulić ◽  
Srđan Mitrović ◽  
Slobodan Simić
Keyword(s):  
Frequency Distribution ◽  
Doppler Frequency ◽  
Energy Concentration ◽  
Frequency Distributions ◽  
Signal Energy ◽  
Time Frequency ◽  
Window Functions ◽  
Radar Echo ◽  
Time Frequency Distribution ◽  
Ku Band

AbstractReal radar echo signals of a pedestrian, vehicle and group of helicopters are analyzed in order to maximize signal energy around central Doppler frequency in time–frequency plane. An optimization, preserving this concentration, is suggested based on three well-known concentration measures. Various window functions and time–frequency distributions were optimization inputs. Conducted experiments on an analytic and three real signals have shown that energy concentration significantly depends on used time–frequency distribution and window function, for all three used criteria.

Signal separation and correction with multiple Doppler acoustic sources for wayside fault diagnosis of train bearings

2016 ◽  
Vol 231 (14) ◽  
pp. 2664-2680
Author(s):  
Shangbin Zhang ◽  
Qingbo He ◽  
Haibin Zhang ◽  
Kesai Ouyang ◽  
Fanrang Kong
Keyword(s):  
Time Series ◽  
Fault Diagnosis ◽  
Frequency Distribution ◽  
Signal Separation ◽  
Frequency Distributions ◽  
Time Frequency ◽  
S Transform ◽  
Generalized S Transform ◽  
Original Time ◽  
Time Frequency Distribution

The extraction of single train signal is necessary in wayside fault diagnosis because the acoustic signal acquired by a microphone is composed of multiple train bearing signals and noises. However, the Doppler distortion in the signal acquired by a microphone effectively hinders the signal separation and fault diagnosis. To address this issue, we propose a novel method based on the generalized S-transform, morphological filtering, and time–frequency amplitude matching-based resampling time series for multiple-Doppler-acoustic-source signal separation and correction. First, the original time–frequency distribution is constructed by applying generalized S-transform to the raw signal acquired by a microphone. Based on a morphological filter, several time–frequency distributions corresponding to different single source Doppler fault signals are extracted from the original time–frequency distribution. Subsequently, the time–frequency distributions are reverted to time signals by inverse generalized S-transform. Then, a resampling time series is built by time–frequency amplitude matching to obtain the correct signals without Doppler distortion. Finally, the bearing fault is diagnosed by the envelope spectrum of the correction signal. The effectiveness of this method is verified by simulated and practical signals.

A Time-Frequency Distribution for Analysis of Signals with Transient Components and Its Application to Vibration Analysis

1999 ◽  
Vol 121 (3) ◽  
pp. 328-333 ◽  
Author(s):  
G. T. Zheng ◽  
P. D. McFadden
Keyword(s):  
Frequency Distribution ◽  
Wigner Distribution ◽  
Vibration Signals ◽  
Frequency Distributions ◽  
Time Frequency ◽  
Frequency Domains ◽  
Harmonic Components ◽  
Cohen Class ◽  
New Distribution ◽  
Time Frequency Distribution

Bilinear time-frequency distributions, which provide simultaneous high resolution in both time and frequency domains, offer advantages for the analysis of vibration signals where the harmonic components and sidebands may be closely spaced. However, the Choi-Williams exponential distribution is found to be unsuitable, and aliasing produced by distributions of the Cohen class also causes problems. An aliasfree exponential time-frequency distribution is introduced, which combines features of distributions of the Cohen class and the generalized Wigner distribution. The new distribution is shown to be well suited to the analysis of signals with transient components.

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