The influence of sampling frequency on tone recognition of musical instruments - USD Repository

Gratis

0
0
18
3 months ago
Preview
Full text
(1)010210345 6789

(2) 9ÿ6ÿÿ7ÿ ÿ!  7 ÿ‚ ƒ6 ÿ8 „

(3) ÿ 7„ z67 ÿz7  ÿƒ 7

(4) 6 ÿ  †7z 

(5)

(6) ƒ

(7) 7 7

(8) 6z +,-. /0123451 64007829 ÿ;1515<12ÿ51 8 ‡851ÿyÿˆ}‰ÿŠ‹ŒÿF}ÿ Ž‘’“”•‘–ÿ˜Ž™š™›œžŸ ›¡¢ œŸÿ£œ¤ž¢ Ÿ¥ š™›¢¦œŸ ›§ÿ¡Ÿ¨ÿ£œŸ¢¦œš© A-BCDEF=CGÿªA€‰€«}¬¬­®¯«°±¯}®Œÿ>}¬²­±¯®³Œÿ-‰€«±|}®¯«ÿ°®´ÿ>}®±|}‰µÿ=,,F¶ÿŠ·¸@·¸¹Œÿ€@=,,F¶ º¹º@¸º¸ÿY0ÿ4ÿu112»21mY1719¼ÿ0[Y13ZY½Y[ÿg8h234iÿuh? @A-BCDEF=CG HD+.FGBÿE-A.=>, JK;ÿLMNOÿÿÿÿÿÿÿÿÿPÿMQLRS TUVWÿ XYZ1J[821ÿLMNOÿPÿMQRV J\]6ÿLMNOÿÿÿÿÿÿÿPÿMQS^M ÿ _`abcd\]beÿY0ÿZf1ÿ<10Z g8h234iÿY3ÿ]398310Y4 LMNO j+=>CÿB=FC, ehZf82ÿkhY91iY31 `9YZ82Y4iÿl84290 ;1mY17120 c3iY31ÿJh<5Y00Y830 e<0Z24[ZY3nÿ439 ]391oY3n 6hDst ÿc2912ÿg8h234iÿu2Y3Z0 Tf429[8uvWÿww[iY[xÿY3 f121yy ehZf820ÿ0f8hi9ÿ0h<5YZÿ83ivÿu4u120ÿZf4Zÿf4m1ÿ<113ÿ[421½hiivÿu288½2149ÿ439ÿu8iY0f19Qÿd43h0[2YuZ0ÿ421ÿ4[[1uZ19 7YZfÿZf1ÿh39120Z439Y3nÿZf4ZÿZf1vÿ421ÿ82YnY34iÿ82ÿ1oZ13919ÿm120Y83ÿ8½ÿu21mY8h0ivÿuhDFA-FA J142[fÿÿ ÿ "#11$% %%1 &%"'$(6789

(9) 9)( & J142[fÿJ[8u1ÿ eii z" ÿ {|}~€ lvÿ]00h1 lvÿehZf82 lvÿ_YZi1 cZf12ÿK8h234i0 41*

(10) 010210345 6789 8

(11) ÿ

(12)  } 6 ÿ#~ ÿ€"! ÿ6€"v6 ÿv6#‚} ÿ‚6! ÿ#‚}"ƒ6v #!!!‚6 6!v „41-ÿuÿa84dVÿVb-ÿG4d./0eÿuÿ) †‡yx†ˆ‰ÿ=|ˆŠ ‹ŒŽ‘’ÿ”•‘– \5UV4.—U/—TbU-˜ ™.Mÿ[4e-ÿFdVUt/4šÿ+/Ui-.,UV0,ÿab105ÿ™0be0/šÿY/54/-,U0 '()* +,-./0120,,34.5 ÿ7-1-18-.ÿ1 %8 9:; <=)>?@AB9?C \5UV4.—U/—TbU-˜ÿ˜4.ÿ243-.ÿ\/jU/--.U/j ™.Mÿab1-Vÿ[-t-šÿTdtd.4i0ÿ+/Ui-.,UVršÿ[d.t-r \5UV4.—U/—TbU-˜ÿ˜4.ÿ\e-WV.4/UW,ÿ\/jU/--.U/j 2.4˜Mÿ™.Mÿ›0rW0eÿ™c-˜˜0ešÿ+/Ui-.,UVrÿ4˜ÿh0V/0šÿh0V/0šÿaej-.U0 \5UV4.—U/—TbU-˜ÿ˜4.ÿ243-.ÿ\e-WV.4/UW,ÿ0/5ÿ™.Ui-, a,,4WMÿ2.4˜Mÿ™.MÿXUtÿ7d1œUÿXUtÿY5.U,šÿ+/Ui-.,UVUÿ[-t/4e4jUÿ`0e0r,U0šÿ`0e0r,U0 \5UV4.—U/—TbU-˜ÿ˜4.ÿT4/V.4eÿ\/jU/--.U/j ™.Mÿadœ0/UÿGU5U/šÿ+/Ui-.,UVUÿ[-t/Ut0eÿ`0e0r,U0ÿ`-e0t0ÿP+[-`Sšÿ`0e0r,U0 D@'*BC>ÿA)=*9:( FG7ÿHIJKÿÿÿÿÿÿÿÿÿLÿIMHNO PQRSÿ TUV-FW4.-ÿHIJKÿLÿIMNR FXY2ÿHIJKÿÿÿÿÿÿÿLÿIMOZI ÿ [\]^_`XY^aÿU,ÿVb-ÿ8-,V c4d./0eÿU/ÿY/54/-,U0 HIJK \5UV4.—U/—TbU-˜ÿ˜4.ÿFUj/0eÿ2.4W-,,U/j a,,4WMÿ2.4˜Mÿ™.MÿXU5b0eÿh4d0r/0r0šÿ7430/ÿ+/Ui-.,UVršÿge0,,84.4šÿXGšÿ+/UV-5ÿFV0V-, \5UV4.—U/—TbU-˜ÿ˜4.ÿ[-e-W411d/UW0VU4/ÿ\/jU/--.U/j 2.4˜Mÿ™.Mÿ]-4ÿ2Mÿ]UjVb0.Všÿ™-e˜Vÿ+/Ui-.,UVrÿ4˜ÿ[-Wb/4e4jršÿX-Vb-.e0/5, \5UV4.—U/—TbU-˜ÿ˜4.ÿ`0WbU/-ÿ]-0./U/jšÿaYÿ0/5ÿF4˜VÿT41qdVU/j 2.4˜Mÿ™.Mÿ]dU,ÿ20de4ÿ7-U,šÿ+/Ui-.,UVrÿ4˜ÿ`U/b4šÿ24.Vdj0e \5UV4.—U/—TbU-˜ÿ˜4.ÿT41qdV-.ÿFWU-/W-šÿY/˜4.10VUW,ÿ0/5ÿY/˜4.10VU4/ Fr,V-1 a,,4WMÿ2.4˜Mÿ™.Mÿ0/žd0/ÿ]UdšÿTd.VU/ÿ+/Ui-.,UVrÿ4˜ÿ[-Wb/4e4jršÿad,V.0eU0 a,,4WU0V-ÿ\5UV4., 2.4˜Mÿ™.Mÿab105ÿF0d5UÿF014,U.šÿ]01qd/jÿ+/Ui-.,UVršÿY/54/-,U0 2.4˜Mÿ›.0/W4ÿ›.0VV4eUee4šÿ2bM™Mšÿ+/Ui-.,UVrÿ4˜ÿF0//U4šÿYV0er 2.4˜Mÿ™.Mÿ„d,,0U/ÿae—ab105šÿ^b0eU˜0ÿ+/Ui-.,UVršÿ+/UV-5ÿa.08ÿ\1U.0V-, 2.4˜Mÿ]4/jžd0/ÿŸ4/jšÿFb00/kUÿ+/Ui-.,UVrÿ4˜ÿ[-Wb/4e4jršÿTbU/0 2.4˜MÿY/jMÿ`0.U4ÿl-.,0WUšÿ`-5UV-..0/-0ÿ+/Ui-.,UVrÿ4˜ÿ7-jjU4ÿT0e08.U0šÿYV0er 2.4˜Mÿ™.Mÿ`U.4, 03ÿF3U-.Wœšÿ24eUV-Wb/Ut0ÿhU0e4,V4Wt0šÿ24e0/5 2.4˜Mÿ™.Mÿ_10.ÿ]-/j-.t-šÿ+/Ui-.,U505ÿadV¡/410ÿ5-ÿhdW0.010/j0šÿT4e418U0 2.4˜Mÿ™.MÿF.U/Ui0,0/ÿae0i0/50.šÿT^ÿT4ee-j-ÿ4˜ÿ\/jU/--.U/jÿ0/5ÿ[-Wb/4e4jršÿY/5U0 2.4˜Mÿ™.Mÿ[0.-tÿh4dtVU.šÿ›-.b0Vÿa88-,ÿ+/Ui-.,UVršÿF-VU˜šÿaej-.U0 2.4˜Mÿ™.Mÿ¢0b.Ue05b0ÿ¢0t0.U0šÿ+/Ui-.,UVUÿ[-t/Ut0eÿ`0e0r,U0ÿ`-e0t0šÿ`0e0r,U0 2.4˜Mÿ™.MMÿ›.0/WU,ÿTM`Mÿ]0dšÿ[b-ÿ+/Ui-.,UVrÿ4˜ÿ„4/jÿ^4/jšÿ„4/jÿ^4/j a,,4WMÿ2.4˜Mÿ™.Mÿ]d/Wb0t4./ÿdVVU,UVVUtdetUcšÿTbde0e4/jt4./ÿ+/Ui-.,UVršÿ[b0Ue0/5 a,,4WMÿ2.4˜Mÿ™.Mÿ`4Wb01105ÿ›0WV0šÿ™Uq4/-j4.4ÿ+/Ui-.,UVršÿY/54/-,U0 a,,4WMÿ2.4˜Mÿ™.Mÿ`4b01-5ÿa.-œtUÿ`-ee0ešÿ`£„01-5ÿh4dj0.0ÿ+/Ui-.,UVršÿaej-.U0 a,,VMÿ2.4˜Mÿ™.MÿFdq0i05--ÿa.01iUVbšÿTbde0e4/jt4./ÿ+/Ui-.,UVršÿ[b0Ue0/5 a,,VMÿ2.4˜Mÿ™.Mÿa/5.-0ÿ›.0/W-,W4ÿ`4.08UV4šÿ+/Ui-.,UVrÿ4˜ÿ7-jjU4ÿT0e08.U0šÿYV0er ™.MÿaWb105ÿU5454šÿ+/Ui-.,UV0,ÿ™Uq4/-j4.4šÿY/54/-,U0 ™.Mÿa.U0//0ÿ`-/W0VVU/Ušÿ+/Ui-.,UVrÿ4˜ÿ741-ÿ¤[4.ÿl-.j0V0¤šÿYV0er ™.Mÿ™-.U,ÿFVU030/šÿ+/Ui-.,UV0,ÿF.U3Uc0r0šÿY/54/-,U0 ™.Mÿ„0.d/0ÿTbU.410šÿ›-5-.0eÿT4ee-j-ÿ4˜ÿ\5dW0VU4/ÿP[-Wb/UW0eSšÿg418-ššÿXUj-.U0 ™.Mÿ„dWb0/jÿ]U04šÿFUWbd0/ÿ+/Ui-.,UVršÿTbU/0 ™.MÿG0W-tÿFV0/54šÿ[-Wb/UW0eÿ+/Ui-.,UVrÿ4˜ÿ]45œšÿ24e0/5 ™MÿGd5-ÿ„-10/Vbšÿ^0.d/r0ÿ+/Ui-.,UVršÿY/5U0 `0.tÿFMÿ„44q-.šÿa/0e4j¥7›ÿYTÿ™-,Uj/ÿ\/jU/--.ÿPT4/,deV0/VSÿ0Vÿ`UW.4,-1Ušÿ+/UV-5ÿFV0V-, ™.Mÿ`d/030.ÿaÿ7Ur05Ušÿ+/Ui-.,UV0,ÿ™Uq4/-j4.4šÿY/54/-,U0 ™.MÿFb0b.U/ÿ`5ÿar48šÿ+/Ui-.,UVUÿ[-t/4e4jUÿ`0e0r,U0šÿ`0e0r,U0 ™.MÿFd.U/5-.ÿFU/jbšÿF]Y\[ÿ]4/j430ešÿY/5U0 ™.Mÿ[dVdVÿ„-.030/šÿ+/Ui-.,UVUÿ`0e0r0šÿ`0e0r,U0 ™.MÿŸ0/jÿ„0/šÿ+/Ui-.,UVrÿ4˜ÿ\e-WV.4/UWÿFWU-/W-ÿ0/5ÿ[-Wb/4e4jrÿ4˜ÿTbU/0šÿTbU/0 ™.MÿŸU/ÿ]UdšÿFr10/V-Wÿ7-,-0.Wbÿ]08,¦ÿT4.-ÿ7-,-0.Wbÿj.4dqšÿ+/UV-5ÿFV0V-, ™.MÿŸ4d,,-˜ÿF0U5šÿ[d/U,U-ÿ[-e-W41ÿFr,£T41ÿ]08šÿX0VU4/0eÿ\/jU/--.U/jÿFWb44eÿ4˜ÿ[d/U,ÿP\XY[Sšÿ[d/U,U0 ™.MÿŸdVVb0q4/jÿ[dqq05d/jšÿ2.4iU/WU0eÿ\e-WV.UWUVrÿadVb4.UVrÿP2\aSšÿ[b0Ue0/5 ™.Mÿ¢bUkU4/jÿ]UšÿTbU/0ÿ+/Ui-.,UVrÿ4˜ÿ`U/U/jÿ0/5ÿ[-Wb/4e4jršÿTbU/0 f'9:?ÿ>9B?( adVb4.ÿgdU5-eU/\5UV4.U0eÿh40.5, 7-iU-3-., _/eU/-ÿFd81U,,U4/, a8,V.0WVU/jÿ0/5 Y/5-kU/j 2d8eUW0VU4/ÿ\VbUW, lU,UV4.ÿFV0VU,VUW, T4/V0WVÿ+, D@'*BC>ÿmC*n:@op ÿ_.5-.ÿc4d./0eÿq.U/V, Pb0.5W4qrSÿssWeUWtÿU/ b-.-uu ÿ D@'*BC>ÿ:@B=)B= F-0.Wbÿÿ F-0.WbÿFW4q-ÿ aee v

