推 Chenwitzki :喔喔 謝謝大大 02/04 16:54
※ 引述《Chenwitzki (王子貓)》之銘言：
: sin(t)sin(t/2)
: Plot the Fourier transform of x(t) if x(t)= ______________
: πt^2
: 推 vicwk :2sin(t)sin(t/2)=cos(t/2)-cos(3t/2) 02/03 16:59
: → vicwk :F[1/t^2](w) = w sign(w) 02/03 16:59
: 不好意思唷 積分兩次算到卡住了
: http://ppt.cc/5ka6
完全不需要積分吧．sin(t)sin(t/2) = (cos(t/2)-cos(3t/2))/2.
查表 F[1/t](w) = j sign(w), 又 1/t^2 = -d(1/t)/dt,
故 F[1/t^2](w) = -(jw)(j sign(w)) = w sign(w).
F[sin(t)sin(t/2)/πt^2](w)
= 1/2π (F[cos(t/2)/t^2](w) - F[cos(3t/2)/t^2](w)) (modulation性質)
= 1/4π ( (w+1/2) sign(w+1/2) + (w-1/2) sign(w-1/2)) -
((w+3/2) sign(w+3/2) + (w-3/2) sign(w-3/2)) ).
我想老師想考的應該不是積分，而是FT各種性質．
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