Title :
On the least squares signal approximation model for overdecimated rational nonuniform filter banks and applications
Author :
Tkacenko, Andre ; Vaidyanathan, P.P.
Author_Institution :
Dept. of Electr. Eng., California Inst. of Technol., Pasadena, CA, USA
Abstract :
With the advent of wavelets for lossy data compression came the notion of representing signals in a certain vector space by their projections in well chosen subspaces of the original space. In this paper, we consider the subspace of signals generated by an overdecimated rational nonuniform filter bank and find the optimal conditions under which the mean-squared error between a given deterministic signal and its representation in this subspace is minimized for a fixed set of synthesis filters. Under these optimal conditions, it is shown that choosing the synthesis filters to further minimize this error is simply an energy compaction problem. With this, we introduce the notion of deterministic energy compaction filters for classes of signals. Simulation results are presented showing the merit of our proposed method for optimizing the synthesis filters.
Keywords :
approximation theory; channel bank filters; data compression; deterministic algorithms; least mean squares methods; minimisation; signal representation; wavelet transforms; deterministic energy compaction filters; deterministic signal; least squares signal approximation model; lossy data compression; mean-squared error; minimization; nonuniform filter banks; optimal conditions; overdecimated rational filter banks; signal representation; signal subspace; synthesis filters; wavelets; Channel bank filters; Compaction; Data compression; Filter bank; Least squares approximation; Least squares methods; MIMO; Signal generators; Signal synthesis; Space technology;
Conference_Titel :
Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03). 2003 IEEE International Conference on
Print_ISBN :
0-7803-7663-3
DOI :
10.1109/ICASSP.2003.1201723
