22-4 ?¼å”±?¸æ?

­µ°Tªº¿ëÃѦ³«Ü¦hÀ³¥Î¡A°£¤F¤W­zªº»y­µ¿ëÃÑ¥~¡A§Ú­Ì²{¦b¨Ó½Í½Í­µ¼ÖÀ˯ÁªºÀ³¥Î¡C§A¬O§_´¿¸g¸g¾ú¤U¦C±¡ªp¡G

³o®É­Ô§A»Ý­nªº¬O¡u­ó°Û¿ïºq¡v¡]query by singing/humming¡A²ºÙ QBSH¡^¡A´«¥y¸Ü»¡¡A§A¥i¥H­ó°Û¤@¬q¥D±Û«ß¡AÅý¹q¸£À°§A¿ëÃÑ¥X¨Ó³o¬O­þ¤@­ººq¡C³o¬O¤@­Ó¦³½ìªºÀ³¥Î¡A¥D­nªº¬yµ{¦p¤U¡G

  1. ¹ï¨Ï¥ÎªÌªº­ó°Û¿é¤J¶i¦æ­µ°ª°lÂÜ¡]pitch tracking¡^¡A¥H²£¥ÍÀH®É¶¡¦ÓÅܪº­µ°ª¦V¶q¡C
  2. ¨Ï¥Î«e­zªº­µ°ª¦V¶q¡A»P¸ê®Æ®wªººq¦±¶i¦æ¤ñ¹ï¡A§ä¥X³Ì±µªñªº«e¤Q­ººq¡C

­º¥ý§Ú­Ì¥²¶·ÁA¸Ñ¡A¦bÁ¿¸Ü©Î°Ûºqªº®É­Ô¡A§Ú­Ì³q±`­Ê¿àÁnªùªº¾_°Ê¡A¤~¯à²£¥Í¶g´Á©Êªºªi§Î¡]¯S§O¬O¥À­µ¡^¡A¦]¦¹Ánªùªº¾_°ÊÀW«ß´NºÙ¬°°ò¥»ÀW²v¡A¹ï©ó¾ã¬qºqÁn¡A§Ú­Ì§Æ±æ¯à°÷§ä¨ì°ò¥»ÀW²vÀH®É¶¡¦ÓÅܪº¦V¶q¡]ºÙ¬°­µ°ª¦V¶q¡^¡A®Ú¾Ú¦¹¦V¶q¡A§Ú­Ì¤~¯à©M¸ê®Æ®w¤¤ªººq¦±¶i¦æ¤ñ¹ï¡A§ä¥X³Ì¬Û¦üªººq¦±¡C

½Ð¯S§Oª`·N¡A®ð­µªºªi§Î³q±`¨S¦³³W«ß©Ê¡A¦]¦¹¤]¤£¨ã¦³°ò¥»ÀW²v¡C§A¥i¥H¸Õ¬Ý¬Ý¡A±N§Aªº¤â«ö¦b³ïÄV¤W¡A¨Ã©ñºC³t«×»¡¡u¤C¡v¡A§A¥i¥Hµoı¡A¦bµo¡u£¢¡v®É¡A³ïÄV¬O¨S¦³®¶°Êªº¡AÁn­µ§¹¥þ¬O¥Ñ¦ÞÀY©M¤ú¾¦¶¡ªÅ®ðªº«æ³t¬y°Ê©Ò²£¥Í¡A¦ý¦bµo¡u£¸¡v®É¡A³ïÄV¶}©l¶i¦æ³W«ß©Ê¾_°Ê¡A§e²{¦b¥~ªºªi§Î¤]´N¦³¤F³W«ß©Ê¡A½Ð¨£¤U¦C¹Ï¨Ò¡C


¹Ï 5.¡G±Nªi§Î©ñ¤j«á¡A¥i¥Hµoı¤@¯ë¤l­µ³£¨S¦³¶g´Á©Ê¡A¦Ó¥À­µ«h¦³©úÅ㪺¶g´Á©Ê¡A©Ò¥H¤]´N¦³©ú½Tªº­µ°ª¡C