(13)  ÿ wxyz{| hrÿY,,dhrÿadVb4. hrÿ[UVe_Vb-.ÿG4d./0e, =)>?@AB9?Cÿ=|‰|§yŠŠ¨©†§ˆ‡†y©ªÿ:yŠ«¨‡†©¬ªÿ)‰|§‡xy©†§{ÿˆ© ÿ:y©‡xy‰ÿ YFFXLÿJN­R—N­RIšÿ-—YFFXLÿHRIH—­H­Rÿ +/Ui-.,UV0,ÿab105ÿ™0be0/šÿ®VbÿT01qd, šÿ­Vbÿ›e44.šÿ]22Yÿ7441 GeMÿ7U/j.405ÿF-e0V0/šÿ^.0jUe0/šÿ[010/0/šÿh0/jd/V0q0/šÿh0/VdeÿšÿŸ4jr0t0.V0šÿY/54/-,U0ÿOOJ­J 2b4/-Lÿ¯NHÿPHK®SÿONROJOšÿOJJZRIšÿRK­®JZšÿRKJJHIÿ-kVMÿ®­IHšÿ›0kLÿ¯NHÿHK®ÿON®NI® ÿ [bU,ÿ34.tÿU,ÿeUW-ÿ/,-5ÿd/5-.ÿ0ÿT.-0VUi-ÿT4114/,ÿaVV.U8dVU4/—X4/T411-.WU0eÿ®MIÿY/V-./0VU4/0eÿ]UW-/,-M 9911  

(14) 

(15) 7

(16) 87187  

(17) 6 !"#$

(18) %

(19) & 9$ 789 8

(20) 

(21)  410

(22) 010210345 678ÿ4 ÿ

(23) 7ÿ4 ˆ"# ÿ%-"‰ ÿ "Š$

(24) ÿ‹Š$‹ ÿ%‹Œˆ ÿŒ‰‹‹

(25)  ÿ%‹Œˆ$6 %

(26)

(27)

(28) Œ#

(29)  “”•ÿ—˜™ÿš”ÿ— 2345 6789:;<8 =;77>?9@ ÿB8<8`@8C;:@ÿ98Ÿp8ba;99;}ÿ;:a8::;ÿC;78@ÿ?:ÿ?9u;:`bÿ7oC7a9;a8ÿ<;a89`;p7 ´µÿ¶µÿª¥¯¢·§ÿªµÿ¸µÿ¶¹°¥¢¯§ÿº®¥»°¢¼¥ÿ½©¦¥¦§ÿºµÿ¾µÿª¥¹»¿¯§ÿ¨µÿ¨¥À¥»¢¼¥¯ _?<|;9;a`t8ÿ7ao@}ÿ?Ÿÿ78p8ba8@ÿ7oCb;99`89ÿ`:@8vÿ;t8ÿ;ba`t8ÿŸ`pa89ÿŸ?9 :;:?7;a8pp`a8Æ7ÿ98b8`t89ÿŸ9?:a 8:@7ÿ;aÿ7 C;:@ ¡¢¦®ÿ¤¥ÿǮĿ¦«§ÿȬ»¦¥»©ÿ²¿Ä»¦¬­§ÿ±Ä¿¦«ÿȥɮÿÊ¢¥ 8t8p?|<8:aÿ?Ÿÿ>`98p877ÿ;:@ÿ`:a8pp`u8:aÿm?<8ÿ;oa?<;a`?:ÿ7}7a8< Ë®¥¯¢¯ÿ½¼®¥ÿª¿®©ÿ½¦¦Ä¥»§ÿªÄ®¥°°¥©ÿÌ¥¢Íÿª¥®¥»¥°§ÿ¨¢·ÿ½¼»¥¦ÿ½Ãÿ´¥©¢§ÿª¿®¥°¥© ´¥¦¢ÀÀÿ´¥»Ä¦§ÿª¿®©ÿÌ¢»©¥Ä¹ÿª¿®©ÿ½Ãÿ´¥¯¢° gt;po;a`?:ÿ?Ÿÿ:8a>?9ÿ78bo9`a}ÿC;78@ÿ?:ÿ:8vaÿu8:89;a`?:ÿ`:a9o7`?: |98t8:a`?:ÿ7}7a8< Ê¢¯¥¦«ÿ¶¦­¥¦ÿǬ»°¥­¥¹¥»¢ÿ±ÄÎÎ¥§ÿ¨¢É¿ÿºÄ»¥¦­®¥ =89Ÿ?9<;:b8ÿ?Ÿÿbpo7a89 C;78@ÿb?u:`a`t8ÿ?97ÿo:@89ÿn?`:a `<|;baÿ?Ÿÿm;9@>;98ÿ:?`787ÿ;:@ÿ:?: `@8:a`b;pÿ|9`<;9}ÿb? bm;::8p `:a89Ÿ898:b8 Ç®¥°ÿª¢¦®ÿ¨¥°§ÿ¤»¥¦ÿ¤»Ä¦«ÿ±ÄϧÿÇ®¥¦ÿÐ¥¦ÿÑ¥ o;p C;:@ÿ;|89ao98ÿb?o|p8@ÿ;:a8::;ÿ>`amÿm;97ÿ;:@ h`:ovÿQ}7a8< ºÄλ¢Ï¥¦­¿ÿÇ»¥Î­¿©¢Ï¿¦¿§ÿ¾¢¥¦ÿº¿À®¥¦§ÿ½¦««¿»¿ÿºµÿÇ»¥°Ä©Ï¿§ÿ¤¬«Ä®ÿÌ¢»°¥¦¹Ï¥®§ ½¼¯¥¦ÿÓ¹°¥¦ 87`u:ÿ?Ÿÿ7|`9;pÿp;C}9`:amÿ<`b9?7a9`|ÿ;:a8::;ÿŸ?9ÿws fÿ;||p`b;a`?: ¶¦©»¥ÿºÄ»Ô¥­¢§ÿºÏ¥®ÿ½¯¥°§ÿ²Ä¯¢¥»­¿ÿË¥»¦¥©¢ l:;p}7`7ÿ?Ÿÿ7>`abm`:uÿ;:@ÿ<;abm`:uÿ7aoC7ÿ`:ÿ98b?:Ÿ`uo9;Cp8ÿ|?>89ÿ@`t`@89 >`amÿQ=fÿ7>`abmÿŸo:ba`?: ¨µÿÕ©Â¥»©§ÿ¨µÿ½µÿº®¥¢»¢§ÿ³µÿ³¥·¥»¢¥§ÿ¶µÿ±µÿº¥¢ÀįÿÈ¥®»¢ _?<|;9`7?:ÿ?Ÿÿ7a8<<`:uÿ;pu?9`am<7ÿ;:@ÿ`a7ÿ8ŸŸ8baÿ?:ÿd:@?:87`;:ÿa8va |9?b877`:u ½À¢¥¦ÿºÏ¥À¥¥©¢ÿ¾¢¼·¢§ÿ½»¢¹ÿ¤Ô¥®Ï¥¦­¿§ÿ¾¥®°¥­ÿ¤»¢¥¯¢® s`?<8a9`bÿ`@8:a`Ÿ`b;a`?:ÿo7`:uÿ;ou<8:a8@ÿ@;a;C;78 ¾¬«¢¦¥ÿ¡¢¿¦¦¢¬§ÿÕ¯¯¢¹¥ÿ½«Ä¹­¢¦¥§ÿÖ¥®ÔÄÿº¬©¢¿¦¿§ÿªÄ©»¢·ÿ½¯¥Ï©»Ä¹ l:;p}7`7ÿ?ŸÿsQ_lcÿ;:@ÿi <8;:7ÿ;pu?9`am<ÿŸ?9ÿ8t;po;a`:uÿ?oap`89ÿ?:ÿB›k `amÿb;p8:@;9ÿt;9`;a`?: 8ŸŸ8ba7 ºÄ®¥»­¿¦¿ÿºÄ®¥»­¿¦¿§ÿ¶ÿª¥©¬ÿÊ©¬ÿª¬»¥¦««¢ÿ±¥¦¥§ÿº¥¦­¢ÿÇÄ­¬»¢ÿ¾¥®¥ÏÄ 11781 78 !"#

