lecture 29 - See me before this Friday if you Test2 score...

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1 Summary of Lecture #29 11/01/2010 Filter realization based on brick wall specification Find n and ϖ c from ϖ p , ϖ 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 ϖ p or f p : Pass band edge freq. ϖ s or f s : Stop band edge freq. Pass band Stop band Transmission Attenuation A( ϖ ) in dB = - 20 log 10 (|H(j ϖ )|) 4 Brick wall specification for LP filters ϖ p : Pass band edge frequency A max : Max. atten. (loss) |H(j ϖ ) | in the pass band ϖ s : Stop band edge frequency A min : Min. atten. (loss) |H(j ϖ )| in the stop band Filter order n ? Cutoff frequecny ϖ c ? A max ϖ p ϖ s A min 5 Brick wall specification If ϖ p and ϖ 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 ϖ p and ϖ s are close, use Eq. (19.5) and (19.6) to determine the filter order n and ϖ c . ϖ p ϖ 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 ϖ + = ϖ + + = 6 2 3 1 1 | ) j ( H | , 1 s 2 s 2 s 1 ) s ( H ϖ + = ϖ + + + = 2 1 1 | ) j ( H | , 1 s 1 ) s ( H ϖ + = ϖ + = 7 n -th order Butterworth LP filters H(s) with cutoff frequency ϖ c of 1 rad/s and impedance level of 1 Butterworth mag. response with ϖ c = 1 rad/s is In terms of the cutoff frequency
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