Dirac’sdelta function The continuous equivalent of the impulse sequence http://www.cl.cam.ac.uk/teaching/0910/DSP/

1-2 基本的连续信号及其时域特性

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直流信号的函数定义式为f(t)=A t∈R ... 若A=1，则称之为单位直流信号。 ... 箭头表示，箭头旁标以(1)，表示δ(t)图形下的面积为1，称为冲激函数的强度，简称冲激强度。


DigitalSignalProcessing
MarkusKuhn
ComputerLaboratory
http://www.cl.cam.ac.uk/teaching/0910/DSP/
Michaelmas2009–PartII
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Dirac’sdeltafunction Thecontinuousequivalentoftheimpulsesequence{δn}isknownas Dirac’sdeltafunctionδ(x).Itisageneralizedfunction,definedsuch that δ(x)= 0,x6=0 ∞,x=0 Z∞ −∞ δ(x)dx=1 0x 1 andcanbethoughtofasthelimitoffunctionsequencessuchas
δ(x)=lim n→∞ 0,|x|≥1/n n/2,|x|<1/n
or
δ(x)=lim n→∞
n √πe−n2x2
Thedeltafunctionismathematicallyspeakingnotafunction,butadistribution,thatisan expressionthatisonlydefinedwhenintegrated.