(30) $!%&'((&7)*& +,-+,./0, =› U V =› e UÁ =› OK25MNIÿL4H5DE3 QRBÿSTUVÿÿÿÿÿÿÿÿÿWÿTXSYZ [\]^ÿ _`a8Qb ?98ÿSTUVÿWÿTXY] Qcd=ÿSTUVÿÿÿÿÿÿÿWÿTXZeT ÿ fghijkcdilÿ`7ÿam8ÿC87a n?o9:;pÿ`:ÿd:@?:87`; STUV UZ SS =› S] ]U =› ]S ]e =› ]œ Áe =› Áœ Zœ =› YT YV =› Ye VZ =› VY eZ =› eY œÁ =› q2DEJÿIDMJ3 loam?9ÿro`@8p`:8 g@`a?9`;pÿs?;9@7 B8t`8>897 j:p`:8ÿQoC<`77`?:7 lC7a9;ba`:uÿ;:@ d:@8v`:u =oCp`b;a`?:ÿgam`b7 w`7`a?9ÿQa;a`7a`b7 _?:a;baÿ67 OK25MNIÿxN5yEKz{ ÿj9@89ÿn?o9:;pÿ|9`:a7 [m;9@b?|}^ÿ~~bp`bÿ`: m898€€ ÿ OK25MNIÿEKMH4MH Q8;9bmÿÿ Q8;9bmÿQb?|8ÿ lpp  ÿ ‚ƒ„ †‡ s}ÿd77o8 s}ÿloam?9 s}ÿf`ap8 jam89ÿR?o9:;p7 œZ UTS =› UT] UTœ =› UUT UUV =› UUe U]T 411

(31) 010210345 678ÿ4 ÿ

(32) 7ÿ4 2345ÿ74849:;9<ÿ:8=>?@A;9<ÿ39ÿB3358@ÿ2CDÿ?3ÿ3E@A:3B@ÿF@AG3AB49:@ÿ;>>=@ 3Gÿ@H8@4A9;9<ÿ>I>?@B MNOPQRQÿTUVPWPRXÿYUWUÿZN[N\Xÿ]^P\ÿYP\UPÿ_` d@eÿ;9>?49:@>ÿ:84>>;G;:4?;39ÿGA4B@e3Afÿ39ÿg=A49ÿ39?383?;39ÿ49>e@A;9<ÿ>I>?@B iURVjÿTkljQÿmlQnQXÿoURRUÿTN^jURUXÿMQpVÿTURN[Pÿ]qnP uv@ÿ5@>;<9ÿ3Gÿ>B4A?ÿ93?;G;:4?;39ÿ39ÿ495A3;5ÿ<45<@?ÿG3Aÿ4:45@B;: 4993=9:@B@9? ]wN[lPRUÿxk^jUlPXÿyzPÿZN{PURlPXÿiU^UVP{{UpÿiU^UVP{{UpXÿ_k|PÿTU^lPWUXÿ_pUnUjURlP _pUnUjURlPXÿ}nk{VUÿTU{NqUXÿ]pnUVÿTURnQ^PRQ @B3?@ÿ;9?@AFA@?@Aÿ‚JƒÿB35@8ÿG3Aÿ>=FF3A?;9<ÿ:3BF=?@AÿFA3;<9ÿ3GÿL4B;8IÿJ8499;9<ÿL;@85ÿŠGG;:@AÿG3AÿL4B;8IÿJ8499;9< ‚<@9:Iÿ‹>;9<ÿŠŒ2ÿ495ÿKL YQ{{jÿMUN{URUÿ]|URwwUXÿTklPU|URÿ][[kwU\\XÿTjU\^PU{ÿiU†p^PÿURkXÿMNpUnnUVÿiP^nUR ŽUp\P ‚ÿ<4B;G;:4?;39ÿGA4B@e3Afÿ?3ÿ@9v49:@ÿ>?=5@9?>ÿ;9?A;9>;:ÿB3?;E4?;39ÿ39 CŠŠ YNOPURlQÿyWQÿTU‘Nl^QXÿTUqP{UpÿTU{UnXÿMQpV`ÿxU\Pqÿ’UWU^PUXÿ“QRPÿ]R|U^ ”93e8@5<@ÿB494<@B@9?ÿ>I>?@BÿDŠJÿ=>;9<ÿ>@B49?;:ÿ9@?e3Af>ÿ:399@:?@5 e;?vÿF@A>399@8ÿ;9G3AB4?;39ÿ>I>?@B•ÿ:4>@ÿ>?=5Iÿ‹9;E@A>;?4> D;9<4F@A749<>4ÿ”4A4e49< }RlURÿN^RUnU[U^PXÿ}^nURÿxk^nUVPXÿZURPÿoN^pUV^jURP ‚>>@>>;9<ÿ>?=5@9?>ÿ:39?;9=49:@ÿ;9?@9?;39ÿ;9ÿ=>;9<ÿB=8?;B@5;4ÿ398;9@ 8@4A9;9< “U–|UÿxU^PwNRUXÿ]WnU{ÿ]WnU{ —8335ÿ;B4<@ÿ4948I>;>ÿ?3ÿ5@?@:?ÿB484A;4ÿ=>;9<ÿG;8?@A;9<ÿ;B4<@ÿ@5<@>ÿ495 :84>>;G;:4?;3 MN^WÿxU[[URÿMknQRXÿ“U^P–ÿ˜UnP{ÿTUP\N{{UpÿŽpURqUVUXÿTpkk^UqÿMknQRXÿTjkVÿYUpkk{ xU[[UR uv@ÿ49?@:@5@9?ÿ3Gÿ:;?;™@9ÿ;9?@9?;39ÿ=>@ÿ3Gÿ@H<3E@A9B@9?ÿ>@AE;:@ “U–|UÿxU^PwNRUXÿ pNRwš‡kRÿxNRwXÿxN[RPÿ“kOUÿTNWnURU C35@88;9<ÿ495ÿ;BF8@B@9?4?;39ÿ3Gÿr?f4ÿ<4B@ÿe;?vÿC4›dÿ48<3A;?vB _PRUÿTlk\URPXÿi^kVk^PWN[ÿ˜`Xÿ}^kRkÿ][lNlPÿ„UqU^N[{PXÿTUnNk{ÿ„NWU[Xÿkl^N[ÿ‡PVOUOU JA;E4?@ÿ:83=5ÿ>?3A4<@ÿ;BF8@B@9?4?;39ÿ=>;9<ÿŠF@9D?4:fÿDe;G? ]wN[lPRN[ÿoQk^lOUpjURUXÿ˜NURÿYkRQXÿxkR^jÿoQzPURN[ÿU{PlXÿ˜N[lPRN[ÿ]RVOU^|P^U|UR ƒ9?@;:48ÿd3?@ÿJ84I@Aÿ=>;9<ÿu;B@HLA@h=@9:Iÿ‚948I>;>ÿ39 =B49ÿJ84I ŽpU\PPqpÿxU[lNlPXÿ]^^jÿMUN{URUÿTjU^P\Xÿ]pnUVÿ’UPRN{ÿiURURPXÿ]lQRÿYN[lURVPÿMN{jURU ‚ÿ:3=F8@5H8;9@ÿ748=9ÿG3Aÿ=8?A4He;5@7495ÿ>;9<8@H74849:@5ÿ5;35@ÿB;›@A M`ÿZ`ÿ]{wNnUkPXÿo`ÿ]`ÿTpUP^PXÿ’`ÿ’UWU^PUXÿ]`ÿM`ÿ’QžP{UpXÿo`ÿyV|U^V uv@ÿ;9G8=@9:@ÿ3Gÿ>4BF8;9<ÿGA@h=@9:Iÿ39ÿ?39@ÿA@:3<9;?;39ÿ3GÿB=>;:48 ;9>?A=B@9?> „PRwwQÿTNnU^RQXÿŽNRlQ^Qÿ]VP D?@A@3ÿB4?:v;9<ÿ74>@5ÿ39ÿ47>38=?@ÿ5;GG@A@9:@>ÿG3AÿB=8?;F8@ÿ37œ@:?> 5@?@:?;39 YQ[lUnÿ]\\kRVPÿxUnqUpXÿMk{zPRÿŸURÿZkQNÿ‡kPXÿoPWÿTjUp^PnÿoPWÿ]R|U^ 3<9;?;E@ÿ4A?;G;:;48H;9?@88;<@9:@ÿG3Aÿ53@A9@97=A<ÿ5;>>38E@5ÿ<4>ÿ4948I>;> ;9?@AFA@?4?;39 ŽU^k{ÿ †lUzPURN[ÿˆU†p^PXÿmnU^ÿŽpUjUnXÿˆUnžURwÿ]RwwQ^QÿTQkVOU^RQXÿ]^|PR _UlNnUjUÿ‡UpjNVPÿTNnU^PXÿ]VURwÿTN|URVPÿ]pnUV ƒBF8@B@9?4?;39ÿ3Gÿe@7ÿ>:A4F;9<ÿ39ÿ<;?v=7ÿ?4>fÿB39;?3A;9<ÿ>I>?@B YQ{{jÿMUN{URUÿ]|URwwUXÿTjU\^PU{ÿiU†p^PÿURkXÿYk[lPjURUÿ_|Pÿ][lNlP uv@ÿ=>@ÿ3GÿB37;8@H4>>;>?@5ÿE;A?=48ÿA@48;?Iÿ;9ÿG@4Aÿ3Gÿ54Af9@>>ÿ?v@A4FI y^P†WÿUN{N[XÿMP^UÿTN^jURPXÿN[‘PlUÿ]VpPÿŽN[NnUÿ‡POUjURlPXÿiP^VUN[ÿk^VURUÿZN[N\X ]N{PUÿ}[WURVU^[jUp @G@A@9:@ÿ7A345:4>?ÿ>I9:vA39;™4?;39ÿ495ÿ?;B@ÿ5;E;>;39ÿB=8?;F8@ÿ4::@>> ;BF8@B@9?4?;39ÿ39ÿŒDd TUž^PUR[jUpÿYPq–PWUÿ]WžU^XÿMQ†pUnnUVÿxURRUl[ÿxURU\Pÿ}†p[URXÿ]N{PUÿ]^P\ÿ_U^nU|UR 11781 78 !"#

(33) $!%&'((&7)*& +,-+,./0, JKL abaHabc JKL abrHast JKL as~Ha€ JKL abHat‰ JKL ataHatr JKL a~‰Ha~c JKL a~rHact JKL ac~Harb JKL arsH€‰a JKL €‰€H€‰r JKL €a‰H€a~ JKL €acH€€ JKL €€tH€bs JKL €bH€s JKL €stH€€ JKL €bH€t‰ JKL €taH€t~ JKL €tcH€~s JKL €~H€ca JKL €c€H€r‰ JKL €raH€rc JKL 011

