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Unformatted text preview: 1 Summary of Lecture #29 11/01/2010 Filter realization based on brick wall specification Find n and c from p , s , A max and A min . Three examples 2 See me before this Friday (11/05/2010) if you Test2 score is less than 24. 3 Low pass filters p or f p : Pass band edge freq. s or f s : Stop band edge freq. Pass band Stop band Transmission Attenuation A( ) in dB = - 20 log 10 (|H(j )|) 4 Brick wall specification for LP filters p : Pass band edge frequency A max : Max. atten. (loss) |H(j ) | in the pass band s : Stop band edge frequency A min : Min. atten. (loss) |H(j )| in the stop band Filter order n ? Cutoff frequecny c ? A max p s A min 5 Brick wall specification If p and s are far apart, use the roll off rate to determine the filter order. n = ==1,-- 20 dB /dec . n = == 2,- 40 dB /dec. n = == 3,- 60 dB /dec. If p and s are close, use Eq. (19.5) and (19.6) to determine the filter order n and c . p s 6 Normalized Butterworth transfer functions ( see Table 19.1 for n =1, 2, 3, 4 and 5, p. 1042) For n = 1 For n = 2 For n = 3 4 2 1 1 | ) j ( H | , 1 s 2 s 1 ) s ( H + = + + = 6 2 3 1 1 | ) j ( H | , 1 s 2 s 2 s 1 ) s ( H + = + + + = 2 1 1 | ) j ( H | , 1 s 1 ) s ( H + = + = 7 n-th order Butterworth LP filters H(s) with cutoff frequency c of 1 rad/s and impedance level of 1 Butterworth mag. response Butterworth mag....
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- Spring '06