Applications of complex valued wavelet transforms to subband decomposition

A method for constructing complex valued linear phase FIR conjugate quadrature filters and associated wavelet bases is described. Each filter is derived by replating certain zeros of a real valued FIR conjugate quadrature filter by their reciprocal conjugates. The derived filters have the same frequency response magnitudes as the original filters and their linear phase property permits the use of symmetrization in subband decomposition to avoid border discontinuities that result from signal periodization. Subband decomposition and reconstruction using both a length 6 filter associated with a Daubechies (1988) wavelet bases and a related length 6 complex valued linear phase filter are compared to illustrate the reduced border effects.<
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