¡¶»úе¹¤³Ì²âÊÔ¼¼Êõ»ù´¡¡·ÐÜÊ«²¨¿ÎºóϰÌâ ´ð°¸ ÏÂÔØ±¾ÎÄ

ÄÚÈÝ·¢²¼¸üÐÂʱ¼ä : 2026/3/17 19:59:14ÐÇÆÚÒ» ÏÂÃæÊÇÎÄÕµÄÈ«²¿ÄÚÈÝÇëÈÏÕæÔĶÁ¡£

|cn2A/| 2A/52A/3¦Ð 2A/¦Õn ¦Ð ¦Ð/¦Ø0 3¦Ø0 5¦Ø-5-3¦Ø0 -¦Ø0 2 2A/32A/5¦Ø 0

¦Ð -5¦Ø -3¦Ø-¦Ø0 0¦Ð

0

0 ¦Ð 0 ¦Ø ¦Ø ¦Ø0 ¦Ð3¦Ø5¦Ø0

ÖÜÆÚ·½²¨¸´Ö¸Êýº¯ÊýÐÎʽƵÆ×ͼ

-¦Ð/2 ÏàÆµÍ¼

·ùƵͼ

1-2 ÇóÕýÏÒÐźÅx(t)?x0sin¦ØtµÄ¾ø¶Ô¾ùÖµ¦ÌxºÍ¾ù·½¸ùÖµxrms¡£

2x1T1T½â´ð£º¦Ìx??x(t)dt??x0sin¦Øtdt?0T0T0T?T20T2x04x02x02?sin¦Øtdt??cos¦Øt0?

T¦ØT¦Ø¦Ð

1-3 ÇóÖ¸Êýº¯Êýx(t)?Ae?at(a?0,t?0)µÄƵÆ×¡£

½â´ð£º

¦Õ(f) 0 0

f f

-¦Ð/2 µ¥±ßÖ¸ÊýË¥¼õÐÅºÅÆµÆ×ͼ

1-4 Çó·ûºÅº¯Êý(¼ûͼ1-25a)ºÍµ¥Î»½×Ô¾º¯Êý(¼ûͼ1-25b)µÄƵÆ×¡£

sgn(t) 1 0 -1

ͼ1-25 Ìâ1-4ͼ

a)·ûºÅº¯ÊýµÄƵÆ×

1 t 0 t t=0´¦¿É²»Ó趨Ò壬»ò¹æ¶¨sgn(0)=0¡£

¸ÃÐźŲ»Âú×ã¾ø¶Ô¿É»ýÌõ¼þ£¬²»ÄÜÖ±½ÓÇó½â£¬µ«¸µÀïÒ¶±ä»»´æÔÚ¡£

¿ÉÒÔ½èÖúÓÚË«±ßÖ¸ÊýË¥¼õÐźÅÓë·ûºÅº¯ÊýÏà³Ë£¬ÕâÑù±ãÂú×㸵ÀïÒ¶±ä»»µÄÌõ¼þ¡£ÏÈÇó

´Ë³Ë»ýÐźÅx1(t)µÄƵÆ×£¬È»ºóÈ¡¼«Ï޵óö·ûºÅº¯Êýx(t)µÄƵÆ×¡£

1

¦Õ(0

t

0

f) 0 ¦Ð/2 f f ·ûºÅº¯ÊýƵÆ×

x1(t)?e?atsgn(t)·ûºÅº¯Êý

b)½×Ô¾º¯ÊýƵÆ×

ÔÚÌø±äµãt=0´¦º¯Êýֵ䶨Ò壬»ò¹æ¶¨u(0)=1/2¡£

½×Ô¾ÐźŲ»Âú×ã¾ø¶Ô¿É»ýÌõ¼þ£¬µ«È´´æÔÚ¸µÀïÒ¶±ä»»¡£ÓÉÓÚ²»Âú×ã¾ø¶Ô¿É»ýÌõ¼þ£¬²»ÄÜÖ±½ÓÇóÆä¸µÀïÒ¶±ä»»£¬¿É²ÉÓÃÈçÏ·½·¨Çó½â¡£

