Research On Methods Of Waveform And Parameter Estimation Of 1/f Fractal Signal In Gaussian White Noise

With the development of science and technology, all kinds of large-scale and ultra largescale integrated circuits rapidly advance. Modern equipment is becoming more integrated,and thus the quality and reliability of semiconductor devices have become increasinglydemanding. In recent years,electrical noise for semiconductor devices reliability testing is anew developed technology. Compared to other traditional means of detection, it has asuperior performance. Within the devices, the low frequency 1/f fractal electrical noise isparticularly popular. Besides the current study found that the strength of 1/f fractal signalcan directly reflects the reliability and it can defect the level of the device. The study on thisfield raises the attention of scholars from various countries. They have explored, studied,and carried out experiments actively which has got a lot of good results.1/f fractal signal is a kind of non-stationary signal and its power spectrum that isexponentially decreasing with the frequency are low-frequency signals, which hascharacteristics of fractal signal, such as self-similarity, long range correlations.We can nothandle 1/f fractal signal well by traditional means due to its non-stationary characteristics.In recent years, the wavelet analysis theory and Wigner-Ville distribution theory are rapidlydeveloping and become a powerful tool as treatment of non-stationary 1/f fractal signal. Atthe present stage,we mainly focus on two aspects of 1/f fractal signal: waveformestimation and parameter estimation. According to the characteristics of waveletcoefficients about 1/f fractal signal,these two aspects were studied.Firstly,we research on the aspect of 1 / f fractal signal waveform estimation in thisarticle. According to the Wavelet Theory, the author analyse 1 / f fractal signal bytransforming wavelet and conclude that wavelet coefficients of 1 / f fractal signal at eachscale decomposition is approximately stationary series among wavelet domain. Accordingto this characteristics, Wiener filter theory that is used to deal with stationary signal isappled to the wavelet domain and wavelet-domain waveform estimation Levinson algorithm,SVD algorithm, SVD-TLS algorithm, give a detailed design process.After filtering,thesignal to noise ratio have significantly improved by SVD algorithm and SVD-TLSalgorithm which is better than Levinson algorithm.By many independent repeated trials,thispaper obtain the optimal decomposition scale.Another research concerns direction-parameter estimation. We propose a novelparameter estimation method based on Wigner-Ville spectrum, which estimates the powerspectrum of 1/f fractal signal using Wigner-Ville spectrum, and it estimates parameterγby means of least square curve fitting to the logarithmic chart of the power spectrum. Wefurther propose an approach of parameter estimation method based on wavelettransformation, according to the scale-variation of wavelet parameter variance of 1/f fractalsignal. The proposed methods are evaluated on simulation experiments, which bothdemonstrate accurate parameter estimation results, and the latter method can performsuperior characteristics in terms of accuracy.