Signal Processing and Linear Systems-B.P.Lathi copy

For example and so on 745 3 t he p arameter e controls

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Unformatted text preview: jO.9978 jO.7143 jO.9001 jO.4586 jO.1580 - 0.0170 ± jO.9935 - 0.0767 ± jO. 7113 - 0.0493 ± jO.8962 - 0.0967 ± jO.4567 - 0.1072 ± jO.1574 - 1.9652 1 1 2 3 4 5 6 7 1 2 3 4 5 6 7 at a2 a3 a4 as 2.8627752 0.5 d b ripple 1.5162026 1.4256245 (i' = 0.5) 0.7156938 1.5348954 1.2529130 0.3790506 1.0254553 1.7168662 1.1973856 0.1789234 0.7525181 1.3095747 1.9373675 1.1724909 0.0947626 0.4323669 1.1718613 1.5897635 2.1718446 1.1591761 0.0447309 0.2820722 0.7556511 1.6479029 1.8694079 2.4126510 1.9652267 1.1025103 0.4913067 0.2756276 0.1228267 0.0689069 0.0307066 2 3 4 5 6 7 1.3075603 0.8230604 0.3268901 0.2057651 0.0817225 0.0514413 0.0204228 1 2 3 4 5 6 7 1.0023773 0.7079478 0.2505943 0.1769869 0.0626391 0.0442467 0.0156621 - 0.7128 ± j l.0040 - 0.5489 3 ao - 2.8628 2 n - 0.6265 - 0.3132 ± j l.0219 - 0.4942 - 0.2471 4 - 0.1754 - 0.4233 ± j 1.0163 ± jO.4209 5 a6 1.1512176 1 d b ripple (i' = 1) 1.0977343 1.2384092 0.9883412 0.7426194 1.4539248 0.9528114 0.5805342 0.9743961 1.6888160 0.9368201 0.3070808 0.9393461 1.2021409 1.9308256 0.9282510 0.2136712 0.5486192 1.3575440 1.4287930 2.1760778 0.8038164 1.0221903 0.5167981 0.4593491 0.2102706 0.1660920 0.9231228 2 d b ripple (i' = 2) 0.7378216 1.2564819 0.7162150 0.6934770 1.4995433 0.7064606 0.7714618 0.8670149 1.7458587 0.7012257 0.3825056 1.1444390 1.0392203 1.9935272 0.6448996 0.9283480 0.5972404 0.4047679 1.1691176 0.5815799 0.4079421 0.5488626 1.4149874 0.5744296 0.1634299 6990977 6906098 1.6628481 0.1461530 0.3000167 1.0518448 0.8314411 0.6978929 10 3 d b ripple (i' = 3) 0.5706979 1.9115507 0.5684201 jO.9868 jO.8365 jO.5590 jO.1962 ± jO.9896 ± jO.8702 ± jO.6459 ± jO.3437 - 0.0138 ± jO.9915 - 0.0401 ± jO.8945 - 0.0625 ± jO.7099 - 0.0788 ± jO.4558 - 0.0873 ± jO.1570 7 F requency R esponse and A nalog F ilters 5 20 7 .6 C hebyshev F ilters 521 From Eq. (7.50) x 0.794 + ----"'-""'------l n e = ~ s inh -1(1.3077) 3 Now from Eq. (7.51), we have 81 = - 0.1844 - 0.1844 - jO.9231. T herefore ?-(8) = (8 + 0.3689)(8 s3 0.1 = 0.3610 + jO.9231, 82 = - 0.3689, a nd 83 Kn + 0.1844 + jO.9231)(8 + 0.1844 - Kn + 0.73788 2 + 1.02228 + 0.3269 jO.9231) 0.3269 83 + 0.73788 2 + 1.02228 + 0.3269 which confirms t he e arlier result. o F ig. 7 .26 = .!. sinh - 1 ~ 10 16.5 A mplitude response o f t he lowpass Chebyshev filter in Example 7.7. S tep 3 : D etermining H (8) Recall t hat W p = 1 for t he n ormalized transfer function. For W p = 10, t he desired transfer function H (s) c an b e o btained from t he n ormalized transfer function ' It (8) by replacing 8 w ith s/wp = 8 /10. Therefore • E xample 7 .7 Design a Chebyshev lowpass filter t o s atisfy t he following criteria (Fig. 7.26): T he r atio f :S 2 dB over a passband 0 :S w :S 10 (wp = 10). T he s topband gain 6 . :S - 20 d B f or w > 16.5 (w. = 16.5). Observe t hat t he specifications are t he s ame as those in Example 7.6, except for t he t ransition b and. Here t he t ransition b and is from 10 t o 16.5, whereas in Example 7.6 i t is 10 t o 20. D espite t his stringent requirement, we shall find t hat Chebyshev requires a lower-order filter t han t he B utterworth filt...
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This note was uploaded on 04/14/2013 for the course ENG 350 taught by Professor Bayliss during the Spring '13 term at Northwestern.

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