Time-Frequency Distributions And Their Comparisons

Time-Frequency (TF) analysis begins at 1940s. Non-stationary signal is its main research target. TF is desired to describe how the frequency of the signal is changing as the time goes and finally how to find a distribution that could gives the energy or intensity of the signal. As the development of time-frequency tools, people expect to find a TD distribution that has high resolutions in both frequency and time and hope that time-frequency analysis has the functionality if adaptive time-frequency resolution. Hilbert-Huang transform (HHT) is the new one. The key of HHT is that any complicated data set can be decomposed into some series of intrinsic mode functions (IMF) using the empirical mode decomposition (EMD) method. Furthermore, the instantaneous frequency of IMF can be solved by Hilbert transform.Firstly, this paper discusses the basic theories of several TF methods. We experimentally compare the frequency resolution of four types of TF analysis methods, namely, Short Time Fourier Transform (STFT), Wavelet Transform (WT), Choi-Williams Distribution (CWD) and Hilbert-Huang transform (HHT). The results suggest that HHT has the highest frequency resolution, CWD is better than WT and STFT is the worst.Secondly, the paper discusses the influence of stop criterion of HHT to EMD. After setting the different values of SD which is a parameter of stop criterion, we found that the number of IMF is reduced as SD is bigger and bigger. And when SD is the default, EMD has the best effect.Additionally, the combine of time-frequency and pattern recognition will leads a good application. In chapter three, we employed the data that comes from Shanghai stock exponent in June, 2007, with the above mentioned 4 types of TF methods and correlation coefficient. The results suggest that only HHT could recognize the rising and descending line from the stock data.TF has applied in engineering, physics, astronomy, chemistry, biology, medicine, mathematics areas and got a lot of valuable results. Finally, the three main application of TF is introduced: fault diagnosis, signal feature extraction, and drift denoising.