1、Chapter 12Sampling and Interpolation of Continuous Images nIII xxn()nIII axaxn nIII xxn()()()nnnxxIIInxnxnIII x III xIII sxIIIIIIsThe Shah function and its spectrum Since III(x)is an infinite train of equally spaced impulses,it also exhibits this behavior under stretching and compression.)(1)(asFaat
2、f 00F sss)()()()()()()()(0 xfxfdxfxfxxfxIII()r t()y t()()()y tr tg t()f x()x()f x()f tIII(t/)()(/)()g ttf tMF(s)-s0s0-1/-s0s01/G(s)=III(s)s)*F(s)F(s)()f t()(/)()g ttf tMTime domain原始信号及其频谱采样后信号及其频谱()G s()F s()g t()f t1()()()2sF sG ss0101sss012s0101sss012s012 sFreq.domain()F s()G s()f x()g x 12sG sF
3、ss0101sssWe have recovered the spectrum of f(x)from the spectrum of the sampled signal g(x)1112sf xF sG ss 111sin 222s xf xg xss xWe convolve the sampled function g(x)with an interpolating function of the form sinc(x)=sin(x)/x to get f(x)0101sss012s So is the band limit 111sin 222s xf xg xss x0101ss
4、s 12sG sF ss()f ttt t t()f tT-2T2T()f tms2mss s1sT 2mst()f ttt()F s()F s1122stt()F s1N st()F s11sN tT s()f t()()()G sH sF s()f t()g ta11()()22f taa2Ttasin(2)()2asF sasms2T0a12a10s t1/2 as01222ttAasaa1TMa sas()jF ssjj 0110()s()f xign xx()f x11()()()()()/22/22xxxg xf xTTT 2()F ss jj 022()sin()2jTG sss11()g xx 2T2T0()/244xTTg xxxT sin/2()2 sin()2TTG sjss 2211()sin()2()cos()222jsTG sF ssTs()G siisi sT 0,1,2,i,2N11()2()cos()22iiG sF si()iF s()iG s0j j()G i ss 5 s10 s()G i s/2T1/2NftNf()t0s 0()F s()G s12 t1t2020sin()()ststtNf()F sNfs 0()F s()G s12 t1t2020sin()()stst()t0t
