Title :
Optimal Two-Sided Diagonal Scaling for Filter Bank Frames
Author :
Chai, Li ; Zhang, Jingxin ; Han, Qing-Long
Author_Institution :
Sch. of Inf. Sci. & Eng., Wuhan Univ. of Sci. & Technol., Wuhan, China
Abstract :
Two-sided diagonal scaling for transfer matrices is formulated. An efficient algorithm is proposed to compute globally optimal solutions using the iterated bi-section and linear matrix inequality (LMI) solver. It is shown that the two-sided scaling of filter bank (FB) frames can be implemented by the adjustment of channel gains and the periodic precoding of source signal, and that the frame-bound-ratio of FB frames can be effectively improved by such scaling. Explicit formulas are established for both uniform and nonuniform FB frames, including detail formulas for discrete Weyl-Heisenberg frames and tree-structured FBs (discrete wavelets). Different examples show the effectiveness of the obtained results.
Keywords :
channel bank filters; iterative methods; linear matrix inequalities; precoding; transfer function matrices; FB frames; channel gain adjustment; discrete Weyl-Heisenberg frames; discrete wavelets; filter bank frames; frame-bound-ratio; iterated bisection solver; linear matrix inequality solver; optimal two-sided diagonal scaling; periodic precoding; source signal; transfer matrices; tree-structured FB; Algorithm design and analysis; Filter banks; Linear matrix inequalities; Matrix converters; Signal processing algorithms; Condition number; diagonal scaling; discrete wavelets; filter banks; frame bound ratio;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2011.2165710