¥Ñ¤W­z¹Ï§Î¥i¥H¬Ý¨ì¡A¥À­µ¦³«Ü©úÅ㪺³W«ß©Ê¡A¦]¦¹§Ú­Ì¥i¥H¥ÑÆ[¹îªk¨Ó§ä¥X°ò¥»¶g´Á¡A¦p¦P¥»³¹²Ä¤G¤p¸`©Ò­z¡A¤èªk¨Ã¤£Ãø¡A¦ý¬O­Y­n¨Ï¥Î¹q¸£¨Ó¦Û°Ê§ì­µ°ª¡A´N»Ý­n¤@¨Ç§Þ³N¤F¡I³o¸Ì¦³«Ü¦h¤èªk¥i¥H¥Î¨Ó§ì­µ°ª¡A³Ìª½Ä±ªº¤@ºØ¤èªk¡AºÙ¬°¦Û¬ÛÃö¨ç¼Æ¡]audo-correlation function¡A²ºÙ ACF¡^¡A¨ä­ì²z¬O¹ï¤@­Ó­µ®Ø¤ÏÂжi¦æ¥­²¾¤Î¤º¿n¡A³Ì«áºâ¥X¤@±ø ACF ¦±½u¡A¦A§ì¦¹¦±½uªº²Ä¤G³Ì¤j­Èªº¦ì¸m¡A¦¹¦ì¸mªºX®y¼Ð©M­ìÂIªº¶¡¹j¡A§Y¬O°ò¥»¶g´Á¡]¥H¨ú¼ËÂI¬°³æ¦ì¡^¡A§Ú­Ì¦A±N¨ú¼Ë²v°£¥H¤W­zªº°ò¥»¶g´Á¡A§Y¥i±o¨ì¨C¬íÄÁ¥X²{°ò¥»¶g´Áªº¦¸¼Æ¡A³o´N¬O­µ°ª¡]¥H Hz ¬°³æ¦ì¡A¦ý³o©M¨ú¼Ë²vªº Hz ¨S¦³¬ÛÃö¡^¡A¥Ü·N¹Ï¦p¤U©Ò¥Ü¡C


¹Ï 5.¡G¨Ï¥ÎACF¨Ó­pºâ¤@­Ó­µ®Øªº­µ°ª¡C

°²³]§Ú­Ì¨Ï¥Î $s(i)$ ¨Ó¥Nªí­µ®Ø¤º²Ä i ­Ó°T¸¹­È¡A¨º»ò ACF ªº¤½¦¡¥i¥Hªí¥Ü¦p¤U¡G $$ acf(\tau)=\sum_{i=0}^{n-1-\tau}s(i)s(i+\tau) $$ ´«¥y¸Ü»¡¡A±N­µ®Ø¨C¦¸¦V¥k¥­²¾¤@ÂI¡A©M­ì¥»­µ®Øªº­«Å|³¡¤À°µ¤º¿n¡A­«½Æ n ¦¸«á·|±o¨ì n ­Ó¤º¿n­È¡A³o´N¬O ACF ¦±½u¡C·í $\tau=0$ ®É¡AACF ·|¦³¤@­Ó³Ì°ªÂI¡A¦ý³o¤£¬O§Ú­Ì­n§äªºÂI¡C·í $\tau$ ºCºCÅܤj®É¡A²Ä¤@­Ó°ò¥»¶g´Á·|©M²Ä¤G­Ó°ò¥»¶g´ÁÅ|¦b¤@°_¡A¦¹®É ACF ¤S·|¥X²{²Ä¤G­Ó°ªÂI¡A³o­Ó°ªÂI´N¬O§Ú­Ì­n§äªº°ªÂI¡A¦¹°ªÂI¥X²{ªº¦ì¸m¡A´N¬O§Ú­Ì­n§äªº°ò¥»¶g´Á¡C

®Ú¾Ú¤W­zªº»¡©ú¡A§Ú­Ì´N¥i¥H¹ï¤@¬qÁn­µ°T¸¹¶i¦æ¤Á­µ®Ø¡B­pºâ ACF¡B­pºâ­µ°ª¡A¨Ã¶i¦Ó§ä¥X¤@¬qÁn­µªº­µ°ª¦V¶q¡A§O§Ñ¤F¡AÀR­µ¬O¨S¦³­µ°ªªº¡A¦]¦¹ÁÙ¥²¶·­pºâ¨C­Ó­µ®Øªº­µ¶q¡]¥i²³æ©w¸q¬°¨C­Ó­µ®Ø¤ºªº°T¸¹¥­¤è©M¡^¡A­Y­µ¶q¤Ó¤p¡A«h±N¦¹­µ®Øªº­µ°ª³]©w¬°¹s¡A¥Nªí¨S¦³­µ°ª¡C

¨Ï¥Î¤W­z§ì¨ú ACF ­µ°ªÂIªº¤èªk¡A´N¥i¥H¹ï¤@¬qÁn­µ¶i¦æ­µ°ª°lÂÜ¡A½d¨Ò¦p¤U¡G


¹Ï 5.¡G¤@¬q­µ°Tªº­µ°ª­pºâ¡A¨ä¤¤¤p¹Ï¤@¬OºqÁnªi§Î¹Ï¡A¤p¹Ï¤G¬O­µ¶q¦±½u¡]¬õ¦â¤ô¥­½u¬°­µ¶qªùÂe­È¡^¡A¤p¹Ï¤T«h¬O­µ°ª¦±½u¡C

