Optimal Windows for the Time-Frequency Analysis of Arbitrary Swept Frequency Signals

1995 ◽  
Author(s):  
James A. Mooney ◽  
Andres Soom
Keyword(s):  
Frequency Analysis ◽  
Wavelet Transforms ◽  
Fourier Transforms ◽  
Rate Of Change ◽  
Effective Bandwidth ◽  
Instantaneous Rate ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Analysis Window ◽  
Constant Bandwidth

Abstract In noise and vibration analysis, as well as in many other engineering applications, it may be necessary to extract or analyze signals with time-varying frequency components. Examples include start-up and shut-down of rotating machinery, transient structural vibrations, vehicle passing noise, and speech analysis. Both Short-Time Fourier Transforms (STFT), representing a set of non-causal filters of constant bandwidth, and Wavelet Transforms, representing a set of non-causal filters of constant Q or constant percent bandwidth, have been used for such Joint Time Frequency Analysis (JTFA). In the present work, an arbitrary swept frequency signal is approximated locally, in time, by a linearized frequency sweep. We show that an optimal time window can be identified which, at a given frequency, is inversely proportional to the square root of the instantaneous rate of change of frequency. We find that the constant bandwidth of the STFT and the constant-Q of the Wavelet transform represent extreme cases which are each optimal for certain types of signals. In between the two extremes there lies a continuous range of variation of the effective bandwidth with frequency. Many important types of signals require analysis window variation in this range between STFT and Wavelet analysis. The paper concludes with some simple rules for optimizing the variation of the analysis window with frequency for various types of signals.

Time-Frequency Analysis of Transient Vibrations to Improve Turbo-Compressor Start-Up

2008 ◽  
Author(s):  
Juan C. Jauregui ◽  
Oscar Gonzalez ◽  
Eduardo Rubio
Keyword(s):  
Frequency Analysis ◽  
Fourier Transforms ◽  
Transient Vibration ◽  
Vibration Signals ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Start Up ◽  
Rotational Systems ◽  
Turbo Compressor ◽  
Different Sources

Diagnosis of turbo-compressors during start-up is a particularly challenging task. One of the reason is the reduced set of instruments that monitor this procedure. It is cumbersome to adjust lubrication and steam valves while controlling the speed and dynamic stability. In order to get the turbo-compressor out of a high vibration zone, it is important to be able to predict instabilities associated to the start-up process. Thus, it is necessary to have a measurement system with the ability of fault detection, especially at early stages of fault appearance. In this way, the start-up time can be significantly reduced. Although recent developed diagnosis methods use information from different sources and measurements, data structures are not designed to carry predictive information related to the turbo-compressor health. Therefore, it is important to extract early warning signals related to instability conditions. Vibration signals during machine start-up are non-stationary in nature, and conventional techniques, such as Fourier transforms and time series analysis, have difficulties to extract the full features of the vibrations signature. In this paper, the features of start-up vibrations in rotational systems like those found in turbo compressors are investigated by time-frequency analysis, and appropriate analysis of the transient vibration during compressor start-up is presented.

Time-frequency analysis of electroencephalogram series. II. Gabor and wavelet transforms

1996 ◽  
Vol 54 (6) ◽  
pp. 6661-6672 ◽  
Author(s):  
S. Blanco ◽  
C. E. D'Attellis ◽  
S. I. Isaacson ◽  
O. A. Rosso ◽  
R. O. Sirne
Keyword(s):  
Frequency Analysis ◽  
Wavelet Transforms ◽  
Time Frequency Analysis ◽  
Time Frequency

Application of bi-Gaussian S-transform in high-resolution seismic time-frequency analysis

2017 ◽  
Vol 5 (1) ◽  
pp. SC1-SC7 ◽  
Author(s):  
Zixiang Cheng ◽  
Wei Chen ◽  
Yangkang Chen ◽  
Ying Liu ◽  
Wei Liu ◽  
...  
Keyword(s):  
High Resolution ◽  
Frequency Analysis ◽  
Time Resolution ◽  
Wavelet Transforms ◽  
Superior Performance ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Gaussian Window ◽  
Hydrocarbon Reservoir ◽  
S Transform

The S-transform is one of the most widely used methods of time-frequency analysis. It combines the respective advantages of the short-time Fourier transform and wavelet transforms with scale-dependent resolution using Gaussian windows, scaled inversely with frequency. One of the problems with the traditional symmetric Gaussian window is the degradation of time resolution in the time-frequency spectrum due to the long front taper. We have studied the performance of an improved S-transform with an asymmetric bi-Gaussian window. The asymmetric bi-Gaussian window can obtain an increased time resolution in the front direction. The increased time resolution can make event picking high resolution, which will facilitate an improved time-frequency characterization for oil and gas trap prediction. We have applied the slightly modified bi-Gaussian S-transform to a synthetic trace, a 2D seismic section, and a 3D seismic cube to indicate the superior performance of the bi-Gaussian S-transform in analyzing nonstationary signal components, hydrocarbon reservoir predictions, and paleochannels delineations with an obviously higher resolution.

Slider Vibration Analysis at Contact Using Time-Frequency Analysis and Wavelet Transforms

2000 ◽  
Vol 123 (3) ◽  
pp. 548-554 ◽  
Author(s):  
Bernhard Knigge ◽  
Frank E. Talke
Keyword(s):  
Frequency Analysis ◽  
Wavelet Transforms ◽  
Contact Dynamics ◽  
Frequency Resolution ◽  
High Time Resolution ◽  
Time Frequency Analysis ◽  
Hard Drives ◽  
Disk Interface ◽  
Time Frequency ◽  
Transient Contact

Time-frequency analysis and wavelet transforms are employed to investigate transient contact dynamics at the head/disk interface of computer hard drives. Wavelet transforms are used to resolve multiple short consecutive contacts at high time resolution at high frequencies. The reassignment method is applied to the time-frequency distribution to enhance the time-frequency resolution, thereby allowing to resolve air-bearing and slider body frequencies simultaneously. The results indicate that strong impacts between slider and disk can lead to excitations of slider body and suspension vibrations. Finite element modal analysis of nano and pico glide sliders is found to be in good agreement with experimentally measured frequencies.

Sign in / Sign up

Export Citation Format

Share Document