Time-frequency Analysis Of Non-stationary Signals

In signal processing domain, signals can be divided into two classes: deterministic signals and stochastic signals. And the stochastic signals can be further divided into stationary and non-stationary signals. The conventional signal processing theories usually focus themselves on stationary signals, however, large amount of signals in real life, such as radar signals, sonar signals, voice, music, biological signals, are non-stationary. In order to analyze and process real life signals, many scholars developed series of signal processing theories derived from Fourier Transform, among which Time-frequency analysis is the most important one. This paper introduces the basic theories and some traditional methods of time-frequency analysis, including Short Time Fourier Transform,Wavelet Transform etc. And a new time-frequency analysis method known as Hilbert-Huang Transform (HHT) [28] proposed by Norden E. Huang et al in 1998 is also presented. HHT proposes a new concept called intrinsic mode function and a new method named Empirical Mode Decomposition (EMD), which can decompose an arbitrary signal into its intrinsic mode functions and defines the instantaneous frequency with physical meanings from a new view of point. It creates a new time-frequency analysis framework with instantaneous frequency as its basic characteristic and with intrinsic mode functions as its basic signals.Empirical Mode Decomposition (EMD) is suitable for processing nonlinear and non-stationary signals. It can decompose a complicated signal into series of intrinsic mode functions ordered from high frequency to low frequency. The frequency components contained in each IMF depend not only on sampling frequency, more importantly, they vary with different signals. so it is an adaptive signal processing method. This method has been widely used for mechanical fault testing, earthquake signal analysis, biomedicine, electromagnetic wave and sound wave analysis and so on.The combination of EMD and Hilbert spectrum analysis is called Hilbert-Huang transform, which owns many advantages. It defines IMF for the first time, and points out that the amplitude of IMF can vary, which breaks the limit of only defining the harmonic signals with constant amplitudes as basic signals. It does not need prior basis when decomposing a signal, and the frequency components contained in each IMF depend not only on the sampling frequency, more importantly, they vary with different kind of signals, so it is adaptive. However, wavelet transform depends only on the scales and the sampling frequency when wavelet basis and the number of decomposition scales are fixed, which is not adaptive. Instantaneous frequency is defined as the derivative of phase, the local frequency can be calculated without the whole time domain signal provided. The wavelet transform is essentially an adjustable windowed Fourier transform. The length of wavelet basis is finite, so it can give rise to energy leakage when applying wavelet transform, which is a big trouble for exact time-frequency analysis.The first few Intrinsic Mode Functions (IMFs) extracted have large bandwidths, which does not satisfy the demand of small bandwidth of Hilbert Transform. To solve this problem, an improved method of constructing masking signal is developed in this paper, which can restrict the bandwidth of IMF signals. Meanwhile, increasing the number of iterative operation can also improve the frequency distinguish ability of EMD. The relationship between the iteration number and the frequency distinguish ability is discussed. An approach for constructing the frequency of masking signals in a weighted manner is proposed, and the criterion of selecting these weights is also experimented. The experiment results demonstrate the scheme is reasonable and efficient.