 Posted: Mon May 10, 2004 6:01 am Post subject: Others: I am confused with dirac delta and kronecker delta function in sampling theorem |
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| I am a graduate student, from electrical engineering. I have no detail mathematical analysis.
====================== Introductory ============================ Let fd(t) be a discritization of f(t). Many books represent fd(t) as follows fd(t)=sigma{f(kT)deltaKronecker(t-kT)} where k goes from -inf to +inf. And then the fourier transform of fd(t) is given by fd^(w)=sigma{f(kT)exp(-iwkT)} where k goes from -inf to +inf. ===================== My Problem ============================= Why is the fourier transform of deltaKronecker the same as that of deltaDirac ? In my opinion, fourier transform of deltaDirac(t-c) is exp(-jwc) and the fourier transform of deltaKronecker(t-c) is zero elsewhere. Maybe I have made misunderstanding, please let me know the correct explanation. THANK YOU VERY MUCH |
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