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线性滤波环路是指使输出均方误差最小的线性滤波系统,在使电子设备的更加精密化和自动化,并使之处于最佳工作状态中,它的作用是突出的。尤其在自动控制、遥控遥测等电子系统中用途更加广泛。使我们颇为关注的情形便是在噪声干扰作用下,当频率发生阶跃时,引起线性滤波环路工作状态变化的数学描述。本文试图从统计数学角度出发,用严格的数学关系去分析环路的实际响应,从而导出在噪声干扰下它的最佳传输函数。由于在推算中利用了围道积分,除能使繁杂的数学计算大大简化外,并能使结果更加精确、明了。同时,由于考虑到应用的方便,还相应地计算了系统的误差。
A linear filter loop is a linear filter system that minimizes the mean squared error of the output. It makes the electronic equipment more precise and automated, and it is in the best working condition. Its function is outstanding. Especially in automatic control, remote telemetry and other electronic systems more widely used. What makes us quite concerned is the mathematical description of how the linear filter loop behaves when the frequency steps up under the influence of noise. This paper attempts to analyze the actual response of the loop from a statistical mathematical point of view using rigorous mathematical relations to derive its optimal transfer function under noise interference. Due to the use of enveloping points in the calculation, in addition to greatly simplifying the complicated mathematical calculation, the result can be more accurate and clear. At the same time, due to the convenience of the application, the system error is also calculated accordingly.