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Recently, digital filters and digital filter banks have played
an important role on many digital signal processing theories and
applications. In this thesis, we apply weighted least squares(WLS)
algorithm and Karmarkar's algorithm as optimization tools to design
1-D Nonuniform-Division Maximally Decimated Filter Banks(NDMDFB)
and 2-D FIR filters with continuous coefficients.
Due to the circuit complexity and high cost of multibit multipliers
while implementing an FIR filter of the conventional structure, we
propose a new FIR filter structure whose main part consists of a
transversal filter with tap coefficients restricted to -1,0,+1 and
cascaded with a simple recursive section with some specific resetting
function. Therefore, it's unnecessary for transversal filter to use
multipliers, the configuration is suitable for hardware implementation.
Based on the new structure, we design NDMDFB and 2-D FIR filter with
coefficients -1,0,and +1. Design examples show the effectiveness of
the proposed design technique in the thesis.
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