Approximation and balancing orders for totally interpolating biorthogonal multiwavelet systems
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We consider totally interpolating biorthogonal multiwavelet systems with finite impulse response two-band multifilter banks, and study balancing order conditions of such systems. Based on FIR and interpolating properties, we show that approximation order condition is completely equivalent to balancing order condition. Consequently, a prefiltering can be avoided if a totally interpolating biorthogonal multiwavelet system satisfies suitable approximation order conditions. An example with approximation order 4 is provided to illustrate the result.
Abstract
We consider totally interpolating biorthogonal multiwavelet systems with finite impulse response two-band multifilter banks, and study balancing order conditions of such systems. Based on FIR and interpolating properties, we show that approximation order condition is completely equivalent to balancing order condition. Consequently, a prefiltering can be avoided if a totally interpolating biorthogonal multiwavelet system satisfies suitable approximation order conditions. An example with approximation order 4 is provided to illustrate the result.
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