冲激偶

${\displaystyle \delta '(t)={\frac {d\delta (t)}{dt}}}$ 

• ${\displaystyle \delta '(t)=-\delta '(-t)}$ 

• ${\displaystyle \delta ^{(n)}(t)=(-1)^{n}\delta ^{(n)}(-t)}$ 

• ${\displaystyle \delta '(t-t_{0})=-\delta '[-(t-t_{0})]}$ 

• ${\displaystyle f(t)\delta '(t)=f(0)\delta '(t)-f'(0)\delta (t)}$ 

• ${\displaystyle f(t)\delta '(t-t_{0})=f(t_{0})\delta '(t-t_{0})-f'(t_{0})\delta (t-t_{0})}$ 

• ${\displaystyle \int _{-\infty }^{\infty }f(t)\delta '(t)dt=-f'(0)}$ 

• ${\displaystyle \int _{-\infty }^{\infty }f(t)\delta ^{(n)}(t)dt=(-1)^{n}f^{(n)}(0)}$ 

• ${\displaystyle \int _{-\infty }^{\infty }f(t)\delta '(t-t_{0})dt=-f'(t_{0})}$ 

• ${\displaystyle \int _{-\infty }^{\infty }f(t)\delta ^{(n)}(t-t_{0})dt=(-1)^{n}f^{(n)}(t_{0})}$ 

• 余成波; 陶红艳; 张莲; 邓力, 信号与系统 (第二版), 清华大学出版社, 2007, ISBN 978-7-302-14690-2 。