(34) 010210345 678ÿ4 ÿ

(35) 7ÿ4 234ÿ6789:8;<=>7ÿ?<@7Aÿ:=ÿ=:A7ÿ6B<>7;7=Cÿ?DÿE7=7CF>ÿoB<6FC<@CF=Eÿo@F=Eÿ2z|nÿ;7CG:A eaRcÿQMRT]RXÿIM^KauÿtJRM^ÿ\^VTSMROMXÿ}~ÿI~ÿYVRM^RJ €6CF;FÿBFEGC@ÿC:ÿ687H7=CÿC8<99F>ÿ>:=E7@CF:=ÿo@F=E 9oDÿB:EF> ‚VMRÿQM^SMRSVXÿƒJTVOMÿ„]^ÿf V MXÿ}]ZVÿsMS]^ÿeVT_V†^M†SVRV qFEFC:o8@7@ÿ?<@7Aÿ:=ÿ‡HF@:9Cj {7B<@7ÿ<@D=>G8:=:o@ÿ67=CÿA7H7B:6;7=CÿF=ÿ7B7>C8:=F>ÿ=:@7ÿA7@@F=Eÿ9:8ÿ?779ÿ‹oCF:=ÿ@D@C7;ÿ9:8ÿAGFC7>Co87ÿA7@FE=ÿ9:8ÿ<ÿ;oBCFj@7=@:8ÿF=9:8;7@@:8 sMSLa^VRaÿuVˆVMÿea^aMSVXÿf^_VRÿ‚MS]NM[MÿYML[]OVÿe]NM^VXÿ^VJÿfOVJRJXÿfOMRc e]_MROVÿfLNMO ‘o<8Cÿ>8D@C8:?7ÿ?<@7Aÿ7B7>C8:=F>ÿ=:@7ÿ@D@C7;ÿF;6B7;7=C7Aÿ:= rF7BAÿp8:E8<;;o87ÿ?o9978ÿ?<@7Aÿ6GD@F>B:=CF:=@ÿ”p•r–@—ÿ9:8ÿA7HF>7 C7==<ÿ™FCGÿGFEGÿE7B7Cÿ9:8ÿG7<8Cÿ8Cÿ>o887=Cÿ;:C:8ÿ6:™78ÿ87‹oF87;7=Cÿ9:8ÿ;<=F{F=ÿ@;<8C F88FE7@@ÿF=ÿ<=ÿ7B7>C8:=F>ÿ;<=o9<>Co8F=E >:;6<=D QM[MSVÿI]gSVÿfTVLXÿsLJRcÿ\]MRcÿdRcXÿœaaÿIaVÿ}LžRc 3‹oF887Bÿ>CF:=ÿ;:C:8ÿ@>:=C8:Bÿ>:=@C<=CÿŸ rÿ<=:=@C<=Cÿ6:™78ÿB:Gÿ7997>Cÿ:=ÿ>:;;:=j;:A7ÿE8:@@j>:o6B7A <;6BF9F7 šMVR]uÿfbVOVRXÿdgMÿIM]uMRMXÿƒMNMOLMRVÿ\]^RVM_MRÿe]b^JSJXÿYVZJRJÿYVZJRJ p:™78ÿB:@@ÿ<=o887=Cj;:AoB7@ÿ?<@7Aÿ;oBCFB7H7Bÿ>o887=Cj@:o8>7 6:™78ÿF=H78C78@ e]^JTJÿe]^JTJXÿYVRMTVTÿYVRMTVTXÿ‚M^]ÿ^Vÿ„]c^JLJXÿYML[]ÿ^VÿsML[MRSJ ¡B<@@F9F>oB<8F:=H:BoCF:=:B:o8j?<@7Aÿ?oFBAF=Eÿ87>:E=FCF:=ÿo@F=Eÿ@o66:8CÿH7>C:8ÿ;<>GF=7 11781 78 !"#

(36) $!%&'((&7)*& +,-+,./0, pqr 011

(37) 010210345 678ÿ4 ÿ

(38) 7ÿ4 234567ÿ9:;<436=36ÿ>9=36ÿ<=?5;@=A39ÿB5ACÿ?D>4@AA@Eÿ:A3@5ADD4FÿGHÿCA@A5 KLMNOPÿRÿRPSMPSTUÿVPWPSÿXTYTMPSUÿKZ[N\[TMÿ]P[T\[^PSNUÿV_SP`ÿ]aO^PLNUÿVPMTO Va[aYMPS G4@45C=3;@=A3ÿABÿ9AD=FÿC;@45=;Dÿf45C=@@=<=@7ÿ>9=36ÿge5=36ÿ549A3;@A5ÿBA5ÿBAAF =3F>9@57 hPiiP[ÿKjÿKYP[LaiNUÿkjÿkPMPSNPUÿk_YMPYLPNLÿ]a[lÿm_\\anUÿoaYTÿV_ONMLaUÿKipS_Y Kq_PLÿ]a[lÿrP[PSUÿKiiPSÿKY[TWPqN uÿ<45=B=:;@=A3ÿABÿf45=AFA65;Cÿ@4:E3=v>4ÿBA5ÿE;5CA3=:ÿ9A>5:4ÿF=;63A9@=: ;3;D7@=:ÿ?7ÿ>9=36ÿDA6=9@=:ÿ5465499=A3 ]jÿ]PLPwUÿ]jÿRjÿxawSNUÿKjÿhjÿKZl_YYP[UÿhjÿyPSNiUÿ]jÿhjÿm_\annUÿKRÿKqP[PS }f44FÿD=C=@45ÿ=3@465;@4FÿB;@=6>4ÿ;3;D7~45ÿ}€Ju‚ƒÿ436=3445=36ÿF49=63ÿ;3F :A3:4f@ RPlNÿ„SPLaOaUÿKj]jÿ TiPLUÿ†P`PSÿKLWWPSPUÿ]_[PiiPlÿy[aYNY u3;D79=9ÿABÿˆu‰ÿC>D@=:Af@45ÿABÿ;=5ÿfEA@A65;fE7ÿ=3ÿŠ4‹ÿŒA67;;5@; 3@453;@=A3;Dÿu=5fA5@9 ŽLlST\^PSNÿV_Sa\aUÿS^[NLÿŽSiP^PL I54F=:@=A3ÿABÿIGÿ:A3@5ADÿCAF4DÿA3ÿI€H S^PLNÿ]TSSpÿVPSONMPUÿojÿh_lNÿVPS`aLaUÿNMNÿ^NÿVPw_OSP u3@E5AfACA5fE=:ÿ@5;395;F=;DÿC7A4D4:@5=:ÿE;3Fÿ>9=36ÿ@43FA3e9f5=36 C4:E;3=9C ]a’[PiiPlÿKSNpPLOaUÿhNnMpÿŽ\iPNYUÿxaWPÿjÿVTONP^PLUÿYWPÿ„jÿm_PLlN IGJ bcdebcc IGJ bcsebst IGJ bsze{|z IGJ {|ce{‡| IGJ {‡de{‡c IGJ {‡se{‘t IGJ {‘ze{bc “”•–—˜™š–›ÿ“žŸ ¡¡¢£¤Ÿ¥¦¤ £§ÿ¨ ¡©¢¦¤£ª§ÿ”žŸ¦« £¤Ÿ¬ÿ¥£­ÿ¨ £¦« žÿ }}Šƒÿdts‘ets‘|®ÿ4e}}Šƒÿ‡‘|‡es‡s‘ÿ ˆ3=<459=@;9ÿuEC;FÿG;ED;3®ÿb@EÿH;Cf>9®ÿs@EÿJDAA5®ÿ€IIÿ¯AAC °D±ÿ¯=365A;Fÿ}4D;@;3®ÿ²5;6=D;3®ÿg;C;3;3®ÿ³;36>3@;f;3®ÿ³;3@>Dÿ®ÿŒA67;;5@;®ÿ3FA349=;ÿ{{dsdÿ IEA34ƒÿ´t‡ÿ‡zb‚ÿ{t‘{d{®ÿ{ddc‘|®ÿ‘zsbdc®ÿ‘zdd‡|ÿ4µ@±ÿbs|‡®ÿJ;µƒÿ´t‡ÿ‡zbÿ{tbt|b gE=9ÿ‹A5ÿ=9ÿD=:4ÿ394Fÿ>3F45ÿ;ÿH54;@=<4ÿHACCA39ÿu@@5=?>@=A3eŠA3HACC45:=;Dÿb±|ÿ3@453;@=A3;Dÿ€=:4394± ‰=4‹ÿg2€²¶·Š²uÿ}@;@9 11781 78 !"#

(39) $!%&'((&7)*& +,-+,./0, 111

(40) 012314526 789

(41) ÿÿÿ98  ,-./01234 ÿ ÿ 7 95ÿ*ÿ5ÿ65ÿ!7ÿÿ ÿ 891ÿ;2<=/12.1ÿ-<ÿ4>0?=;2@ÿ=ÿ;243A/01234ÿ D4526EÿFGHIJKLMINÿPFGHGQJKKRLMQNSMJLÿTJKURSMLVÿWHGQSXJLMQYÿNLZÿTJLSXJH[5ÿ2\ÿD2E5ÿ ÿ4304&5ÿÿ ÿ ,]^_ÿ252464'1`a*!#bcd!6e2\222&5'ÿ ÿ ÿ ÿ9fÿa(88(ÿa5ÿ7ÿÿge

(42) "5ÿ!

(43) ÿddd5ÿ5ÿb 9h95ÿ 9)5ÿ7(5 i9")5ÿ334'45ÿd9

(44) ÿ 7ÿ ÿ9fÿdf98

(45) ÿa 5ÿ7ÿÿge

(46) "5ÿ!

(47) ÿddd5ÿ5ÿb 9h95ÿ 9)5ÿ7(5 i9")5ÿ334'45ÿd9

(48) ÿ ÿ jk43A>.3ÿ 7 (fl 8"ÿ9fÿ

(49) 8(ÿ

(50)  

(51) ÿ9ÿ899ÿ(("ÿf9((9

(52) ÿÿ79ÿ

(53)  (ÿ9ÿ`

(54) ÿ   m (9

(55) ÿÿf( 8ÿ9fÿ

(56)  (ÿfl 8"ÿÿ9

(57) ÿ9ÿf9((9ÿÿ79ÿ

(58)  (ÿ95ÿÿÿ9ÿ899

(59) "

(60) ÿ

(61) ÿ

(62) ÿeÿf9ÿf ÿm89ÿÿ (ÿ8ÿf9ÿ8(

(63)

(64) f89ÿ`ÿ

(65) 8(ÿ

(66)  

(67) ÿ

(68) ÿÿ7(("5ÿf( 5ÿÿ 85ÿÿ8ÿ9fÿÿ 

(69) ÿÿ

(70) 8(ÿ

(71)  ÿÿÿ95ÿÿf5ÿÿ"

(72) f8ÿ(98(ÿ )

(73) ÿÿÿ

(74) 8ÿ$9 ÿ`

(75) f9ÿD$`Eÿ9ÿn

(76) ÿ9ÿ9 ÿm 

(77) 5ÿ (ÿÿ

(78)  ( fl 8"ÿ

(79) ÿ

(80) ÿ(9ÿ

(81) ÿ024ÿop5ÿ899ÿÿ f98ÿ9fÿ7(("ÿÿf( ÿ9

(82) ÿÿf( 8ÿÿ((ÿ

(83) 8ÿ  8ÿÿÿÿ9fÿ3qÿo9e5ÿ899ÿÿ f98ÿ9fÿ 8ÿ9

(84) ÿ

(85) ÿ9ÿf( 8ÿ7"ÿÿ

(86)  ( fl 8"ÿ`f95ÿfÿÿ)ÿ9fÿ 8ÿ899ÿÿ89 (ÿ7ÿ88 5ÿÿ

(87)  (ÿfl 8"ÿ

(88) ÿ(9ÿ

(89) ÿ024ÿop 89 (ÿ7ÿ

(90) ÿf9ÿ9ÿ899ÿ9fÿ

(91) 8(ÿ

(92)  

(93) ÿrÿ4526ÿge

(94) 

(95) ÿ6ÿ(ÿ ÿ j/39-Aÿs1Ct-Au4ÿ 7 (ÿfl 8"vÿÿ79ÿ

(96)  (ÿ9vÿÿ`9ÿ899ÿ ÿ w-AA14?-2u12.1ÿjuuA144ÿÿ 7 9ÿ*vÿ ÿ9fÿa(88(ÿa5ÿ7ÿÿge

(97) "5ÿ!

