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本文利用随机信号处理理论来研究频率稳定性理论,提出了一种新的时域方差-广义阿仑方差(σ_(p,q)~2,(T))。 作者的主要工作:(1)证明了σ_(p,q)~2(T)为目前已知的几种时域方差(包括阿仑方差及修正阿仑方差)的一般表达式。(2)在幂律谱条件下获得如下结果:导出了由谱密度S_y(f)算出σ_(p,q)~2(T)的数学模型及公式,导出了σ_(3,2)~2(T)与S_y(f)之间,以及由σ_(3,2)~2(T)算出其他时域方差的换算公式;论证了S_y(f)与σ_(p,q)~2(T)可以互相换算,已知σ_(p,q)~2(T)时,可立即算出其他任何时域方差;在计算机上验征了σ_(3,2)~2(T)理论表达式的正确性。
In this paper, we use the theory of stochastic signal processing to study the theory of frequency stability and propose a new time-domain variance-generalized Allan variance (σ_ (p, q) ~ 2, (T)). The main work of the author: (1) It is proved that σ_ (p, q) ~ 2 (T) is the general expression of several known time-domain variances, including the Allan variance and the modified Allan variance. (2) The following results are obtained under the power law: The mathematical model and formula of σ_ (p, q) ~ 2 (T) calculated from the spectral density S_y (f) are deduced and σ_ (3,2) ~ 2 (F) and σ_ (p, q) ~ 2 (T) and S_y (f) as well as other time-domain variances calculated from σ_ (3,2) ~ 2 ) Can be scaled to each other, and any other time-domain variance can be calculated immediately when σ_ (p, q) ~ 2 (T) is known. The computer simulation of σ_ (3,2) ~ 2 Correctness