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by: Eloy Ferry


Eloy Ferry
GPA 3.84

John Gowdy

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John Gowdy
Class Notes
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This 18 page Class Notes was uploaded by Eloy Ferry on Saturday September 26, 2015. The Class Notes belongs to E C E 467 at Clemson University taught by John Gowdy in Fall. Since its upload, it has received 56 views. For similar materials see /class/214305/e-c-e-467-clemson-university in ELECTRICAL AND COMPUTER ENGINEERING at Clemson University.

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Date Created: 09/26/15
ECE 71 467 667 Introduction to Digital Signal Processing LECTURE22 Example Design highpass filter using windowinq method with Kaiser windowthat extends over 0 s n s M Ideal highpass filter Hej 71 0G Dc 39 7139 0 For linear phase to permit causality I 00 5 s 1006 H e DM 917mc S 03lt 7t Recall for ideal lowpass filter with linear phase Hej 1 2 lfiCll39i T467567 Introduction to Digital Signal Processing To get high39gass filter minus 7E 71 l I Dc Dc sin quotnM sinw M 2 2 hnpnl M 39I 1 9 r t 2 n n l 2 2 a C n M 7 3 2 Sinnn M M me If M is even then M Z o for i Z NOW E For FIR approximation MPY by Kaiser window that ranges from OSnSM Will get an He quothav39ing the following form Hem 15 X 39 vl V quot 18 5 A 39V 139 5 TC 03 9 m l M CDC Let 5 021 08 357t and up 5n ECIL 14671667 nimcluctiun 3 Digital Sign3 chewing 357t57t Set DC w 4257r A 2010910 5 2mogo021 3355 Since 213 A lt 50 4 B 58423355 21 078863355 21 A A 26 And estimate of M is A 2 3355 3 22355n 35n W A0 237 gt 24 M is even Mn is Symmetric Type FIR lter 39EZquot 39quot quotI7 lfy397367 inl mduc am tn D39Egirz gnnl Pmomdng Sec 75 Examples of FR Filter Design by the Kaiser Window Method 08 06 39 04 o2 quot Amp mde 10 20 30 Sample number n a dB 400 39 x 0 02 04 067 08 tr P dian frequency w b quot 004 002 gt L JV VVV Amplitude o 002 004 l J l l 0 02 CAR 0611 08 tr Radian frequency w c Figure 734 Response functions for type I FIR highpass lter a Impulse response M u 24 b Log magnitude c Approximation error 4 1394 7it x7 infrnduminn in 39i39iigimi Qignni Prni fm39ing Since actual 5 0213 gt 021 design spec try increasing M to 25 Consider M 25 odd Mgt Type II Filter Has a gel at z 1 gt not good for high pass gt Consider M 26 Type I again OK 06 J u Fitter Design Techniques 04 02 Amplitude 1 A T 702 I 04 06 k 0 5 1039 15 20 2539 Sampls number n a 20 m 1 U 02 3904 06 087 1 Egd39lun frequency w b 39 10 08 06 2 E 39 g 04 E lt 02 O W O2 39 I I I 02 04 06 08 w Radim lrcquancy tw c3 131C113 quotE 1fr7667 Introduction to Diem S icm Pxmclts nsz Chap 7 Figure 735 Response functions for type II FIR highpuss lter a Impulse tesponsc M a 25 bLog magnitude c Approxima ion error 39I 39F Q F quotI39d f l r 39 l nrmdnr linn m 39Dtgim Sigma inesdng Generalized multi Band Filter G15 e 32 A3n