(98) ÿdddd9

(99) vÿ( (

(100) x

(101) 8ÿ ÿ y/k=;491A_ÿge

(102) 

(103) ÿ6ÿ(ÿ ÿ ^zz{_ÿ2&60&605ÿ |>2@/>@1ÿ-<ÿ]A;@;2>=ÿ,-./0123_ÿa(

(104) ÿ jkkA1};>31uÿz-/A.1ÿ8;3=1_ÿ`()9)ÿ`(89 ÿ~9 ÿa(8ÿ~99(ÿ 4

(105) 45'35&44&5024ÿ ,-./0123ÿ8C?1_ÿ68(ÿ y/k=;.>3;-2ÿz3>@1_ÿ$(ÿ z-/A.1_ÿ789

(106) ÿ ÿ ÿ ÿ ~9 "ÿrÿ4526ÿa(

(107) eÿnÿ6((ÿ

(108) ÿ

(109) eÿ789

(110) €ÿ

(111) ÿÿ

(112)  )ÿ9fÿa(

(113) eÿn 

(114) 11

(115) 89

(116) 891891  989 

(117) 

(118) 8

(119)

(120) !"#$%25&3233334 4

(121) 45'35&44&5024

(122) 9 8(8)*+ 212

(123) 010210345 6789

(124) 9 #$%&'()*)$&+)(',-'%./0#1&2' 3456789'5:3;5;<;59:3'=7:>5:83 3./0#1&'?&@AB#$'C'4&@BDA-'=#BE ƒ 7'„  8'687 '†‡‡ˆ' '‰Š87'ˆ

(125) 7 F&0) RMSOTUV \S]^J_T'`UJQ'QOa RQTJbMUV dS]KPefJU dS]KP_QTPMO'TViJ j\\k RMsJUQbJ \_MiJ ?&@AB#$'=#BE/B1% 4&@BDA-'=#BE/B1% G/H';&&$% IJKLMNOPLQ F)$+ ' 7,&@D'<% 5B(&B)%/#''W' '35='=#BE/B1'&X'5B(&B)%/# cB1/B))A/B1' c$).DA/.#$'#B('c$).DA&B/.'cB1/B))A/B1' F'5B()[ 5B%D/D@D)'&X'7(*#B.)('cB1/B))A/B1'#B('3./)B.)'g57c3h ?&@AB#$% lmnlolomp'qromromn lnqqW&B1&/B1 ;ct>96:5>7'g;)$).&00@B/.#D/&Bp'4&0+@D/B1p'c$).DA&B/.%'#B('4&BDA&$h'533:2'qromWromnp')W 533:2'lmnlWolom'/%'#'+))AWA)*/)u)(p'%./)BD/v.'w&@AB#$'+@,$/%x)(',-'96:5>7'u/$$',) +@,$/%x)('#%'#',/0&BDx$-'w&@AB#$'gr'/%%@)%-)#Ahz';x)'w&@AB#$'A)1/%D)A)('/B'Dx)'4A&%%=)X %-%D)0'u/Dx'y/1/D#$'9,w).D'5()BD/v)A'gy95h'+A)v['qnzqlol~z';x)'?&@AB#$'x#%',))B'/B()[)(',349|<3p'8&&1$)'3.x&$#Ap'3.x&$#A'6)DA/.%')D.€'#..A)(/D)('7'8A#()',-'y8Fc'g6/B/%DA-'&X =)%)#A.xp';).xB&$&1-'#B('F/1x)A'c(@.#D/&Bp'=)+@,$/.'&X'5B(&B)%/#h€'A)1/%D)A)('y/A).D&A-'&X 9+)B'7..)%%'?&@AB#$%'gy97?hp'}73c'W'}/)$)X)$('7.#()0/.'3)#A.x'cB1/B)'#B('49=c'>6/p')D.z ;x)'?&@AB#$'#$%&'x#*)'#'$/.)B%)'#1A))0)BD'u/Dx'|A&‚@)%D'tt4'#B('c}349'|@,$/%x/B1z F&0)+#1) F&u'D&'+@,$/%x'/B'Dx/%'w&@AB#$ 4&BD#.D ?&/B'Dx)'.&B*)A%#D/&B'#,&@D'Dx/%'w&@AB#$ ‚@#AD/$)% x/1x)%D'*#$@)%'#B('‚‹'gA)(h'Dx)'$&u)%D'*#$@)%z RQTJbMUV c$).DA/.#$'#B('c$).DA&B/.'cB1/B))A/B1 c$).DA/.#$'#B('c$).DA&B/.'cB1/B))A/B1 c$).DA/.#$'#B('c$).DA&B/.'cB1/B))A/B1 c$).DA/.#$'#B('c$).DA&B/.'cB1/B))A/B1 c$).DA/.#$'#B('c$).DA&B/.'cB1/B))A/B1 c$).DA/.#$'#B('c$).DA&B/.'cB1/B))A/B1 ŒJQU lnql lnqm lnq‹ lnqŽ lnqr lnq SQUTPKJ ‚m ‚m ‚m ‚m ‚m ‚m 11

(126)  

(127) 1  87044330 434!"!87 3 41

(128) 010210345 6789

(129) 9 "#$ G)1+1)5.*ÿ0'2ÿ/548A'.1 b%>a&i'ÿ"#$ÿ)*ÿ+ÿ*),'-)./'0'./'.1ÿ02'*1)3'ÿ)./)4+152ÿ1&+1 2+.6*ÿ7582.+9*ÿ:;ÿ1&')2ÿ<+='2+3'ÿ02'*1)3'ÿ0'2ÿ+21)49'<>ÿ?1ÿ)* b:>a+`*'/ÿ5.ÿ1&'ÿ)/'+ÿ1&+1ÿ<+99ÿ4)1+1)5.*ÿ+2'ÿ.51ÿ42'+1'/ 'b@>a8+9<>ÿ"#$ÿ)*ÿ+ÿA'+*82'ÿ5Bÿ*4)'.1)C4ÿ).D8'.4'ÿ5B 7582.+9*ÿ1&+1ÿ+4458.1*ÿB52ÿ:51&ÿ1&'ÿ.8A:'2ÿ5Bÿ4)1+1)5.* b2>'c4h')='/ÿ:;ÿ+ÿ7582.+9ÿ+./ÿ1&'ÿ)A0521+.4'ÿ52ÿ02'*1)3'ÿ5B 1&'ÿ7582.+9*ÿE&'2'ÿ*84&ÿ4)1+1)5.*ÿ45A'ÿB25Aÿ?1 A'+*82'a*bÿc1a&'ÿ*4a)'b.c1e)C4ÿ).aDb8c'`.4'ÿ5aBbÿ1c&g'ÿ+='a2b+c3h'ÿ+21)a4b9'cf ).+7582.+9)1'F02'**'*&5E4'.12+9151&'395:+9 %51+9ÿG)1'*ÿ "'9B-G)1'* `jb=b5981)5.ÿ5Bÿ1&'ÿ151+9ÿ.8A:'2ÿ5Bÿ4)1+1)5.*ÿ+./ÿ7582.+9<* *'9B-4)1+1)5.*ÿ2'4')='/ÿ:;ÿ+ÿ7582.+9<*ÿ08:9)*&'/ /548A'.1*ÿ/82).3ÿ1&'ÿ1&2''ÿ02'=)58*ÿ;'+2*> a#b5b82.+9ÿ"'9B-4)1+1)5.ÿ)*ÿ/'C.'/ÿ+*ÿ1&'ÿ.8A:ÿ '2ÿ5Bÿ4)1+1)5. B25Aÿ+ÿ7582.+9ÿ4)1).3ÿ+21)49'ÿ15ÿ+21)49'*ÿ08:9)*&'/ÿ:;ÿ1&' *+A'ÿ7582.+9> b e ]WaObc` abcg abch abcf LMNOPabcc abZcOa[Sabc\[ "9BG)1 abcc b jF1'2.+9ÿG)1'*ÿ0'2ÿ_54ÿ G)1'*ÿ0'2ÿ_54 cj>a=5981)5.ÿ5Bÿ1&'ÿ.8A:'2ÿ5Bÿ151+9ÿ4)1+1)5.ÿ0'2ÿ/548A'.1 +./ÿ'F1'2.+9ÿ4)1+1)5.ÿ0'2ÿ/548A'.1ÿJ)>'>ÿ7582.+9ÿ*'9B4)1+1)5.*ÿ2'A5='/Kÿ2'4')='/ÿ:;ÿ+ÿ7582.+9<*ÿ08:9)*&'/ b/>h548A'.1*ÿ/82).3ÿ1&'ÿ1&2''ÿ02'=)58*ÿ;'+2*>ÿjF1'2.+9 4)1+1)5.*ÿ+2'ÿ4+9489+1'/ÿ:;ÿ*8:12+41).3ÿ1&'ÿ.8A:'2ÿ5B *b'9B-4)1+1)5.*ÿB25Aÿ1&'ÿ151+9ÿ.8A:'2ÿ5Bÿ4)1+1)5.*ÿ2'4')='/ :;ÿ1&'ÿ7582.+9k*ÿ/548A'.1*> abcc abca abce abc` abcg abch abcf LMN Z \] G)1+:9'ÿ/548A'.1*ÿ p5.-4)1+:9'ÿ/548A'.1* ip5 bb1ÿ'='2;ÿ+21)49'ÿ).ÿ+ÿ7582.+9ÿ)*ÿ45.*)/'2'/ÿ02)A+2; 2'*'+24&ÿ+./ÿ1&'2'B52'ÿq4)1+:9'qHÿ1&)*ÿ4&+21ÿ*&5E*ÿ1&' 2+1)5ÿ5Bÿ+ÿ7582.+9<*ÿ+21)49'*ÿ).498/).3ÿ*8:*1+.1)+9ÿ2'*'+24& `Jb2'b*'+24&ÿ+21)49'*Hÿ45.B'2'.4'ÿ0+0'2*ÿ+./ÿ2'=)'E*Kÿ). 1&2''ÿ;'+2ÿE)./5E*ÿ=*>ÿ1&5*'ÿ/548A'.1*ÿ51&'2ÿ1&+. 2'*'+24&ÿ+21)49'*Hÿ2'=)'E*ÿ+./ÿ45.B'2'.4'ÿ0+0'2*> b bcY cNPabca abce aZbOc[`S ab\[ cg]WOabch abcf rUVWaXO p )1:9/ 1 abcc b c%>a&g)*ÿ)./)4+152ÿ458.1*ÿ1&'ÿ.8A:'2ÿ5Bÿ4)1+1)5.*ÿ2'4')='/ÿ:; /548A'.1*ÿB25Aÿ+ÿ7582.+9ÿ+./ÿ/)=)/'*ÿ1&'Aÿ:;ÿ1&'ÿ151+9 .8A:'2ÿ5Bÿ/548A'.1*ÿ08:9)*&'/ÿ).ÿ1&+1ÿ7582.+9>ÿ%&' 4&c+21ÿ*&5E*ÿ1&'ÿ'=5981)5.ÿ5Bÿ1&'ÿ+='2+3'ÿ.8A:'2ÿ5B 1)A'*ÿ/548A'.1*ÿ08:9)*&'/ÿ).ÿ+ÿ7582.+9ÿ).ÿ1&'ÿ0+*1ÿ1E5H 1 ''ÿ+./ÿB582ÿ;'+2*ÿ&+='ÿ:''.ÿ4)1'/ÿ).ÿ1&'ÿ4822'.1ÿ;'+2> b%>&f&2g' ÿ1E5ÿ;'+2*ÿ9).'ÿ)*ÿ'@8)=+9'.1ÿ15ÿ7582.+9ÿ)A0+41ÿB+4152 IÿJ%&5A*5.ÿ$'81'2*KÿA'12)4> b>g LMNOPÿROSÿTUVWXOYN ZO[S \[]WO G) '*ÿ^ÿ_54>ÿJ`ÿ;'+2*K abcc b>bbb b>G) ag1 1'*ÿ^ÿ_54>ÿJ`ÿ;'+2*K abca c>ccd G)1'*ÿ^ÿ_54>ÿJ`ÿ;'+2*K abce b>fce G)b1'*ÿ^ÿ_54>ÿJ`ÿ;'+2*K abc` b>gde G)1'*ÿ^ÿ_54>ÿJ`ÿ;'+2*K abcg b>gda bcc4>ÿJ` abÿ;c'a+2*aKbceabc ah bc` b> aibcceg abch abcf G)1'*ÿ^aÿ_5 G)1'*1'ÿ^*ÿÿ_5 44>ÿ>Jÿ`J`ÿ;ÿ;''++22**KK abcf b>hba ^ÿ_5 G)1G) ' * ÿ ^ ÿ _5 4 G)1'*ÿ^ÿ_54>ÿ>Jÿe Jeÿ; ÿ;''+ +2 2* *KK abcc b>bbb G)1G) '*1'ÿ^*ÿÿ_5 44>ÿ>JÿeJaÿ;ÿ;''++22**KK abca c>ccd ^ÿ_5 G)1'*ÿ^ÿ_54>ÿJeÿ;'+2*K abce b>fce lÿ?.1'2.+1)5.+9ÿG599+:52+1)5. a?`.1'2.+1)5.+9ÿG599+:52+1)5.ÿ+4458.1*ÿB52ÿ1&'ÿ+21)49'*ÿ1&+1 &+='ÿ:''.ÿ025/84'/ÿ:;ÿ2'*'+24&'2*ÿB25Aÿ*'='2+9 c4i58.12)'*>ÿ%&'ÿ4&+21ÿ*&5E*ÿ1&'ÿ2+1)5ÿ5Bÿ+ÿ7582.+9<* 548A'.1*ÿ*)3.'/ÿ:;ÿ2'*'+24&'2*ÿB25AÿA52'ÿ1&+.ÿ5.' c/ 4a58.12;mÿ1&+1ÿ)*ÿ).498/).3ÿA52'ÿ1&+.ÿ5.'ÿ458.12;ÿ+//2'**> h ZO[SabccnYNOaSbYc[aNMUYa[b]ÿcLU ]][aobUcS`[NMUaYbcg abch abcf e abcc cf>ed abca ccie G)1'/ÿ/548A'.1*ÿ s.4)1'/ÿ/548A'.1* i$+ bb1)5ÿ5Bÿ+ÿ7582.+9<*ÿ)1'A*Hÿ32580'/ÿ).ÿ1&2''ÿ;'+2* E)./5E*Hÿ1&+1ÿ&+='ÿ:''.ÿ4)1'/ÿ+1ÿ9'+*1ÿ5.4'ÿ=*>ÿ1&5*' .51ÿ4)1'/ÿ/82).3ÿ1&'ÿB5995E).3ÿ;'+2> `bb rUVWXOYNP ZO[S \[]WO s. )1'/ÿ/548A'.1* abcc b b4 s. 4)1a'b/cÿ/c548aA' .1*abceabcaabc`ecabcg abch abcf bca. s.4)1'/ÿ/548A' 1* abce ia s.4)1'//548A'.1* abc` cfa t "&5Eÿ1&)*ÿE)/3'1ÿ). ;582ÿ5E.ÿE':*)1' ÿ #8*1ÿ450;ÿ1&'ÿ45/'ÿ:'95E +./ÿ0+*1'ÿE)1&).ÿ;582ÿ&1A9 45/'u vÿ7xy11  11   1 

