第三章 连续信号的频谱

1、 ) 2 ( T 1 1n1n0 )sincos()( n tnbtnaatf 1 n1n0 )cos( n tnAa T ttf T a 0 0 d)( 1 T n ttntf T a 0 1 dcos)( 2 T n ttntf T b 0 1 dsin)( 2 2 n 2 n baAn 0d)( 1 0 0 T ttf T a 0dcos)( 2 2 2 1 T Tn ttntf T a 2 0 1 1 2 0 1 2 2 1 cos4 dsin 4 dsin)( 2 T TT Tn n tn T A ttnA T ttntf T b ), 5, 3, 1( 4 n n A ), 6,

2、4, 2(0n )5sin 5 1 3sin 3 1 (sin 4 )( 111 ttt A tf ( )f t t 1 0.50.5TT t f t 1 TO )cos() 2 sin( 12 )( 1 1 1 tn n nT tf n )sin( 11 2 1 )( 1 1 tn n tf n 方波脉冲中取到5次谐波合成 取直流到11次谐波 取到37次谐波 tAtAtAatf 1312110 3cos2coscos)( 2 ee cos jjxx x )e(e 2 )e(e 2 )( 1111 j2j2 2 jj 1 0 tttt AA atf 3, 2, 1e 2 1 j n 0 n A

3、 a n tn ， n tn Ftf 1 j ne )( 2 T 2 T - j n n de )( 1 2 1 ttf T A F tn 2 T 2 T j nnn de )( 2 j 1 - tn ttf T baA 2 n n00 A FaF， 2 T 2 T - j n de )( 1 1 ttf T F tn )5 , 3 , 1( j 2 de 2 2 T 0 j 1 n n A tA T tn 0 00 aF )5 , 3 , 1(e j 2A )( 1 j n n tf n tn n nTtt)()( T T tt T F tn 1 de )( 1 2 T 2 T - j n

4、1 n tn T t 1 j T e 1 )( )5sin 5 1 3sin 3 1 (sin 4 )( 111 ttt A tf ) 2 3cos( 3 1 ) 2 cos( 4 11 tt A ttf T F T T tn de )( 1 2 2 j n 1 n tn Ftf 1 j ne )( ttfTFnF T T tn de )()( 2 2 j n1 1 ttfF t de )()( j de )( 2 1 )( j t Ftf ) 2 (Sa ) 2 ( ) 2 sin( de)( 2 2 - j tF t 2 1 t 2 0 t )(tG 1de )()( - j ttF t

5、1)(t )(21 j 1 de)( 0 )j( tF t j 1 )( e t t )0, 0(e)( ttf t j 1 )()(F )(2 j 1 )( 21)(2)sgn( tt )()(),()( 2211 FtfFtf若 )()()()( 22112211 FaFatfatfa则 j 2 )()(Ftf若 )( 1 )( a F a atf 则 )()(Ftf若 0 j 0 )()( t eFttf 则 )(j e)()( FF )(jj 00 e)(e )( tt FF )()()()( TtGTtGtGtf ) 2 sin( ) 2 3 sin( ) 2 Sa( )cos21)

6、( 2 Sa( )ee1)( 2 Sa()( jj T T T F T-T )()(Ftf若 )()( 0 j 0 Fetf t 则 )()( 2 1 cos)( 000 FFttf ttgtf 0a cos)()( 2 )( Sa 2 )( Sa 2 )( 00 a F n tn Ftf 1 j ne )( e )( 1 j n n tn FF F )(2 1n nF n )()(jsin )()(cos 000 000 t t n n n T F)-() 2 Sa( 2 )( 1 1 ) 2 (Sa) 2 Sa() 2 Sa()( 22 F )()()( tGtGtf )()(),()( 2211 FtfFtf设 )()()()( 2121 FFtftf则 )()()( )()()(