成果小滤波器组.pdf

Happy Children’s day! Problem • Many wavelet ….. • Good ! vs Bad! • Different? Or same? • How to choose? Energy Compaction filter bank y (n) v 0 0 H0 2 v (or y )have some properties: 0 0 al energy with arbitrary x(n) Length. y (n) v1 Which one? 1 H1 2 formulation Given signal s :={s ,k =0,1,,L }, find filter k hopt := {hopt ,k =0,1,,N } such that k hopt = arg max ||s *h || with constrains h={hk ,k =0,1,,N } 2 2 | H (z ) | +| H (-z) | =2 H (1) = 2 Difficult • Nonlinear • Real time conputation Moulin’s method The energy is: 2 E =|| s * h || Denot S (z ) and H (z ) is the z-transform of s and h respectively. Let f(z ) = S (z ) * S (z ) = r + r (z n +z -n ) 0 n P (z ) = H (z ) * H (z ) = 1 +an (z +z ) n -n then 2 2 E =|| s * h || =|| S (z )H (z ) || 2p 1 = 2p  S (e -iw )H (e -iw )S (e -iw )H (e -iw )d w 0 1 2p -iw -iw =  f(e )P (e )d w 2p 0 N E =r +2a r 0 n n