(130) 87044330434   ! 87

(131) 3 01

(132) 010210345 6789

(133) 9 "#$ÿ&'$('ÿ)*ÿ+,-./0)ÿ1)&(2/3ÿ4ÿ5)&26(7ÿ8/29ÿ#/:$ÿ6#$ÿ;)''-<-3-67ÿ6)ÿ=-/3)0&$ÿ6#()&0#ÿ,)..$26'ÿ3-29$=ÿ6)ÿ/ ';$,->,ÿ?)&(2/3@ÿ"#$ÿ;&(;)'$ÿ-'ÿ6)ÿ#/:$ÿ/ÿ*)(&.ÿ-2ÿA#-,#ÿ0$2$(/3ÿ=)&<6'ÿ/<)&6ÿ6#$ÿ;(),$''$'ÿ)*ÿ;&<3-,/6-)2ÿ-2ÿ6#$ ?)&(2/3Bÿ$C;$(-$2,$'ÿ/2=ÿ)6#$(ÿ-''&$'ÿ=$(-:$=ÿ*().ÿ6#$ÿ;&<3-,/6-)2ÿ)*ÿ;/;$('ÿ/($ÿ($')3:$=@ÿD)(ÿ6);-,'ÿ)2ÿ;/(6-,&3/( /(6-,3$'Bÿ./-26/-2ÿ6#$ÿ=-/3)0&$ÿ6#()&0#ÿ6#$ÿ&'&/3ÿ,#/22$3'ÿA-6#ÿ7)&(ÿ$=-6)(@ E$:$3);$=ÿ<7Fÿ G)A$($=ÿ<7Fÿ ÿ D)33)Aÿ&'ÿ)2ÿH+,-./0)18ÿ ÿ +,-./0)ÿI/
(134) 87044330434   ! 87

(135) 3 1

(136) TELKOMNIKA, Vol.17, No.1, February 2019, pp.253~260 ISSN: 1693-6930, accredited First Grade by Kemenristekdikti, Decree No: 21/E/KPT/2018 DOI: 10.12928/TELKOMNIKA.v17i1.11608  253 The influence of sampling frequency on tone recognition of musical instruments Linggo Sumarno*1, Kuntoro Adi2 1Department of Electrical Engineering, Sanata Dharma University Kampus III, Paingan, Maguwoharjo, Depok, Sleman, Yogyakarta, Indonesia 55282 2Department of Informatics Engineering, Sanata Dharma University Kampus III, Paingan, Maguwoharjo, Depok, Sleman, Yogyakarta, Indonesia 55282 *Corresponding author, email: lingsum@usd.ac.id Abstract Sampling frequency of musical instruments tone recognition generally follows the Shannon sampling theorem. This paper explores the influence of sampling frequency that does not follow the Shannon sampling theorem, in the tone recognition system using segment averaging for feature extraction and template matching for classification. The musical instruments we used were bellyra, flute, and pianica, where each of them represented a musical instrument that had one, a few, and many significant local peaks in the Discrete Fourier Transform (DFT) domain. Based on our experiments, until the sampling frequency is as low as 312 Hz, recognition rate performance of bellyra and flute tones were influenced a little since it reduced in the range of 5%. However, recognition rate performance of pianica tones was not influenced by that sampling frequency. Therefore, if that kind of reduced recognition rate could be accepted, the sampling frequency as low as 312 Hz could be used for tone recognition of musical instruments. Keywords: sampling frequency, Shannon sampling theorem, tone recognition Copyright © 2019 Universitas Ahmad Dahlan. All rights reserved. 1. Introduction Nowadays, the development of technology leads to digital technology. This digital technology requires the conversion of data from analog type to discrete type. In order to convert data from analog to discrete, the existence of a sampler is required. The major parameter in a sampler is sampling frequency. Generally in the field of digital signal processing, the sampling frequency used is the frequency that follows the Shannon sampling theorem. Basically, this theorem needs to be followed in order that analog signal can be perfectly recovered from its sampled version [1]. In addition, in the field of pattern recognition, the Shannon sampling theorem is generally followed, such as: in researches relating to tone recognition using the time domain approaches [2-5], the transformation domain approaches that are based on fundamental frequencies [6-11], and the transformation domain approaches that are not based on fundamental frequencies [12-18]. If it is analyzed further, in researches relating to musical instruments tone recognition, signal processing is not carried out on processes that contribute to producing the output signal. In this case, signal processing will stop before feature extraction process. There were no previous researches, relating to musical instruments tone recognition made use of sampling frequencies that did not follow the Shannon sampling theorem. Thus, a research of musical instruments tone recognition that makes use of sampling frequencies that do not follow the Shannon sampling theorem, is still wide open. As a note, the advantage of using sampling frequencies that do not follow the Shannon sampling theorem is smaller data for processing. This paper will discuss the influence of sampling frequency that does not follow the Shannon sampling theorem, on musical instruments tone recognition. The tone recognition system uses a transformation domain approach that does not use fundamental frequencies [18]. The musical instruments use bellyra, flute, and pianica. They are chosen to represent tones that have one, a few, and many significant local peaks in the Discrete Fourier Transform (DFT) domain as shown in Figure 1. In more detail, it will be explored if there is a lowest sampling frequency that does not follow the Shannon sampling theorem, which can be used for tone recognition system. Received July 31, 2018; Revised October 9, 2018; Accepted November 4, 2018

