Signal Identification Based On The Strategy Of Non-prior Functions

Signal analysis is applied to various scientific research fields. It not only involves in research and production technology, but also involves in medical diagnosis. It is closely related to daily life of people. The research and application of signal analysis as well as its intercross of the difference subjects promote the development of the research in signal processing.It is difficult to master numerous signal analysis methods. This paper attempts to grasp the different analysis methods from the perspective of calculation operation method. It is without using the different basis functions to distinguish the different analysis method.For practical engineering signal, DFT is the most commonly used signal processing method. The idea of orthogonal basis for DFT was widely accepted. However, we can't accurately identify any frequency of the sine or cosine signal by construction an orthogonal basis function. The reason is that such an orthogonal basis is surreal. The orthogonal prior basis of DFT is constructed; at the same time the inverse transform of DFT must be satisfied in order to reconstruct the signal. The orthogonal prior basis of DFT exist frequency separation. The origin error of the DFT analysis is produced when the frequency of the orthogonal prior basis discordance with the signal frequency. A non-prior basis strategy is proposed based on the above analysis. For an engineering signal, there are only a finite number of different frequency components. After searched the basis function of its corresponding frequencies, then the mathematic function system is formed by these basis functions. We can accurately analyze the signals by the basis function system. The problem is transformed into the issue of establishing and searching the non-prior basis function. Under the guidance of this idea, non-priori basis function strategy proposed. Single-frequency spectrum, non-dense spectrum, common dense spectrum and ultra-dense spectrum are calculated and analyzed from the simple to complex various situations. The method of non-prior basis function can find a function system coincide with the real signal, so as to eliminate leakage errors. Constructed the equation is the necessary mean for the current spectrum correction method. Solving the equations is suitable for single-frequency and non-dense spectrum. For dense spectrum, solving equations is too complicated. If taking into account the negative spectrum, solving equation is difficult to implement for multi-frequencies signal. Searching for non-prior basis function is based on optimization calculation. The method of non-prior basis function has its advantage of solving negative frequency impact (ultra-low frequency signal recognition) and dense spectrum identification. The selection of non-prior basis function of non-prior method is depended on the practical signal without limitation of frequency intervals. The truncation of the signal has no influence on precisely diagnosing the sine cosine signal in theory. However, the truncation of the signal is an inevitable process in practical engineering signal.After identification of a practical engineering signal, the series expansion approximation is studied. The subtraction is researched for identification of sine and cosine signal to eliminate cross-interference. Because the subtraction is too simple, so it did not get too much attention for the approximation. Non-prior basis function approach has two core operations:one is the inner product, one is subtraction. The subtraction is to ensure convergence of this method. Once the Non-prior basis function system has been identified, then we can make the best approximation operator. Compared with the DFT method, the approximation mechanism of non-prior basis method is not same as the interpolated approximation mechanism. The approach mechanism of non-prior method is a gradual approach, and DFT is a tectonic interpolation approach. This article analyzes the difference of approach and identification method. They are essentially different; the analysis should be taken on different routes. The core difference of identification and approximation is that the signal entropy is different. Identification has large semaphore and its result can be extended, while the approach method can not be extended. Approximation rate is compared between the non-prior approximation and DFT approximation by an example. The results show that the non-prior approximation has much higher approximated efficiency and extensive application fields of basis function. Therefore, it can be applied to different signals flexibly.Convolution is also a common signal processing operation. The convolution formula Y(ω)=H(ω)X(ω) has its application range. It can be applied for energy limited signal. When Y(ω) and X(ω) are subjected to noise interference, the convolution formula Y(ω)=H(ω)X(ω) and the inverse filter formula X(ω)=Y(ω)/H(ω) will bring back a large error. Basis function convolution operation is proposed for power signals and energy signals analysis. Combined with noise limits, basis functions convolution can be applied to the situation of noise interference. The diagnosed results demonstrated that when the deconvolution operation is applied to the strong noise pollution, high accuracy is also achieved.Under the guidance idea of non-priori basis function system, damping identification is solved as an application. The approximation and identification are discussed. Then we can get a conclusion that damping identification and cosine signal identification is the same kind of problem. They can use the same technology route. The only difference is the basis function selected. The damping identification method using non-prior basis function system is proposed. There is no specific need of the length of the signal for this approach in theory. So it is an accurate identification. The success of damping identification proves that the method of non-prior basis function system is reasonable. The non-prior basis analysis method is also applied in the two-microphone sound intensity measurement. Both simulation example and the experiment are carried out. The result verifies that the method can avoid leakage errors and measure the sound intensity accurately.The non-prior method of DFT emphasizes on its ideal situation. However, it is difficult to meet the ideal condition, even it is possibly a surreal condition. So we can't built a complete orthogonal basis function to ensure precisely diagnose any frequency sine cosine signal. In prior basis analysis, the construction of basis function plays dominant role, while in non-prior basis analysis, the practical engineering signal plays dominant role. The selection and determination of basis function is depended upon the practical signal.