A j Vquotquot Anax G4 iv v 41453 A G3 vvv For linear phase filter Low pass lter hmpm ak where G 0 k1 n n Nmb1 2 and where Nmb no of bands between 0 and rt For the above filter Nmb 4 and the 4 lowpass filters represented by the above sum are rG1 G2532 Tim quotFan67 introduction to Digital Signal Processing O 03 quotG4 G5 2 02 defihggaso 0 1t To determine A for the Kaiser window method Let or minl v m smallest 5 on either side of transition frequency mi and U 5 min iGJ1 Gii This normalizes the ripple size by the size of the magnitude change at transition frequency 1 39 i12Nmb Also in finding M for the Kaiser window use Am 39 j12N Gi1 Aw min 1 mb Example Design of MultiBand Digital Filter Using Kaiser Window Method Prgblem spegificatignsz 01 41 Am1057c 81 1 611 032 67 A031051t 82 05 G2 6 03 815 Aw3051t 53 05 GB O 04 113 Aw405n 84 05 G4 4 Step 1 Calculate 0ci 393 a1 min8182 05 a2 min8283 05 a3 min5354 05 glep 2 Calculate 639 0 1 3905 125 l lG2 G1 I 4 2 3905 0833 L min 0833 539 IG3 G2 6 3 3905 125 G4 G3 I 4 Step 3 Calculate Aco39 Aw I 051 2 125 l IG2 G1 I 4 39 A 2 3905 08331 lmin 08337 Aw39 IG3 G2 I 6 Acog 2 051 239 125 IG4 433 I 4 39 Step 4 Calculate Kaiser window parameters using 539 and 130339 A 20og10839 21583 3 5842A 21 4 O7886A 21 5170 A 8 227 a 24 2285Aw39 Use M 24 instead of M 23 since Type II filter will not work when desired response at a 1 is not 0 4 sin wk n hmp n Gk1 n72 l l nn 2 sin4nn 1 2 sin61tn 1 2 112n 12 6 042 I4sin8un 12l4sinnn 12 n 7512 1n 12 n 12 M 2 10 The candidate FIR filter is then formed by multiplying hmpm by the Kaiser window function wkm which extends fromn OtonM 24 hn hmpnwkn where 12 IO517O Z l 5170 LEW wkn 11 v x u v tiii i il q a u II a v a o a p u 0 IE a Nrn sa q urowz i await 39a a a a ww wamumg ms 5 i o w 6 lQOiDtampiUO 4 t s a tiquot aK u n J twvm Hri lrbvlv sop 5 a a o as a v A n U eat ilht e p 0 a a v a ere i 9 s w v a k u a gaiev gaub aeha w w 9 Ir 9 a a a 9 a 1 h g a l f 9 amp i tdiaa Qat e bi 399 a o a 7 w 2 a 4 I w a w y 4 a a a w a 5 399 ti e 2 a WI r uea i It c a bi ciiidf il v mai A l DI rmt viv wa 9053 q I l a 96 119 If a qaiaeig s a wwmtqvvyv c rawievay o o at m w 3 4 Ir 1 i w c i amp t a uauw i a QAV v v vv rvddbnqvw v v 6040 3tt lbtv 4v sltua 3 xn vulltv vw o uvv v41 o 1 1 u u v t a 395 y a v gt7 1 a o n s y a v wotwomwsau maaya a y4 t r o a z u u o w 1 v 9 1 v o a u w w s v 39 o i 0t5m 9wtvitrvbviv wlqvbv wi lltillivv vdl v 1 1 o w a a v n wavywt w neuyivuwvnwswsrsrXtrr o 5 399 b39a auxvvvwov39 wymvthvr 1 No oiiv m 1 km 3 Kt Wmhw wmwwm Matlab m File for Kaiser window example with M 50 MS wcl4pi ch6pi wc38pi wc4pi alphaMZ n 1M mn alpha Fclwc1pi Fc2chpi fc3wc3pi fc4wc4pi hdl4fc1sincfc1m hdZ6chsincFcZm hd3 4Fc3sincfc3m hd44fc4sincFc4m beta517 wkaiCkaiserCMlbeta39 hhChdlwkaihd2wkaihd3wkaihd4wkai a1 Hwfreqzhha HHl15 139 ww115 139 magabsCH wlwpi plotw1mag grid on K


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