(137) 254  ISSN: 1693-6930 Figure 1. Representation of tone C in the normalized DFT domain X(k) for bellyra, flute, and pianica, by using a sampling frequency 5000 Hz and a DFT 128 points. As a note, only the left half of the normalized DFT domain is shown. 2. Research Method 2.1. Overall system development A tone recognition system shown in Figure 2 had been developed in order to explore the influences of sampling frequency. The input is an isolated signal tone in wav format. The output is a text that indicates the recognized tone. The input and the function of each block in Figure 2 are described in details in Subsections 2.1.1-2.1.11. Figure 2. Block diagram of the developed tone recognition system 2.1.1. Input The input of the developed tone recognition system was an isolated tone signal from a musical instrument (bellyra, flute, or pianica) in wav format. There were eight tones (C, D, E, F, G, A, B, and C) of each musical instrument. The tones were obtained by using various sampling frequencies: 5000 Hz, 2500 Hz, 1250 Hz, 625 Hz, 312 Hz, and 156 Hz. The highest sampling frequency of 5000 Hz was chosen because it met the following the Shannon sampling theorem [1]: 𝑓𝑠 ≥ 2𝑓𝑚𝑎𝑥 (1) where 𝑓𝑚𝑎𝑥 is the highest frequency component of the analog signal to be sampled, and 𝑓𝑠 is the sampling frequency. Based on the evaluation of the signal spectrum, the highest significant frequency components for C’ on bellyra, flute, and pianica were 2109 Hz, 1602 Hz, and 2100 Hz, respectively. The recording duration of 2 seconds was chosen since based on the evaluation of signal amplitude, it was sufficient to get more than half of the signal that was already in the steady state condition. The three musical instruments we used for generating the tone signals above were, Isuzu ZBL-27 bellyra, Yamaha YFL-221 flute, and Yamaha P-37D pianica, as shown in Figure 3. In order that the generated tone signals could be processed by the computer, they were captured by using a Samson Meteor USB microphone. TELKOMNIKA Vol. 17, No. 1, February 2019: 253-260

(138)  255 ISSN: 1693-6930 TELKOMNIKA (a) Bellyra (b) Flute (c) Pianica Figure 3. Bellyra, flute, and pianica, which were used for this research 2.1.2. Frame Blocking Frame blocking is the process of taking a short signal from a long signal [19]. This process is needed in order to reduce the number of signal data from the input. By reducing the number of signal data, it could reduce computing time. In this research, a short signal was taken from the beginning area of the tone signal that had been in the steady state condition. Based on the evaluation of the tone signals, 200 milliseconds after the silent part of the signal, the steady state condition had been reached. In this research, frame blocking length was evaluated with values of 16, 32, 64, and 128 points. 2.1.3. Initial Normalization Initial normalization is a process for setting a maximum absolute value to a value of one. Initial normalization is required since the signals from the frame blocking process have variations in maximum absolute value. Initial normalization is carried out using the following (2): 𝒙𝑜𝑢𝑡 = 𝒙𝑖𝑛 𝑚𝑎𝑥(|𝒙𝑖𝑛 |) (2) where signal vectors xin and xout are the input and output of normalization process respectively. 2.1.4. Windowing Windowing is the process of reducing discontinuities in the areas of signal edges. These areas appear as a result of signal cutting in the frame blocking process. Discontinuity reduction will reduce the appearance of harmonic signals, after the normalized signals is transformed using FFT (Fast Fourier Transform). Hamming window [20] is a type of window that can be used for windowing purposes. This type of window is commonly used in digital signal processing [21]. In this research, the window width was the same as the frame blocking length. 2.1.5. FFT FFT is a process to transform a discrete signal from windowing process, from the time domain to the DFT domain. Basically FFT is an efficient method to perform the DFT calculation. In this research, DFT calculation was performed using a radix-2 FFT. This type of FFT is widely used in the field of digital signal processing [21]. As well as the above windowing, the FFT length in this research had the same length as the frame blocking length. 2.1.6. Symmetry Cutting Symmetry cutting is the process of cutting half part of the FFT result. This cutting is necessary since between the left and right half of the FFT result shows a symmetry property. The influence of sampling frequency on tone recognition of musical... (Linggo Sumarno)

(139) 256  ISSN: 1693-6930 Therefore, when only half part of the left or right of the FFT result, it will be sufficient. In this research, only the left half part of the FFT result was used. 2.1.7. Segment Averaging Segment averaging is a process to shorten the signal length from symmetry cutting. In this case, the shortened signal still shows similarity to the basic shape of the long signal. Segment averaging [18] used in this research using the principles of segment averaging inspired by Setiawan [22]. In this research, the segment length in segment averaging was evaluated with values 1, 2, 4, ..., and 2log2 (N / 2) points, where N is the length of frame blocking. 2.1.8. Final Normalization As with initial normalization, final normalization is also the process of setting the maximum absolute value to a value of one. Final normalization is necessary because the results of segment averaging have variations in the maximum absolute value. As with initial normalization, final normalization also carried out using (2). As a note, the final normalization result is called feature extraction of the input signal. 2.1.9. Distance calculation Distance calculation is a comparison process between an input signal feature extraction and a number of tone signal feature extractions stored in the tone database. Distance calculation is an indication of pattern recognition using a template matching method [23, 24]. The Euclidean distance function can be used for this kind of distance calculation. This distance function is commonly used in the field of pattern recognition [25]. 2.1.10. Tone decision Tone decision is the process of deciding an output tone that corresponds to the input signal. The first step of tone decision is finding a minimum value from a number of distance calculation results. These are the results of distance calculation between an input signal feature extraction (after final normalization process) and a number of tone feature extractions in the tone database. The next step is to decide an output tone. A tone associated with one of the signal feature extraction in the tone database that has a minimum distance, will be decided as the output tone. 2.1.11. Tone database The tone database shown in Figure 2 is generated using the tone feature extraction shown in Figure 4. In this research, for each musical instrument, we took 10 samples for each tone (C, D, E, F, G, A, B, and C'). It was assumed that by taking 10 samples, all variations for each signal tone have been obtained. The results of these 10 samples were 10 feature extraction results for each tone. Furthermore, the 10 feature extraction results were averaged as follows: 𝑅𝑇 = 1 10 ∑10 𝑖=1 𝑍𝑖 (3) where vector {Zi | 1 ≤ i ≤ 10} is the 10 results of feature extraction, and vector {RT | T = C, D, E, F, G, A, B, and C'} is a vector of eight tones stored in a tone database. As a note, a tone database is generated from a value of sampling frequency, a value of frame blocking length, and a value of segment length. Figure 4. Block diagram of tone feature extraction TELKOMNIKA Vol. 17, No. 1, February 2019: 253-260

(140)  257 ISSN: 1693-6930 TELKOMNIKA 2.2. Test Tones and Recognition Rate Test tones were used to examine the developed tone recognition system. The developed tone recognition system was tested using 160 tones for each musical instrument, each sampling frequency, each frame blocking length, and each segment length. Tones come from eight tones (C, D, E, F, G, A, B, and C), where each of these tones was recorded 20 times. In order to measure the performance of the developed tone recognition system, we used the recognition rate formula as follows. 𝑅𝑒𝑐𝑜𝑔𝑛𝑖𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑟𝑒𝑐𝑜𝑔𝑛𝑖𝑧𝑒𝑑 𝑡𝑜𝑛𝑒𝑠 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑒𝑠𝑡 𝑡𝑜𝑛𝑒𝑠 × 100% (4) 3. Results and Analysis The developed tone recognition system as shown in Figure 2, was used to test the effect of sampling frequency of the tone recognition system. The results of these tests are shown in Tables 1, 2 and 3, each of which is the result of pianica, flute, and bellyra, respectively. As a note, based on Figure 1, bellyra, flute, and pianica tones have one, a few, and many significant local peaks in the DFT domain, respectively. Tables 1 and 2 indicate that from a sampling rate 5000 Hz down to 312 Hz, there is a little influence on the recognition rate, since it is reduced in the range of 5%. However, Table 3 indicates that from a sampling rate 5000 Hz down to 312 Hz, there is no influence on the recognition rate. As a note, the highest frequency components of bellyra, flute, and pianica are 2109 Hz, 1602 Hz, and 2100 Hz, respectively. Therefore, based on these highest frequency components, (1), and also Tables 1, 2 and 3, the sampling frequency of 5000 Hz follows the Shannon sampling theorem. Starting from a sampling frequency of 2500 Hz and below, the sampling frequency deviates from the Shannon sampling theorem. Table 1. Test Results of Bellyra Musical Instrument, in Various Combinations of Sampling Frequency, Frame Blocking Length, and Segment Length. Results Shown: Recognition Rate (%) Sampling frequency (Hz) 5000 2500 1250 625 312 156 Frame blocking length (points) 16 32 64 128 16 32 64 128 16 32 64 128 16 32 64 128 16 32 64 128 16 32 64 128 1 98.75 99.38 100 100 98.13 98.75 98.75 98.75 90.63 92.50 96.88 98.75 82.50 96.88 98.75 98.75 93.13 97.50 98.75 98.75 82.50 91.25 91.88 93.25 2 91.88 98.75 100 100 86.88 98.75 98.75 98.75 89.38 91.88 94.38 97.50 73.13 91.88 96.25 98.75 75.00 96.25 98.75 98.75 78.13 90.00 91.25 91.25 4 44.38 78.13 98.75 100 56.25 68.75 92.50 98.75 66.25 90.00 92.50 96.25 65.00 85.00 95.63 98.75 46.25 94.38 96.25 98.50 51.25 68.75 83.75 86.88 Segment length (points) 8 12.50 42.50 80.63 81.88 12.50 52.50 72.50 90.63 12.50 68.25 91.25 96.25 12.50 60.00 86.25 97.50 12.50 48.75 90.00 96.25 12.50 48.75 62.50 80.00 16 – 12.50 37.50 71.88 – 12.50 40.00 80.63 – 12.50 65.00 90.00 – 12.50 59.38 70.63 – 12.50 55.00 87.50 – 12.50 46.88 53.75 32 – – 12.50 37.50 – – 12.50 34.38 – – 12.50 52.50 – – 12.50 39.38 – – 12.50 47.50 – – 12.50 36.25 64 – – – 12.50 – – – 12.50 – – – 12.50 – – – 12.50 – – – 12.50 – – – 12.50 The influence of sampling frequency on tone recognition of musical... (Linggo Sumarno)

