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设x(t)是平稳的,各态历经的随机过程,则在频率f的功率谱密度W(f)为在用电子模拟设备求功率谱密度时,积分时间T、带宽B及积分器的积分常数都不是理想的,从而模拟设备一次处理的结果是一个随机变量。本文分析了积分器的时间常数的影响。分析表明:由于积分器的时间常数RC的存在,模拟设备输出的功率谱密度是真功率谱密度的有偏估计,当T≥4RC时,其相对偏差可小于2％。分析表明:RC对统计误差基本上没有影响。但积分时间如选得过短,将可能产生多达20db的相对偏差。用标定的正弦信号可判定所选的积分时间是否合适。文中附有试验的记录曲线,它说明试验与理论分析是一致的。
Let x (t) be a stationary, stochastic, random process, then the power spectral density W (f) at frequency f is the integral of time T, bandwidth B, and the integrator’s The integral constant is not ideal, so the result of a simulation device’s processing is a random variable. This paper analyzes the effect of the integrator time constant. The analysis shows that the power spectral density output by the analogue device is a biased estimation of the true power spectral density due to the existence of the RC time constant of the integrator, and the relative deviation can be less than 2% when T ≥ 4RC. Analysis shows that: RC has no effect on statistical error. However, if the integration time is too short, a relative deviation of up to 20db may result. Use a calibrated sinusoidal signal to determine if the selected integration time is appropriate. Text attached to the test record curve, which shows that the test and theoretical analysis is consistent.