Time-Frequency Analyses and Their Fast Implementation Algorithm
Date Issued
2009
Date
2009
Author(s)
Wang, Wen-Fu
Abstract
The Fourier transform is an important tool in frequency analysis, but it cannot use for non-stationary or time-varying signals. Since The Fourier transform only deal with the stationary and linear signals. The time-frequency distribution function deals with the non-stationary and linear signals. It describes signals in terms of joint time-frequency form and is a powerful tool for analyzing signals. It has been widely applied in much kind of fields, such as speech, physics, electrocardiography (ECG), earth science and music. It is particularly useful for people to analyze signals with continuously time-varying frequency way. A lot of the time-frequency analysis have been widely used and researched for a number of years, such as the short time Fourier transform, the Wigner distribution, the Gabor transform, and other distributions. This thesis mainly has three parts: The first part is the time-frequency analysis. We will introduce a lot of algorithm of the time-frequency distribution, including the theorem of algorithms, advantages and disadvantages, simulations, and applications. We will propose some fast implementation algorithms to reduce the computation. The second part will introduce a recently method, the Hilbert-Huang transform (HHT), by Huang (1998). Traditional data analysis methods are all based on linear and stationary assumptions. The HHT can to solve the problem that the data is non-linear and non-stationary.he third part we will discuss the relation between the random process (including the stationary and the non-stationary ones) and several well-known time-frequency distributions.
Subjects
time-frequency analysis
short time Fourier transform
Wigner distribution
Gabor transform
Hilbert Huang transform
adaptive time-frequency distribution
random process
Fourier transform
Type
thesis
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