(141) 258  ISSN: 1693-6930 Table 2. Test Results of Flute Musical Instrument, in Various Combinations of Sampling Frequency,Frame Blocking Length, and Segment Length. Results Shown: Recognition Rate (%) Sampling frequency (Hz) 5000 2500 1250 625 312 156 Frame blocking length (points) 16 32 64 128 16 32 64 128 16 32 64 128 16 32 64 128 16 32 64 128 16 32 64 128 1 85.00 97.50 100 100 94.37 97.50 100 100 97.50 100 100 100 86.88 95.63 99.38 100 93.75 96.88 98.75 98.75 90.00 91.25 93.75 93.75 2 83.75 96.88 100 100 93.13 97.50 100 100 88.75 100 100 100 64.38 96.88 97.50 100 85.00 95.63 97.50 98.75 88.13 90.00 92.50 93.75 4 55.00 94.38 97.50 100 49.37 80.00 98.75 100 26.88 95.63 100 100 23.75 66.25 95.00 100 63.13 85.63 87.50 98.75 38.75 81.25 88.75 88.125 Segment length (points) 8 12.50 46.25 91.25 95..63 12.50 45.63 79.38 96.88 12.50 45.00 93.75 95.00 12.50 30.00 61.88 90.63 12.50 63.13 72.50 87.50 12.50 47.50 78.13 85.00 16 – 12.50 43.75 83.13 – 12.50 31.25 73.75 – 12.50 38.13 85.00 – 12.50 36.25 61.25 – 12.50 58.75 74.38 – 12.50 50.63 67.50 32 – – 12.50 36.88 – – 12.50 23.75 – – 12.50 48.75 – – 12.50 45.63 – – 12.50 70.63 – – 12.50 50.00 64 – – – 12.50 – – – 12.50 – – – 12.50 – – – 12.50 – – – 12.50 – – – 12.50 Table 3. Test Results of Pianica Musical Instrument, in Various Combinations of Sampling Frequency, Frame Blocking Length, and Segment Length. Results Shown: Recognition Rate (%) Sampling frequency (Hz) 5000 2500 1250 625 312 156 Frame blocking length (points) 16 32 64 128 16 32 64 128 16 32 64 128 16 32 64 128 16 32 64 128 16 32 64 128 1 98.13 100 100 100 75.00 100 100 100 93.75 100 100 100 92.50 100 100 100 74.38 100 100 100 88.13 100 100 100 2 92.50 99.38 100 100 39.37 100 100 100 81.88 100 100 100 64.38 100 100 100 70.00 100 100 100 61.88 100 100 100 4 52.50 93.13 100 100 22.50 78.13 100 100 40.00 97.50 100 100 34.38 90.63 100 100 45.00 76.88 100 100 41.25 71.88 100 100 Segment length (points) 8 12.50 49.37 91.88 100 12.50 36.88 93.75 100 12.50 63.13 99.38 100 12.50 50.00 98.13 100 12.50 49.38 97.50 100 12.50 34.38 89.38 99.38 16 – 12.50 61.25 94.38 – 12.50 46.25 94.38 – 12.50 72.50 98.75 – 12.50 53.13 95.63 – 12.50 50.00 96.25 – 12.50 51.88 95.00 32 – – 12.50 61.25 – – 12.50 37.50 – – 12.50 80.63 – – 12.50 56.88 – – 12.50 50.00 – – 12.50 56.25 64 – – – 12.50 – – – 12.50 – – – 12.50 – – – 12.50 – – – 12.50 – – – 12.50 From the point of view of signal reconstruction, in general, when the sampling frequency decreases, the aliasing area (which is a high frequency region) increases. Therefore, the effect obtained from decreasing the sampling frequency is low pass filtering by decreasing the cutoff frequency. By the same reasoning, from the point of view of signal sampling, if the sampling TELKOMNIKA Vol. 17, No. 1, February 2019: 253-260

(142) TELKOMNIKA ISSN: 1693-6930  259 frequency decreases, low pass filtering (with a decrease in the cutoff frequency) will also appear. The effect is that the number of significant frequency components that can be obtained will be fewer. Therefore, if the number of significant frequency components (which in this case is represented by a number of significant local peaks in the DFT domain) of the signal becomes fewer, the recognition process will be more sensitive, when the frequency of sampling decreases. This is caused by the number of significant frequency components that are used to distinguish a tone with other tones becoming fewer. This incident will decrease the recognition rate. From the point of view of data size, based on Tables 1 and 2, a decrease in the sampling frequency of 93.76% (from 5000 Hz down to 312 Hz) will reduce data size by 93.76%. However, a decrease in this data size will only cause a decrease in the recognition rate of less than 5%. This indicates that the tone recognition system is not sensitive to sampling frequencies that do not follow the Shannon sampling theorem. 4. Conclusion The conducted research aims to explore if there was a lowest sampling frequency that did not follow the Shannon sampling theorem that could be used for the tone recognition system. For this purpose, we used the tone recognition system using segment averaging for feature extraction and template matching for classification. Based on our experiments, until the sampling frequency is as low as 312 Hz, if the tone recognition system was used to recognize the tones that have one and a few significant local peaks in the DFT domain (such as bellyra and flute tones), the sampling frequency has a little influence on the recognition rate, since it reduced the recognition rate in the range of 5%. However, if the tone recognition was used to recognize the tones that have many significant local peaks in the DFT domain (such as pianica tones), that sampling frequency has no influence on the recognition rate. If the reduced recognition rate (in the range of 5%) could be accepted, the sampling frequency as low as 312 Hz could be used for the musical instruments tone recognition. In other words, if that kind of reduced recognition rate could be accepted, the sampling frequency does not need to follow the Shannon sampling theorem when recording musical instrument tones. For further research, the exploration of sampling rates that do not meet the Shannon sampling theorem can be conducted for other tone recognition systems. In this case, the tone recognition systems could use a different approach of feature extraction (not segment averaging), and a different approach of classification (not template matching). Acknowledgement This work has been supported by the Institute of Research and Community Services of Sanata Dharma University, Yogyakarta. References [1] [2] [3] [4] [5] [6] Tan L, Jiang J. Digital Signal Processing: Fundamentals and Applications 2 nd Ed. Elsevier Inc. Oxford. 2013: 15-56. Cheveigné A, Kawahara H. YIN, A Fundamental Frequency Estimator for Speech and Music. The Journal of the Acoustical Society of America. 2002: 111-117. McLeod P, Wyvill G. A Smarter Way to Find Pitch. Proceedings of the International Computer Music Conference (ICMC’05). Barcelona. 2005. Tadokoro Y, Yamaguchi M. Pitch Estimation of Polyphony Based On Controlling Delays of Comb Filters for Transcription. Proceedings of 11th DSP Workshop. Taos Ski Valley, New Mexico. 2004: 371-375. Tadokoro Y, Saito T, Suga Y, Natsui M. Pitch Estimation for Musical Sound Including Percussion Sound Using Comb Filters and Autocorrelation Function. Proceedings of the 8th WSEAS International Conference on Acoustics & Music: Theory & Applications. Vancouver. 2007: 13-17. Noll M. Pitch Determination of Human Speech by the Harmonic Product Spectrum, the Harmonic Sum Spectrum and a Maximum Likelihood Estimate. Proceedings of the Symposium on Computer Processing in Communications. Brooklyn, New York. 1970; 19: 779-797. The influence of sampling frequency on tone recognition of musical... (Linggo Sumarno)

(143) 260  [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] ISSN: 1693-6930 Brown JC, Puckette MS. A High Resolution Fundamental Frequency Determination based on Phase Changes of the Fourier Transform. The Journal of the Acoustical Society of America. 1993; 94(2): 662-667. Mitre A, Marcelo Q, Régis F. Accurate and Efficient Fundamental Frequency Determination from Precise Partial Estimates. Proceedings of the 4th AES Brazil Conference. Brazil. 2006: 113-118. Pertusa A, Inesta JM. Multiple Fundamental Frequency Estimation using Gaussian Smoothness. Proceedings of IEEE International Conference on Audio, Speech, and Signal Processing (ICASSP 2008). Las Vegas. 2008: 105–108. Yeh C, Robel A, Rodet X. Multiple Fundamental Frequency Estimation and Polyphony Inference of Polyphonic Music Signals. IEEE Transactions on Audio, Speech, and Language Processing. 2010; 18(6):1116–1126. Duan Z, Pardo B, Zhang C. Multiple Fundamental Frequency Estimation by Modeling Spectral Peaks and Non-peak Regions. IEEE Transactions on Audio, Speech, and Language Processing. 2010; 18 (8):2121–2133. Smaragdis P, Brown JC. Non-negative Matrix Factorization for Polyphonic Music Transcription. Proceedings of IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA 2003). New Palz, New York. 2003: 177–180. Bertin N, Badeau R, Richard G. Blind Signal Decompositions for Automatic Transcription of Polyphonic Music: NMF and K-SVD on the Benchmark. Proceedings of IEEE International Conferenece on Acoustics, Speech and Signal Processing (ICASSP 2007). Honolulu, Hawaii. 2007: I-65 – I-68. Woojay J, Changxue M, Yan C. An Efficient Signal-matching Approach to Melody Indexing and Search using Continuous Pitch Contours and Wavelets. Proceedings of the 10th International Society for Music Information Retrieval Conference (ISMIR 2009). Kobe. 2009: 681–686. Tjahyanto A, Suprapto YK, Wulandari DP, Spectral-based Features Ranking for Gamelan Instruments Identification using Filter Techniques. TELKOMNIKA Telecommunication Computing Electronics and Control. 2013; 11(1): 95-106. O’Hanlon K, Nagano H, Keriven N, Plumbley MD. Non-negative group sparsity with subspace note modelling for polyphonic transcription. IEEE/ACM Transactions on Audio, Speech and Language Processing (TASLP). 2016; 24(3): 530–542. Sumarno L. On The Performance of Segment Averaging of Discrete Cosine Transform Coefficients on Musical Instruments Tone Recognition. ARPN Journal of Engineering and Applied Sciences. 2016; 11(9): 5644-5649. Sumarno L, Iswanjono. Feature Extraction of Musical Instrument Tones using FFT and Segment Averaging. TELKOMNIKA Telecommunicatin Computing Electronics and Control. 2017; 15(3): 1280-1289. Meseguer NA. Speech Analysis for Automatic Speech Recognition. MSc Thesis. NTNU. Trondheim; 2009: 4-25. Harris FJ. On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform. Proceedings of the IEEE. 1978; 66(1): 51-83. Jenkins WK. Fourier Methods for Signal Analysis and Processing. In: Madisetti VK. Editor. The Digital Signal Processing Handbook 2nd Ed: Digital Signal Processing Fundamentals. CRC Press. Boca Raton. 2010: 1-1 - 1-29. Setiawan YR. Numbers Speech Recognition using Fast Fourier Transform and Cosine Similarity (in Indonesian). Undergraduate Thesis. Sanata Dharma University. Yogyakarta; 2015: 66-70. Jain AK, Duin, RPW, Mao J. Statistical Pattern Recognition: A Review. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2000; 22(1): 4-37. Theodoridis S, Koutroumbas K. Pattern Recognition. 4th Ed. Elsevier Inc. San Diego California. 2009: 481-519. Wilson DR, Martinez TR. Improved Heterogeneous Distance Function. Journal of Artificial Intelligence Research. 1997; 6: 1-34. TELKOMNIKA Vol. 17, No. 1, February 2019: 253-260

(144)

Dokumen baru

Tags

Dokumen yang terkait

The influence of the sampling dots on th
0
4
5
The influence of lipoprotein(a) on fibrinolytic activity
0
2
5
On the performance of segment averaging of Discrete Cosine Transform coefficients on musical instruments tone recognition.
0
0
6
The analysis of cable forces based on natural frequency
0
0
9
The influence of karma on the struggle for survival of poor people as seen in dominique lapierre`s the city of joy - USD Repository
0
0
104
A study on the development recognition of english derivational suffixes in senior high school - USD Repository
0
0
103
The influence of Montgomery`s sexual deviation on Nicolette`s personality development as seen in Gwen Hunter`s betrayal - USD Repository
0
0
125
The influence of intrinsic motivation and learning styles on the classroom performance of extensive reading II students - USD Repository
0
0
121
The influence of childhood experiences on the main character`s personality in Jean Rhys`s wide sargasso sea - USD Repository
0
0
65
The influence of minor characters on lilly`s personality development in sue monk kidd`s the mermaid chair - USD Repository
0
0
95
The influence of environment on Luke`s personality changes in Grisham`s a painted house - USD Repository
0
0
91
The influence of parents` abuse on Anson`s personality development as seen in Dean Koontz`s The Husband - USD Repository
0
0
105
The influence of American dream on Willy Loman in Arthur Miller`s Death of a Salesman - USD Repository
0
0
67
The influence of voodoo beliefs on Zarite`s survival from slavery in Allende`s Island Beneath the Sea - USD Repository
0
0
68
The influence of setting on Orchid`s character changes in Anchee Min`s Empress Orchid - USD Repository
0
0
68
Show more