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在信号与线性系统课程中,三处出现微分性质,即卷积的微分性质、付氏变换的微分性质和拉氏变换的微分性质。具体如下: 如 y(t)=f(t)*g(t),则y′(t)*g(t)=f(t)*g′(t)=f′(t)*g(t)(1) 如 f(t)←→F(jω),则f′(t)←→jω)F(jω)(2) 如 f(t)←→F(S),则f′(t)←→SF(S)-f(O~-) (3) 合理地利用这些微分性质,可以简化运算。以下我们给出一类在通常的书籍中难于见到的例子,以供作教学的参考。
In signal and linear system courses, there are three differential properties, namely the differential nature of the convolution, the differential nature of the Fu’s transformation, and the differential nature of the Laplace transform. Specifically, y ’(t) * g (t) = f (t) * g’ (t) = f ’(t) * g (y) f (t) ← → jω) if f (t) ← → F (jω), then f ’(t) t) ← → SF (S) -f (O ~ -) (3) The rational use of these differential properties simplifies computations. Below we give a class of difficult to see in the usual books example for teaching reference.