Title :
Frame-theoretic analysis and design of oversampled filter banks
Author :
Bolcksei, H. ; Hlawatsch, Ranz ; Feichtinger, Hans G.
Author_Institution :
Inst. fur Nachrichtentech. und Hochfrequenztech., Tech. Univ. Wien, Austria
Abstract :
We provide a frame-theoretic analysis of oversampled and critically sampled, FIR and IIR, uniform filter banks (FBs). Our analysis is based on a relation between the polyphase matrices and the frame operator. For a given oversampled analysis FB, we parameterize all synthesis FBs providing perfect reconstruction, and we discuss the minimum norm synthesis FB and its approximative construction. We find conditions for a FB to provide a frame expansion. Paraunitary and biorthogonal FBs are shown to correspond to tight and exact frames, respectively. A new procedure for the design of paraunitary FBs is formulated. We show that the frame bounds are related with the eigenvalues of the polyphase matrices and the oversampling factor, and that they determine important numerical properties of the FB
Keywords :
FIR filters; IIR filters; band-pass filters; digital filters; eigenvalues and eigenfunctions; filtering theory; FIR; IIR; biorthogonal FBs; critically sampled filter banks; eigenvalues; frame expansion; frame operator; frame-theoretic analysis; minimum norm synthesis; oversampled filter banks; paraunitary FBs; perfect reconstruction; polyphase matrices; uniform filter banks; Channel bank filters; Delay; Eigenvalues and eigenfunctions; Filter bank; Finite impulse response filter; Immune system; Mathematics; Polynomials; Signal synthesis; Transfer functions;
Conference_Titel :
Circuits and Systems, 1996. ISCAS '96., Connecting the World., 1996 IEEE International Symposium on
Conference_Location :
Atlanta, GA
Print_ISBN :
0-7803-3073-0
DOI :
10.1109/ISCAS.1996.541733
