关于冲激响应和冲激信号的思考

利用冲激信号和冲激响应推导线性时不变系统的卷积表示需要有平滑假定的支持,该假定的成立并不是线性时不变系统定义的必然结果。本文从频域考察了平滑假定的准确表述,系统的频率响应绝对可积是这一假定成立的前提。而在频域中定义冲激信号可以容易地验证冲激信号的性质,也可以方便地确定某个信号序列是否趋于冲激信号。

Speculation on the Impulse Response and the Impulse

In the derivation of the convolution representation of linear time-invariant systems with the concepts of impulse and impulse response, it is implied that a smoothing hypothesis holds, which is not the consequence of the definition of LTI systems. To clarify the statement of the smoothing hypothesis, it is explored in the frequency domain. This hypothesis does not hold until the frequency response .is absolutely integrable . The impulse signal is defined in the frequency domain. By this definition , the properties of impulses can be easily justified , and the determination of whether a sequence of signals tends to the impulse signal sometimes is easy.