Chapter_15 - CHAPTER 15 15.1 For the output error method...

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314 CHAPTER 15 15.1 For the output error method (1) Taking the z -transform of both sizes of Eq. (1) (2) For the equation error method (3) Taking the z -transform of both sides of Eq. (3): , (4) which explains why the transfer function comes in. yn () a i n un - i b i n - i i =1 N + i =0 M = Yz Az Uz Bz + = y n a i n - i b i n dn - i i =1 N + i =0 M = a i n - i b i n e n - i y n - i + [] i =1 N + i =0 M = a i n - i b i n e n - i b i n y n - i i =1 N + i =1 N + i =0 M = Y z + = E z Y z + 1 Ez Y z + + = 1 Y z 1 + = Y z 1 1 ------------------- + = 1 1
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315 15.2 The approximation used in Eqs. (15.18) and (15.19), reproduced here for convenience of presentation, is based on the following observation: When the adaptive filtering algorithm reaches a convergent point, then the parameters of the filter could be held constant, at which point the two equations become exact. Hence, 15.3 To mitigate the stability problem in adaptive IIR filters, the following measures can be born in mind in formulating the algorithm: 1. Use of the “equation error method” to replace “output error method” for rough approximation. 2. Use of a lattice structure for the IIR filter 1 3. Combine IIR and FIR structures to devise hybrid filter, e.g., Laguerre transversal filter. 15.4 LMS Algorithm for Laguerre transversal filter: Initialization: Initialize the weights w 0 , w 1 ,..., w M by setting them equal to zero, or else by assigning them small randon values.
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Chapter_15 - CHAPTER 15 15.1 For the output error method...

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