系统频域分析的等效激励法和传递函数法

Equivalent Excitation Method and Transfer Function Method of System Analysis in Frequency-Domain

本文讨论了应用于线性时不变LTI系统的频域分析的两种技术。通过使用傅立叶变换FT的因果时域微分性质,给出了计算非零初始条件下因果激励的LTI系统响应的频域等效激励法;同时通过使用FT的非因果时域微分性质,给出了计算非因果激励的LTI系统响应的传递函数法。频域等效激励法和传递函数法分别是时域分析中的等效激励法和卷积法的频域版本,与时域等效激励法等效于时域卷积法一样,频域等效激励法也等效于传递函数法。

Two frequency-domain analysis techniques of LTI（linear time-invariant） system are discussed in this paper. After the causal differential property of FT（Fourier transformation） is proved,the equivalent excitation method in frequency-domain is applied to computing the responses of an LTI system excited by a causal input under non-zero initial condition. When the non-causal differential property of FT is employed,the transfer function method in frequency domain is applied to computing the responses of an LTI system excited by a non-causal input. Since the equivalent excitation method and the transfer function method in frequency-domain are the frequency-domain versions of the equivalent excitation method and the convolution method in time-domain, respectively, therefore the equivalent excitation method and the transfer function method in frequency-domain are equivalent due to the equivalence of the equivalent excitation method and the convolution method in time-domain