Time-frequency analysis

One of the main advantages of the WT is its adaptative ability to perform time-frequency analysis [28, 29] when using complex analyzing wavelets like the Morlet s wavelet ... 

An allpass filter has a flat magnitude response, and we might expect it to solve the problem of timbral coloration attributed to the comb filter. However, the response of an allpass filter sounds quite similar to the comb filter, tending to create a timbral coloration. This is because our ears perform a short-time frequency analysis, whereas the mathematical property of the allpass filter is defined for an infinite time integration. 

We calculate the laser propagation along the propagation axis using a onedimensional (ID) model and display the results using the time-frequency analysis. A distribution function in the time-frequency domain [11] is a powerful tool to analyze the chirp structure that cannot be revealed by a standard... 

L. Cohen, Time-Frequency Analysis, Prentice-Hall, Madison, WI, 1995. 

R. Carmona, W.-L. Hwang, and B Torresani. Practical Time-Frequency Analysis. Gabor and Wavelet Transforms with an Implementation in S. Acar demic Press, 1998. 

Ibrahim, K. and Bachalo, W., Time-Frequency Analysis and Measurement Accuracy in Laser Doppler and Phase Doppler Signal Processing Applications. 

When localisation is an issue, the intuitive solution still making use of the Fourier transform would be to cut up the signal and to transform the pieces. This approach is called the short-time Fourier transform, it adds a dimension to the Fourier transform, namely time, as it allows following frequencies over time. Where the Fourier transform is a frequency analysis, the short-time Fourier transform is a time-frequency analysis. Instead of describing the signal in either the time or the frequency domain, we describe it in both, a joint time-frequency domain. When we do this, we are faced with a fundamental limitation we cannot localise in the time domain and the frequency domain at the same time. 

This type of time-frequency analysis gives us a very rich view of the data, but it is poor when we are after an efficient representation. The results of the Fourier transforms of two neighbouring, not disjoint but severely overlap-... 

A wavelet basis allows a time-frequency analysis similar to that of a short-time Fourier basis. It is different in that its time-localisation is better hence its frequency localisation is worse, for high frequencies than for low fre-... 

The authors also made use of the wavelet transform for time-frequency analysis, as in Permann s work above. Noting that the wavelet. 

For thin shell structures, the most promising methods are those based in the analysis of the propagation of elastic waves. The wave propagation methods have often used piezoelectric wafer active sensors (PWAS) as transmitters to generate waves and simultaneously as receivers to measure the echo signals due to the defects. A time-frequency analysis allows an estimation of crack size on the basis of the relationship between new and baseline response. The sensitivity of Lamb waves to defects depends largely on the frequency, and for complex structures the dispersive Lamb waves interact with reinforcements with partial reflections and refractions. These systems have not reached the level of maturity required for industrial applications. A full discussion with alternatives is presented in the book by Giurgiutiu (2008). 

Wavelet analysis is a method for time-frequency analysis, which can obtain weak information from climate records. Wavelet transform can translation and stretch the original climate record, then transform with multiple scales to get the cycles. Qinghai Lake is located at the western side of Gaoligong Mountain in Yunnan Plateau, which mainly influenced by the Asian southwest monsoon. In this paper, we investigating the Holocene climate variance by analysis the grain-size. Total Organic Carbon content (TOC), carbonate content (CaCOj) and Magnetic susceptibility records, then use the wavelet analysis to get the Holocene climate cycles for further study the characteristics and mechanism of Asian southwest monsoon. 

In joint time-frequency analysis, impedance is presented as function of time. This however, does not mean that time and frequency domains are mixed together. Any impedance at a given time should be considered as time invariant that is true for any time interval approaching zero. The consequence is that the impedance should change negligibly within the smallest given time interval. Sophisticated, nonlinear models for time variant impedances are not considered here. 

Looking at Figure 9.36, it is obvious that the signal could be represented by only one or two frequency components if the transformation was performed within a moving time window. This kind of time-frequency analysis is available in the so-called short-time Fourier transform (STFT). The problem with STFT is that the resolution in time and... 

Compared vv ith the STFT, whose time-frequency resolution is constant, the time-frequency resolution of the wavelet transform depends on the frequency of the signal. At high frequencies, the wavelet reaches a high time resolution but at a low frequency resolution whereas at low frequencies, high-frequency resolution and low time resolution can be obtained. Such adaptability of time-frequency analysis reinforces the important status of the wavelet transform in the fault diagnostics field. 

Li, X. and Guan, X.P. (2004) Time-frequency-analysis-based minor cutting edge fracture detection during end milling. Mechanical Systems and Signal Processing, 18 1485-96. 

Figure 7 shows the time frequency analysis results of SSEPs in right and left primary sensory cortex. The MCAO... 

In this study, we applied non-invasive approach for evaluating focal cerebral ischemia. The pattern of SSEP response shows that the Pl-Nl amplitude was sipiflcant attenuated but the PI latency was not significant decayed. The hemodynamic response was detected when somatosensory evoke potential was measured from surface recording region. The result of time frequency analysis shows that the high frequency shifts in the initial of the SSEPs. Several studies have also indicated that phenomenon may be caused by brain injury. The results of neurovascular coupling are consistent with previous studies [9]. 

Blind source separation Modal identification Sparse representation Structural health monitoring Time-frequency analysis... 

Feng Z, Liang M, Chu F (2013) Recent advances in time-frequency analysis methods for machinery fault diagnosis a review with application examples. Mech Syst Signal Pr 38(1) 165-205... 

P. Steeghs, R. Baraniuk and J.E. Odegard (2003) Time-frequency analysis of seismic reflection data. Applications in Time-Frequency Signal Processing,... 

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