¦b¤W¹Ï¤¤¦@¦³¤T­Ó¤p¹Ï¡A»¡©ú¦p¤U¡G

¤@¥¹§ä¨ì­µ°ª¦±½u«á¡A§Ú­Ì­n©M¸ê®Æ®w¤¤ªººq¦±¶i¦æ¤ñ¹ï¡C·íµM¡A¸ê®Æ®wªº¨C¤@­ººq¦±¤]³£¬O¨Æ¥ýÂন­µ°ª¦V¶qªº§Î¦¡¡A³q±`§Ú­Ì¨úªº­µ®Øªø«×¬O 32 ms¡A¦]¦¹¨C¬íÄÁ·|¦³ 1/32 = 31.25 ­Ó­µ°ªÂI¡A­Y¤@­ººq¦³ 3 ¤ÀÄÁ¡A¹ïÀ³ªº­µ°ª¦V¶q´N·|¦³ 3*60*31.25 = 5625 ÂI¡C¦Ó§Ú­Ìªº­ó°Û¿é¤JºqÁn¡A­Y¥H 8 ¬í¬°¨Ò¡A«h·|²£¥Í 8*31.25 = 250 ­Ó­µ°ª­È¡A§Ú­Ìªº¥Ø¼Ð¡A´N¬O­n§ä¥X¦b³o 5625 ­ÓÂI¸Ì­±¡A­þ¤@¬q³Ì¹³§Ú­Ì°Û¥X¨Óªº 250 ­Ó­µ°ª­È¡C

¨ä¹ê¡A·í§Ú­Ì»¡¡u³Ì¹³¡v®É¡A³o¬O¤@­Ó¼Ò½kªº·§©À¡A©Ò¿×¡u¹³¡v©Î¡u¤£¹³¡v¡A§¹¥þ®Ú¾Ú©ó§Ú­Ì©Ò¥Î¨ìªº¶ZÂ÷¨ç¼Æ¡A¶ZÂ÷¶V¤p«h¶V¹³¡A¤Ï¤§¡A«h¶V¤£¹³¡C¦b­pºâ¨â¬q­µ°ª¦V¶qªº¶ZÂ÷®É¡A§Ú­Ì¥²¶·¦Ò¼{¨ì¤U¦C°ÝÃD¡G

¹ï©ó²Ä¤@­Ó°ÝÃD¡A§Ú­Ì¥i¥H¥ý±N¨â¬q­µ°ª³£¥­²¾¨ì¦P¤@­Ó­µ°ª°ò·Ç¡A¦A¶i¦æ¤ñ¹ï¡C¹ï©ó²Ä¤G­Ó°ÝÃD¡A§Ú­Ì¥i¥H¥ý°²³]³t«×ªºÅܤƬO§¡¤Ãªº¡]­Y³t«×§Ö¡A´N±qÀY§Ö¨ì§À¡F­YºC¡A´N±qÀYºC¨ì§À¡A¦Ó¤£·|©¿§Ö©¿ºC¡^¡A¦b¦¹±¡ªp¤U¡A§Ú­Ì´N¥i¥H±Ä¥Î¡u½u©Ê¦ùÁY¡v¡]linear scaling¡A²ºÙ LS¡^ªº¤èªk¨Ó¶i¦æ¤ñ¹ï¡A¦p¤U¹Ï©Ò¥Ü¡G


¹Ï 5.¡G¨Ï¥Î LS ¨Ó­pºâºqÁn­µ°ª©M¸ê®Æ®w¤ºªººq¦±­µ°ªªº¶ZÂ÷¡A¥H¥»¨Ò¦Ó¨¥¡A·í¦ùÁY¤ñ¬O 1.25 ®É¡A¥i¥H±o¨ì³Ìµu¶ZÂ÷¡C

