A method for the design of a second-order recursive filter, optimal in terms of the bias error, and a method for the synthesis of the parameters of correlation filter spectrum analyzers based on it are presented. The improvement of technical characteristics of spectrum analyzers based on dynamic filters is obtained by the transition from analog to digital filtering. The structure of the recursive narrowband digital dynamic filter of the second order is optimized by the minimum relative dispersion of the power spectral density estimation. It is justified that the correlation-filter spectrum analyzer has two components of methodological error: approximation error and statistical error. Expressions for the relative approximation error of the power spectral density estimate for two versions of optimization respectively with the constant and piecewise-step law of change of the relative attenuation coefficient of the proposed second-order digital dynamic filter are derived. The results of experimental studies suggest that the spectrum analyzer based on the proposed recursive filter of the second order provides considerably higher accuracy (of the order of several percent) in comparison with classical filter analyzers with stationary non-reconfigurable filters of even higher-order (third and fourth). The advantages in the accuracy of digital correlation-filter spectrum analyzers with the use of a narrow-band digital dynamic filter of the second order are demonstrated. The theoretical and practical principles of their design are presented.

提出了一种设计二阶递归滤波器的方法，在偏置误差方面是最佳的，以及一种基于该方法合成相关滤波器频谱分析仪参数的方法。基于动态滤波器的频谱分析仪技术特性的改进是通过模拟滤波向数字滤波的过渡获得的。二阶递归窄带数字动态滤波器的结构通过功率谱密度估计的最小相对分散进行优化。相关滤波器频谱分析仪具有方法学误差的两个组成部分是合理的：近似误差和统计误差。根据所提出的二阶数字动态滤波器的相对衰减系数的恒定和分段变化规律，推导出了两种优化方案的功率谱密度估计的相对近似误差表达式。实验研究的结果表明，与具有更高阶的静止不可重构滤波器的经典滤波器分析仪相比，基于所提出的二阶递归滤波器的频谱分析仪提供了更高的精度（几个百分点）。第三和第四）。展示了使用二阶窄带数字动态滤波器的数字相关滤波器频谱分析仪在精度方面的优势。