Research On Theory And Application Of Alignment Of Noisy Signals

An important way to improve the signal-to-noise ratio is to average the noisysignals collected. Random relative shifts among signals make the signal estimatedblurred, so they should be aligned before averaging. Centroid estimation algorithmand correlation function algorithm are classical methods. In order to make algorithmbe robust against noise, some improved methods was presented such as adaptive cen-troid estimation algorithm, complete correlation function algorithm and adaptive cor-relation function algorithm. But till now, the performance evaluation of them arebased on simulation and experimentation instead of systematic theory analysis, so ef-fects of various factors on performance can not be studied roundly. At the same time,support vector machine based on statistic learning theory obtains tremendous successin few years. It substitutes artificial neural network in many fields due to its rigoroustheory and perfect algorithms. Now it is mainly applied to pattern recognition andprediction. If it can be used to suppress the additive random noise according to its ex-cellent generalization performance, a new application of support vector machine willbe opened up. In this dissertation, the theory of alignment of noisy signals is studiedsystematacially, and improved algorithms are proposed.Firstly, the centroid of noisy signal is a random variable due to the noise, so theeffects of mean, standard deviation and length of noise on the distribution of centroidof noisy signal are studied by theory and simulation method respectively. The theo-retical model of centroid of noisy signal and signal estimated by centroid estimationalgorithm are built. Through these models, the key factors that affect the performanceof estimation are obtained and the improved method is proposed.Secondly, theoretical model of adaptive centroid estimation algorithm is estab-lished, the principle of it is studied and the limitations of it is discussed. When SNRis below to some extent, the distortion of signal will be so great that the new randomshift invalidates the algorithm, so an improved adaptive centroid estimation algorithmis presented according to signal grouping and the principle of grouping is analyzed.Correlation function algorithm is a classical method on shift estimation. Three classi-cal signal models are built to obtain the conditions of invalidation. The disadvantage of...