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We derive a new set of necessary and sufficient conditions for the filter coefficients of the two-scale difference equation to yield an orthogonal wavelet of compact support. The conditions constitute a linear set of equations of an arbitrary decision vector of half the filter size. The vector of the filter coefficients is a differentiable function of the decision vector. The formulation enables the...
We describe a time-domain procedure for designing the synthesis filters of perfect-reconstruction oversampled filter banks. A condition matrix is derived from the basic magnitude distortion and aliasing canceling conditions and we derive the necessary and sufficient conditions for perfect reconstruction. The formulation is general for any decimation scenario, but it is particularly useful with nonuniform...
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