Dig Sig Proc&Analys
Dig Sig Proc&Analys EECS 451
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This 2 page Class Notes was uploaded by Ophelia Ritchie on Thursday October 29, 2015. The Class Notes belongs to EECS 451 at University of Michigan taught by Andrew Yagle in Fall. Since its upload, it has received 9 views. For similar materials see /class/231528/eecs-451-university-of-michigan in Engineering Computer Science at University of Michigan.
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Date Created: 10/29/15
Recitation 10 EECS 451 Winter 2009 April 1st7 2009 OUTLINE 0 Review of Important Concepts 0 Practice problems Concepts Design of Digital Filters 1 Design of digital HR lters from analog lters a HR lters can generally offer better approximation to a desired magnitude response than FIR lters at the expense of linear phase b For a given analog lter7 we can convert it into a digital lter using a transformation from the s plane to the ziplane7 eg bilinear transformation 2 Bilinear Transformation BLT l l 2 a The mapping of BLT is de ned as s TS iijrjj equivalently z b When analog lter Has has a rational form7 BLT yields a which has a rational form c The entire left half of the s plane is mapped inside the unit circle in the z plane d The entire right half of the s plane is mapped outside the unit circle in the z plane e The imaginary axis in the s plane is mapped onto the unit circle in the z plane 3 Bilinear Transformation BLT a A stable Has yields a stable by performing BLT since all poles in the left half s plane is mapped inside the unit circle in the z plane b Hw depends only on HAD since the imaginary axis in the s plane is mapped onto the unit circle in the z plane c The relationship between w and Q is highly nonlinear called frequency warping given by 2 w 9 itani d Poleszeros at s oo map to poleszeros at z 71 by BLT e Real poleszeros remain real and complex conjugate pairs remain complex conjugate pairs after applying BLT 4 Butterworth lter a They have rational system function Has b The frequency response is given by 1Haltngt12 where N is the order of the lter c The lter has N poles equally spaced on a circle of radius 90 in the left half plane d Pro Maximally at in the pass band e Con Not a sharp cut off 5 Chebyshev lter Type I a They have a rational system function Has b They have equi ripples in the passband and monotonically decreasing in stopband c They are all pole analog lters and the frequency response is given by 7 1 7 1 62012Q c where ON is the N th order Chebyshev polynomial 6 Elliptic lter 1319 a The frequency response is given by 1 H o 2 4 l 1 we where UNz is the Jacobian elliptic function something which we need not know and MATLAB takes care of b Pro Sharpest transition for a given N c Con Ripple in both passband and stopband Problems 1 Use the bilinear transformation to convert the analog lter with system function 3 01 H aw s 012 9 into a digital HR lter Select T9 01 and determine the location of the poles and zeros of 1112
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