½â·¨1£ºÀûÓ÷ûºÅº¯Êý

½á¹û±íÃ÷£¬µ¥Î»½×Ô¾ÐźÅu(t)µÄƵÆ×ÔÚf=0´¦´æÔÚÒ»¸ö³å¼¤·ÖÁ¿£¬ÕâÊÇÒòΪu(t)º¬ÓÐÖ±Á÷·ÖÁ¿£¬ÔÚÔ¤ÁÏÖ®ÖС£Í¬Ê±£¬ÓÉÓÚu(t)²»ÊÇ´¿Ö±Á÷Ðźţ¬ÔÚt=0´¦ÓÐÌø±ä£¬Òò´ËÔÚÆµÆ×Öл¹°üº¬ÆäËüƵÂÊ·ÖÁ¿¡£

¦Õ(f) 0 0

¦Ð/2 f f

µ¥Î»½×Ô¾ÐÅºÅÆµÆ×

½â·¨2£ºÀûÓó弤º¯Êý

x(t) 1 ¸ù¾Ý¸µÀïÒ¶±ä»»µÄ»ý·ÖÌØÐÔ

1-5 Ç󱻽ضϵÄÓàÏÒº¯Êýcos¦Ø0t(¼ûͼ1-26)µÄ¸µÀïÒ¶±ä»»¡£

??cos¦Ø0tx(t)????0t?Tt?T-T 0 T t w(t)

1

-T

0

ͼ1-26 ±»½Ø¶ÏµÄÓàÏÒº¯Êý

T t

½â£ºx(t)?w(t)cos(2?f0t)

w(t)Ϊ¾ØÐÎÂö³åÐźÅ

11w(t)ej2?f0t?w(t)e?j2?f0t 22ËùÒÔx(t)?¸ù¾ÝÆµÒÆÌØÐԺ͵þ¼ÓÐԵãº

¿É¼û±»½Ø¶ÏÓàÏÒº¯ÊýµÄƵÆ×µÈÓÚ½«¾ØÐÎÂö³åµÄƵÆ×Ò»·ÖΪ¶þ£¬¸÷Ïò×óÓÒÒÆ¶¯f0£¬Í¬Ê±

Æ×Ï߸߶ȼõСһ°ë¡£Ò²ËµÃ÷£¬µ¥Ò»ÆµÂʵļòгÐźÅÓÉÓڽضϵ¼ÖÂÆµÆ×±äµÃÎÞÏÞ¿í¡£

X(f) T -f0 ±»½Ø¶ÏµÄÓàÏÒº¯ÊýƵÆ×

f0 f

1-6 ÇóÖ¸ÊýË¥¼õÐźÅx(t)?e?atsin¦Ø0tµÄƵÆ×

x(t) Ö¸ÊýË¥¼õÐźÅ

½â´ð£º

ËùÒÔx(t)?e?at1j?0t?j?0te?e 2j??

µ¥±ßÖ¸ÊýË¥¼õÐźÅx1(t)?e?at(a?0,t?0)µÄƵÆ×ÃܶȺ¯ÊýΪ

¸ù¾ÝÆµÒÆÌØÐԺ͵þ¼ÓÐԵãº

X(¦Ø) ¦Õ(¦Ð ¦Ø) 0 ¦Ø -0 ¦Ø Ö¸ÊýË¥¼õÐÅºÅµÄÆµÆ×ͼ ¦Ð

1-7 ÉèÓÐһʱ¼äº¯Êýf(t)¼°ÆäƵÆ×Èçͼ1-27Ëùʾ¡£ÏÖ³ËÒÔÓàÏÒÐÍÕñµ´cos¦Ø0t(¦Ø0?¦Øm)¡£

ÔÚÕâ¸ö¹ØÏµÖУ¬º¯Êýf(t)½Ð×öµ÷ÖÆÐźţ¬ÓàÏÒÕñµ´cos¦Ø0t½Ð×öÔØ²¨¡£ÊÔÇóµ÷·ùÐźÅ

f(t)cos¦Ø0tµÄ¸µÀïÒ¶±ä»»£¬Ê¾Òâ»­³öµ÷·ùÐźż°ÆäƵÆ×¡£ÓÖÎÊ£ºÈô¦Ø0?¦Ømʱ½«»á³öÏÖʲô

Çé¿ö£¿