泊松求和公式推导设 x(t)x(t)x(t) 具有傅里叶变换。频率表示 X(f)=∫−∞∞x(t)e−j2πft dt X(f)=\int_{-\infty}^\infty x(t)\mathrm{e}^{-\mathrm{j}2\pi ft}\mathrm{~d}t X(f)=∫−∞∞x(t)e−j2πft dt 则有 ∑n=−∞∞x(n)=∑k=−∞∞X(k)=∑k=−∞∞∫−∞∞x(k)e−j2πkt dt \color{red} \sum_{n=-\infty}^\infty x(n)=\sum_{k=-\inf