1．伝達関数とインパルス応答 - トップページ

1 (t) h(t) f(t) g(t)L 1/8 (t) h(t) f(t) g(t)L f(t) g(t) Lf(t)=g(t)( ) f1(t),f2(t) Laf1(t)+bf2(t)=ag1(t)+bg2(t)( ) Lf(t t0)=g(t t0)( ) t0 (t) h(t) L (t)=h(t)( ) h(t) f(x) Lf(x) (t x)=f(x)h(t x)( ) Lf(x) (t x)dx =f(x)h(t x)dx ( ) Lf(t) ( ) g(t) g(t)=f(x)h(t x)dx =f(t) h(t)( ) 2/8 h(t) H( ) G( )=F( )H( )( ) H( ) (Transfer Function) H( ) f(t) g(t) g(t)=kf(t td)( ) G( )=kF( )e j td( ) H( ) H( )=k H( )= td( ) 2.

2 H( )=1( < L)0( > L)( ) L Sinc h(t)=12 exp (j t)d L L= L sin ( Lt) Lt( ) 3/80 L L t1 L L L H( ) h(t) h(t) t<0 t 0 t<0 ( ) td - td 3. 0 window function f(t) w(t) F( ) W( ) 0 0 W( ) 3 4/8t0 T2 T21 w(t)40200dB logW( )

3 3 30dB 0 Hanning, Hamming, Kaiser Hanning Hamming Hamming Kaiser HanningHammingKaiser Wx= xWx=12+12cos 2xWx= + 2xWx=I0 1-x2I0 - 13 dB- 32 dB- 41 dB- 46 ( =2 ) 1225 5/84. f(t) 1 E=f2tdt- ( ) ( ) energy signal) P= limT 1Tf2tdt-T2T2( ) power signal).

4 P=12 limT 1TF 2d - =12 limT F 2Td - =12 S d - ( ) S = limT F 2T( ) ( ) F-1S =12 limT 1TF 2ej td - 6/8=12 limT 1TF- F ej td - Fft gt=F G f(-t) F(- ) F-1S =12 limT 1Tf t ft = limT 1Tf xft xdx-T2T2 T/2<x<T/2 - T/2<x<T/2 - x t R( ) F-1S = limT 1Tf(t)f(t+ )dt T/2T/2( ) R( ) auto-correlation function time lag ( ) Wiener-Khintchine s theorem ( ) R(0) = limT 1Tf2(t)dt T/2T/2=12 S d - ( ) 0.

5 7/85. F( ) S( ) S( ) R( ) ( ) f(t) f(t t0) S( ) R( ) f(t) (t) (t) = limN 1 Nfi(t) i=1N( ) R(t, ) = limN 1 Nfi(t)fi(t+ ) i=1N( ) i i ensemble average t ergodic = limT 1Tf(t)dt T/2T/2( ) ( ) ( ) white noise n(t) Rn( ) = limT 1Tn(t)n(t+ )dt T/2T/2=C ( )( ) 8/8S =Rn( )e j dt =C( ) 0 f(t) h(t) n(t) 5 5 H( ) H5