qiushidaren wrote on Sep 14th, 2008, 1:12am:πX(0)δ(ω) come from in the formulation for Fourier Transform of Integration.
I can’t find any details from Oppenhim’s classical book Signals and Systems,
can anybody help me about this confused question?
As far as my memory is correct, such issue is descripted also in a famous classical text book you refer.
Or see text books written by "A.Papoulis".
From direct thought, if X(0) is not zero, it is very reasonable there is an impulse spectrum around ω=0 for integral of x(t).
Here X(ω) is fourier transform of x(t).
[Mathematical Hint]
Fourier transform of step function u(t) is πδ(ω)+1/jω.
Here you have to learn a nature of delta function δ(ω).
If ω*F1(ω)=ω*F2(ω), it must be F1(ω)=F2(ω)+k*δ(ω), here k is any constant.