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牧野泰才 - lab.sdm.keio.ac.jp

Fourier ? ? Fourier tetfFtd)()(j tte j t t-100-80-60-40-200020406080100120140160 Frequency (Hz) 2 2 iiibababababa 332211 2 ttgtfd)()(0d)()( ttgtf tttftttftetfFtd)sin()(jd)cos()(d)()

時間・空間領域の波形を、周波数で展開する (以降では、時間の場合のみ表記) 時間波形は、様々な振動成分の線形足し合わせとし て表現できる

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Transcription of 牧野泰才 - lab.sdm.keio.ac.jp

1 Fourier ? ? Fourier tetfFtd)()(j tte j t t-100-80-60-40-200020406080100120140160 Frequency (Hz) 2 2 iiibababababa 332211 2 ttgtfd)()(0d)()( ttgtf tttftttftetfFtd)sin()(jd)cos()(d)()

2 (j = 0 F( ) F( 0) f(t) cos( 0 t) sin( 0 t) (x) sin(x) cos(x) Fourier )(j)()(000 BAF .. Fourier cos A sin B Fourier )cos(sincos22 xBAxBxA22BA Fourier Fourier Fourier =0 Fourier Fourier.)

3 1d)()(0jj tttetetF t 1 cos 0 2a Fourier aaaeeetetetfFaaaataatt)sin(2jj1dd)()(jjj jj )otherwise(0)(1)(atatf t0a-a 0 sin(a ) = 0 0= /a a 0 1/a .. 2)(atetf aAeF4/2)( cf. d)()()(* tgftgf g t=0t=a a.

4 ( )t*tFourier Sinc LPF 0 ! Fourier t * t LPF 0 PC ? Fourier t tt * t 0Hz.

5 T0 0 =2 / T0 0 0 0 2 02 03 0 3 0tt * 0 0 0 0 0 0 0 0 0 2 02 03 0 3 0 CM ( ) 0 0 0 = 0 !!0 0 0 0/2- 0/2 2 10 2 LPF


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