Ch4-2up

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Unformatted text preview: QB8 @r ¬y V6 3 6 I64 a 6 4R 3@ QC CA 6C P7 UA 5 3@ 38 @R UA y Q Q 3D 64 6 A A 4 65 CD 6C 7D S6 @ 0 3 3 W 65 98 78 r 6D 4@ 8E 8 ER UAC A 3 P8 4 @ 6 E5 3 Q I6 Q 38 D 7 A 4@ A 4 V3 C4 V @5 † £B `C 6 F4 A@ 3 8@ 6H 64 A 4@ F ‡ Ì 3 @ g 4 65 3 8E U76 @ 4 3 6@ E 6 C 68 H @ 6 3C 3D A A 4@ B 4@ U 8 A 4@ A4 6 8 ED 64 T E4 3@ 35 V B@ ` E 6 ER 9Q 3 A I3 78 S FE AC H AC A a 3B 4 @ 8H @ 3 3@ Q H EC 3 4 65 6 2 π 5000 8H @ 64 E 3 CH E I 38 @R E B4 B4 4 8 RY 64 6 A 4@ 3 E 9R EC wv T i 5 I @a 4 938 @ CW 7D6 5 3 @H @ 64 C4 CD @5 CH 6C A 7 3@ 4 D 67 H E@ 4 E8 8 6 H 3@ P 4@ E R 6C 6 @R 3D @ 5 U8 6” I DH @ 6H E “ @R 6H EC 4 C 4@ E IP jωT ) 8 CD C E A 6 P8 4 @ 678 4 5 W T6 65 6 E@ 6R 3 78 64 96 P 4@ E 4 6 E8 @H H 6 GAC 4 @ C V ABC @ Q 6 6 3 E CD B E 6 P ` 3 3 8 E H E4 6 3@ AC 4 @ 3 6 a 6 W5 F AC 4 @ V AC 4 @ B 3 3 `D QB8 r@ D S6 AB8 r U 67 H 3 V6 8 8 W @ 5 68 @ 6 @R 6 5 C † 4 678 7 84 C 4 A4 B d 4 EC 65 6 65 8 3 8 4P 6 6 A T 6 @ P8 3 E R E4 A a 4 E P A4 P AC 4 @ GAC 4 @ “C @ V 3 C7 5 @ 6 ER 6T U4 6 6 3 4 65 CD E 3 C 6 64 Q@ 3 H 7 6 AC 6 GH E 68 ‡ CD 4 R 678 V C 6 6 I64 3 E4 A 4@ • E 3 3 @ 6H E –† U G ir ABC I X(e B7 g 6C I 88 8W 65 UAC R AC 4 @ i 3 3 E QB @T S SABC 8 R 678 E 3 R P 4@ Ar ˆ C à Äi 9Q @ 6 S3 i g F a Ì F 3R @ Q ÖØ g QB8 @r 6 3 8Y V 6 6 4R F Da i E 3 3B 4 @ V † ‡ H X(jω) E F 3Q @ E 4 S6 5 4 BA R BC `D A5 R 8H Aa P @ 4 A 3 @H A 4@ 3 PBC wEC IA 4 D D8 8 AB 4 6C 5 7D @A x g 6 D E@ CR E wy @A g 6 A Ea C E @R I8 6 6C iT E P7 W ˆ9 A @ gg E 3 H 4 65 A ÌÙ ' @ 6H 4 65 i R 38 @  FFg A 67 4 A E8 R A4 †i £ y d ‚ p€ ˆ @A x g i VÜ V `3 † ‡ SP † wv g ÃÄi CÌ ˆ @A x g Ãi QB8 @r V6 Ö3 @ E 986 T 6 † d p P B g  Ì' ” SP8 FÖi ' E  U x(n) Q à ‘ AC 6 a E sin[ π (t−nT)/T] π (t−nT)/T 4 à Î P7 9E 5 DTFT 3 @R Q E 8D c X ( jω ) = { H X(e jθ) j T X(e θ ) , ω < π T 0, else { £– ÐÏ l h gÒ Ñ c z { X (j ω) 3 1 Σ X ( j θ + j 2π k ) cT T T AC 38 D B4 ’ " Σ x(n) 6 à H BC T 6 GH T ˆi a 3 6 i @A g  8 38 A’ 6C 6R 4 EC  c à @ 6Y S F g 6 A 9 AB8 r Fi 68 @ D IP GH A8 4 @ Æ g † £i Fourier transform GH i 4 65 C S `~ aT bP } T Aa P8 6 V ‡ @5 x(n) = x (nT) à F xg iT wy @A g S S B B V V Ã} C DC ˆ C  SD C h| fg h| fg | V g F7i i h F 7i h| g BÌ SD TGH DEC i C D IP GH wv wv g  g B F} 7i hÌ D GH DC wv }F7ig D ~ GH P } 6 ER AC 4 @ 3 V 7C 5 @ ER AC 4 @ 3 7 xc(t) ˜— j kl h i em n 8 c QB8 r@ V6 CD ‡ B 7D 4 V6 V B4 E 3 AC 4 H E SC 1000 678 4@ C 68 H E 7B ” CD 8H 7 @C A 6 6 I64 4 P 4@ E 5 6 ˆ e4 UA R g I7 C EC 6@ a 4 S6 5 8Y R ”ã “ ö QB8 r@ •ë ó AC C 8 à W 38 B4 A 4@ f j gÏ C g 68 AB B4 7 B4 P Ñ n Ñ ekg lÒ 4 ˆ ω AC 6C | g à Äi H (jω) eff S 3@ Q AD F xg F 9g G G à Äi r Äi r à Á i F g g ÖØ … g Ï j j em n g Ìx ' i P 4@ ideal interpolator 300 F 9g T G ir