In this thesis, based on Principal Component Analysis (PCA), covariance stationary processes and spectral analysis theory of linear operator, spectral principal component analysis (SPCA) is put forward. We proof the covariance function of covariance stationary processes is equivalent with Mercer kernel function. That is, the covariance function of covariance stationary processes is a Mercer kernel function; in reverse, for a given Mercer kernel function, there exists a covariance stationary processes, and the covariance function corresponded to this covariance stationary processes is the given symmetry positive-definite kernel function. It means that the covariance function is equivalent to symmetry positive-definite kernel function. The relationship of the SPCA, PCA and KPCA are established.According to the Covariance Stationary Processes, SPCA arithmetic also has certain stability and convergent similar to PCA arithmetic. For the given sample points, and matrix formed by covariance function with sample points as parameters, when the number of sample points approaches infinite, it is proven that this matrix spectrum will approach the spectral approach theorem for positive-definite kernel of integral equation. At the same time, similar to PCA, SPCA can filter data noise. According to the statistic characteristic of covariance function, parameter estimation can be given for kernel function. If the covariance stationary processes are one dimension, for given data, covariance function and spectral density function can be estimated, and there is no need to select kernel function and its parameters.The results of numerical calculations show that: the number of spectral principal component and cumulate variance contribution are different its depending on kernel functions. SPCA arithmetic has smaller number of spectral principal components and greater variance contribution than PCA by choosing proper kernel functions and parameters. In the case of high dimension data, SPCA is more effective than PCA.SPCA is applied to multi-index evaluation system. Via numeric sample analysis, it is found that evaluation functions are constructed by weighing principal components for PCA. However, evaluation functions can be quite different when there are more than three principal components and characteristic vectors other than first one are chosen in different directions. For SPCA, variance contribution can be greater than 90% by selecting just one principle component. Therefore, SPCA gotten via selecting polynomial kernel functions is more accurate than PCA in multi-index evaluation system, and has fewer dimensions. Comparatively, for SPCA using Gauss Kernel Function and Laplace Kernel Function, it is required to normalize original data according to the category, and the constructed evaluation functions are better than the ones constructed via using PCA. However, if variance contribution of first principal component of PCA is more than 85%, evaluation function curves of SPCA and PCA are similar.Under MATLAB environment, the program for SPCA often has 10 ~ 20 statements and the results for data analysis and chart analysis can be gotten easily.