Estimating The Instantaneous Frequency Of A Non-stationary Signal

Instantaneous frequency is essential to analyze the non-stationary signals. The estimate of instantaneous frequency has a very important position in the application of signals processing, it has been widely applied in radar, sonar, biomedical, seismic signal processing, speech processing and many other fields.Firstly, this paper introduces the research background, the origin of the notion, the definition of the instantaneous frequency, and then lists some estimating methods, such as Phase difference, Phase model and the instantaneous frequency estimation methods which based on time-frequency distribution. Some researchers have been concluded from the experimental results of these methods that there are some paradoxes if the definition of the instantaneous frequency is the derivative of the phase function of analytical signals.From the perspective of physics, the signal can be divided into mono-component and multi-component signal. The classical definition of the instantaneous frequency is only valid for mono-component signals. But actually what can we get usually are multi-component real signals, so we have to decompose a multi-component signal into several mono-component ones. In this paper, some decomposition methods are introduced briefly. The EMD method that proposed by N.E. Huang has been focus on, this method is adaptive, so it's more effective than any other decomposition methods, but the experimental results of this method have border effect unfortunately. In the screening process of the EMD method, both ends of data sequence may be not the extreme points of the original signal, so there will be some errors in the upper and lower envelope interpolated by the extreme points, and the error can be spread throughout the data sequence with the ongoing screening process. In this paper, maximum entropy spectral estimation method is used to extent the boundary of the original signal, adding a maximum and a minimum at both ends of the data sequence, the border issue has been improved. For changing a real signal to a complex one, we introduce two methods, they are analytical method and orthogonal. The analytical method has limitations, and it is prone to spectral leakage. In addition, analytical signal is usually got by calculating the Fourier transform of the original signal, the calculated amount is very large. Although the later method is simple, but how to create two time functions by one is a problem not yet fully resolved, in this paper, the upper envelope obtained by EMD is used to estimate the amplitude, it overcomes the difficult mentioned above. By comparison, orthogonal is simpler than the analytical method, it is widely used.Based on these ideas, we propose a new estimating method—orthogonal envelope method, this method divides the multi-component signal which has been extended by the burg method into several mono-component ones, adopts orthogonal to change the real signal to a complex one, and then estimates the instantaneous frequency. Compared with other estimation methods, the result is more satisfactory.