¥Ñ¤W¹Ï¤¤¥i¥H¬Ý¥X¡A·í§Ú­Ì±N¿é¤J­µ°ª¦V¶q©Ôªø 1.25 ­¿¡]¦P®É±N¿é¤J­µ°ª¦V¶qªº¥­§¡­È¥­²¾¨ì¹ïÀ³ºq¦±­µ°ª¦V¶qªº¥­§¡­È¡^¡A±N©M¸ê®Æ®w¤¤ªº¬Y¤@­ººq¦±±o¨ì³Ìªñªº¶ZÂ÷¡A¦¹¶ZÂ÷§Y¬O¦¹¿é¤J­µ°ª¦V¶q©M¦¹ºq¦±ªº¶ZÂ÷¡C¡]¦b¦¹ªº¶ZÂ÷¨ç¼Æ¥i¥H²³æ¦a©w¸q¬°¨â­Ó¦V¶q¦b°ª«×ªÅ¶¡ªºª½½u¶ZÂ÷¡C¡^¦]¦¹¦b¤ñ¹ï¤@­ººq¦±®É¡A§Ú­Ì¥i¥H¹Á¸Õ¤£¦Pªº¦ùÁY­¿¼Æ¡A¨Ò¦p±q 0.5¡B0.51¡B0.52¡B...¡B1.49¡B1.50 µ¥¡A¦@ 101 ºØ¥i¯à¡A¨Ó§ä¥X³Ì¨Îªº¦ùÁY­¿¼Æ¥H¤Î¹ïÀ³ªº³Ìµu¶ZÂ÷¡C­Y¸ê®Æ®w¤¤¦³ 1000 ­ººq¦±¡A±N±o¨ì 1000 ­Ó³Ìµu¶ZÂ÷¡A§Ú­Ì¥i®Ú¾Ú³o¨Ç¶ZÂ÷¨Ó±Æ§Ç¡A¶ZÂ÷¶Vµuªººq¦±¡A´N¶V¥i¯à¬O§Ú­Ì­ó°Ûªººq¡C

Hint
¦pªG§A°Ûºq©¿§Ö©¿ºC¡A³o®É­Ô´N¤£¯à¨Ï¥Î LS¡A¦Ó­n¨Ï¥Î¹Bºâ¶q§ó¤jªº DTW¡]dynamic time warping¡^¤èªk¨Ó¶i¦æ¤ñ¹ï¡C

»¡©ú¦Ü¦¹¡A§Ú¬Û«H¤j®a¹ï­ó°Û¿ïºq¤w¸g¦³¤@­Ó°ò¥»ªºÁA¸Ñ¡A©Î³\§A­Ì·|°Ý¡A¨º¤U¤@¨B¬O¤°»ò¡HÁÙ¦³¤°»ò§Þ³N°ÝÃD©|«Ý§JªA¡H¨ä¹ê°ÝÃDÁ٫ܦh¡A¬ÛÃöªº¬ã¨s¤]¤@ª½¦b¶i¦æ·í¤¤¡A¥H¤U¦C¥X´XÂI¡G

Ãö©ó²Ä¤@­Ó§xÃøÂI¡A§A¥i¯à·|°Ý¡G¦ý¬O¤H¦Õ³£Å¥±o¥X¨Ó MP3 ­µ¼Ö¤º¤HÁnªº­µ°ª°Ú¡A¬°¤°»ò¹q¸£°µ¤£¨ì¡H¨þ¨þ¡A³o¬O¤@­Ó¤j«v°Ý¡A§Ú­ÌÁÙ¤£¬O«Ü©ú½T¦aª¾¹D¤H¸£¦p¦ó°µ³o¥ó¨Æ¡A¦ý§Ú­Ì©ú½T¦aª¾¹D¹q¸£³o¥ó¨Æ°µ¤£¦n¡C¨C¦~¦³¤@­Ó¥@¬Éª¾¦Wªº¬ã°Q·| International Society of Music Information Retrieval¡]²ºÙ ISMIR¡^·|Á|¿ì¦U¶µ­µ¼ÖÀ˯Áµû¤ñ¡A¨ä¤¤¦³¤@¶µ¬O audio melody extraction¡AÁöµM¨C¦~ªº®Ä¯à³£¦³¼W¥[¡A¦ý¥Ø«eªº raw pitch accuracy ÁÙ¤£¨ì 85%¡A¥i¨£¤H¦Õ©M¤H¸£¦b¥Ø«eªº½T¤ñ¹q¸£¼F®`«Ü¦h¡C·íµM°Õ¡A¹q¸£¤@ª½¦b¶i¨B¡A¦Ó¤H¸£¶i¨Bªº´T«×¦³­­¡A¡u¹q¸£¦Õ¡v°l¤W¡u¤H¦Õ¡v¥i¯à¥u¬O®É¶¡ªº°ÝÃD¡I

§@·~

  1. ½Ð±qºô¸ô¤W´M§ä¥ô¤@­Ó®i¥Üºô­¶¡A¨Ó¹Á¸Õ­ó°Û¿ïºqªº®i¥Ü¨t²Î¡C
    1. ½Ð¥¿±`¦a°Û¤@­ººqªº¨ä¤¤¤@¥y¡A½Ð°Ý®i¥Ü¨t²Î¥i¥H§ä¨ì§A°Ûªººq¶Ü¡H
    2. ¦pªG§A¦b°Ûºq®É©¿§Ö©¿ºC¡A¨t²ÎÁٯॿ½T§äºq¶Ü¡H

Audio Signal Processing and Recognition (­µ°T³B²z»P¿ëÃÑ)