Abstract
Perfect reconstruction FIR filter banks implement a particular class of signal expansions in l2(Z). These expansions are studied in this paper. Necessary and sufficient conditions on an FIR filter bank to implement a frame or a tight frame decomposition are given, as well as the necessary and sufficient condition for a feasibility of perfect reconstruction using FIR filters. Complete parameterizations of FIR filter banks satisfying these conditions are given. Further, we study the condition under which the minimal dual frame to the frame associated to an FIR filter bank is also FIR, and give a parameterization of a class of filter banks having this property. We then concentrate on the least constrained class, namely nonsubsampled filter banks, for which these frame conditions have particular forms.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
