小样本多元数据分析和数据压缩、编码等是装备维修与故障分析中的常用技术,这些技术的理论研究常常归结到用函数的Fourier系数刻画可积函数类问题。研究了正弦级数和余弦级数属于Lp函数类的条件,建立了在NBVS假设条件下的判别准则,推广了已有结果。 Multivariate analysis of small samples and data compression and coding are common techniques in equipment maintenance and fault analysis. The theoretical research of these techniques often comes down to the problem of describing the integrable functions by Fourier coefficients of functions. The conditions that the sine series and the cosine series belong to the class of Lp functions are studied. The criterion of discrimination under the NBVS assumption is established and the existing results are generalized.