| Summary: | 碩士 === 大同工學院 === 資訊工程研究所 === 82 === In this thesis, a new approach is presented for the design of
1-D and 2-D two-channel FIR filter banks employing
linear-phase filters. For the design of perfect
reconstruction (PR) system, we first design one of the
analysis filter first using general least-squares approach,
and formulate the design problem as a quadratic programing
problem with linear constraints. Then the Lagrange
multiplier approach is used to obtain the closed- form
solution for the other of the analysis filter pair. Although
this approach can find a PR filter banks which can yield
high quality coding system at low bit rates, the filter
bank's operation requires numerous multiplications and
additions. Multiplicaton, in particular, is extremely time
consuming. So, if a multiplication operation could be
replaced by only a few additions or subtractions, then the
complexity of the entire filter bank could be reduced quite
dramatically, such that a fast real-time system becomes
feasible. In this thesis, the Lagrange multiplier approach
associating with a tree search algorithm is used
iteratively. For each branch of the tree, the Lagrange
multiplier approach is used to optimize the remaining
unquantized coefficients of the designed filters. Examples
including 1-D and 2-D design are presented to demonstrate
the usefulness and effectiveness of the approach.
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