ˆ W9 @g h| fg Ea eÒ W B 2” 8 7D 4 RY 64 3 6 I64 P 4@ 678 D ‡ 37 @ Q D –† pD € GH ˜™— ˜ ™— D8 6 à V6 — ˜– H A4 V W ˆ9 A @ gg ÖØ 3 G ir hÌ ABC I 6C • ÌÙ ' Q@ V3 i y (t) c i E g † R ω U‡ i a wv A • 3B 4 @ ÌÙ ' ii wy @A g i V S6 @ iT Ì P @R D 96 @5 W 65 à@ à Ci @ F g ET 3 H 64 H 8Y R A4 64 6 4@ E P E Q 3 6 H 3@ digital filter AC Q UD AC 5 6 EC P7 64 3 @R Q ideal sampler P7 à C 8 P 4 6 I64 67 R %© C 68 o† 8 F C r@ o† p 8 E P 4@ 6CD V A3 R 3@ ‡Î Î 37 @ QB8 @r X (jω) E 64 E 9A T 6 C ‡– Ì à@ D 6 # • ©  à 6C H • • B `DC @ 4 A 3 H F@ A 4@ 3 ABC I A P 4@ 6C V3 R di x (t) c Ö AD Î Ea y Ó A 3 3B 4 @ ‡– “y B @ 6D 8 ·Π4E 8 Î 6H B E C 67 A 4 CD H h AC A‚ 6 3 a 68 g 8 Î ‡ E Î £o 6 EV CD “y D 67 H V H h 7D i 6 @ ” E Q@ V E g † ‡ £o 7 E ¯ °® ¯ † ² QB8 r@ V6 À ‡ ¾ † ‡Î p CD 8à @ T À ¸ˆ ¾8 6 I64 D 8 ST 6D @ ¡ Í P8 8A C 6 6C AW AC C4 3 @ D38 QC 5 B4 7 @ E A P7 V 4 F 3@ A@ 3 U4 3 4 E8 5 4 6 6 P AC E 3 6 DEC 8@ 6H 3@ BD @R C " #! ) 6R 3 Q 6 H A DT Da T 64 6 CW 65 6 ER 6 S @ 4 65 35 3@ A 4@ 3 E BC H ABC A4 I H q67 8 … r § x 6 x 0 9ED 5 t¨ ¬y T y (n) da D/A converter G (jω ) r recon− struction filter y (t) c 8 3 P 64 C ¯ u 6 † à WŒ ± µ´ v ¦¢ SE ü ý • g 0 ¦ )( § B Ö T C4 6C R 6C 3 4 65 (b) (a) 6H P @ E 3C H A 3 QB8 @r V 6 V† ‡ X(j ω ) ‡ π/T π/T’ 4 65 E 3 E AR Q E 3 I4 E@ C 3 D8 H 6 F g G à Äi r  ‚ ƒƒ @ g ‡ x ’„ • ‘ ’ g † D C S P 4 @ F q6 R E UÍ 6 RR C 6 U4 6 8 P7 RY S 86 4 6BC E5 AR CR R 46 w6 EC 6 38 6 84 65 8H 6a A a 3D @ 6 BD 6” a E R q6 3 AC 4 @ P7E A 4@ 3 V3 F A 4@ 7 3 6R F † £ EC @5 i 7D S6 6D 3 V @ Ά Y VX “y E AC 4 @ 6C 3 E 4 E@ C E @R A ‡E Ì ' P7 Ì Ã C 38 @R 7DA 4 Q S6 F  © E  6D 4 @U a q6 46 67 5 6 8 g 9E 5 6 H 6 6 Ì Q3 @ D A@ à • @H eÎ  © t CD i Î  C ÎS 8H @ CD @ • 74 6 V‡ I64 6 I @ 6R @R E 37 @ 4 BC F 3AC @ D I6R UA 5 A 968 6H F 6 4@ 5 B H ÐÏ l h gÒ Ñ ˜— j kl h i em n 8 E C6 4 S@ ˜™— ˜ ‹lÒ D 74 SE @ D h Ï Ñ RR e Ï ih C A5 υ 6 3 A4 m j efgÒ † 4 CP @ 6 h eÑ … j H QH 68 E 3 8 6D 6a B `D E I8 A 4@ m 4 67 5 C EC I ET 3 6 P A 3@ Q ER 8Y 6 4R U W 65 6 UÎ 8 Aa Ãx Î t eÎ  0 V ‡– H 8Y V G6C 4 R 64 H 3@ C E @R 3@ 6R 68 4 R B8 ` 6@ P S C 8 7 7 D7 A 4 8 Y ECC E 8 S R P7 64 I F 3A 5 6H S@ 6 98 C C6 g E 38 @R A8 4 RR H 3E T 4Q E P Q@ 6D 65 E P7 3 6 H 9D B S6 E H 6C 4 4 CR QH A 6 @ 3 @R @6 T @ 6C E QD E VE CR 83 @ E 4 4 8 6H E@ 4 C36 5 3Q @ B V 6C U CE V E` Q3 @ @5 ECD 8 X R E 6 A H P7 @ 64 C “y 8 32 8 E ET Ar 6H A 6 R C3 A 3 P7 P H 6 H B H q6 6 7 D7 RR E 7 @ 4 I A 4 P @R P7E DE7 E4 – 4@ F V X E T 6 4@ A 4@ S 3 UA R “ y 3 H AR I7 T 6H E C 8 H EC W Q H 3E 6 5 68 Aa...
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This note was uploaded on 01/15/2014 for the course ECE 600 taught by Professor Clymer,b during the Winter '08 term at Ohio State.

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