Abstract Spectral analysis and system identification techniques require suitably long data sets. Linear time-invariant (LTI) systems under random input can be demanding in terms of accurate simulation of all dynamics because of calculation time. This paper details an extension of the state-space formulation of LTI systems for higher order holds, for periodic and for exponential inputs. Exact solutions of the differential state equation are implemented into loops computing only matrix-vector multiplications. The algorithmic complexity is compared to other ordinary differential equations solvers. The presented methods can be applied to arbitrary inputs. In particular, it is shown that long system responses under random input can be computed efficiently and accurately in the time and frequency domains.

中文翻译：

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在具有任意输入的 LTI 系统响应的准确性和速度方面改进计算

摘要 光谱分析和系统识别技术需要适当长的数据集。由于计算时间的原因，随机输入下的线性时不变 (LTI) 系统在所有动力学的准确模拟方面可能要求很高。本文详细介绍了 LTI 系统状态空间公式的扩展，用于高阶保持、周期性和指数输入。微分状态方程的精确解被实现为仅计算矩阵向量乘法的循环。算法复杂度与其他常微分方程求解器相比。所提出的方法可以应用于任意输入。特别是，它表明随机输入下的长系统响应可以在时域和频域中高效准确地计算。