bandlimited wavelets

# bandlimited wavelets - Bandlimited Wavelets The orthonormal...

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Bandlimited Wavelets The orthonormal basis generating wavelets which are bandlimited are said to be bandlimited wavelets. It is possible to have orthonormal basis generating wavelets that are bandlimited; that is, their Fourier transforms are supported compactly in frequency. Its Fourier transform, given by is bandlimited to the frequency range . It also satisfies the Poisson summation formula equation (1), indicating that ( ) H and its integer translates are orthogonal. In fact, ( ) t satisfies the orthonormality condition. If it were also to satisfy the two-scale relation, it would qualify as a scaling function. Let us verify that it does by substituting Equation (2) into Equation (3) and then transforming it into the frequency domain. We are looking for a filter H with an impulse response h(n) such that Taking Fourier transform on both sides ( ) H which satisfies the above equation is which is an ideal LPF with cutoff frequency / 2 . It can be verified that

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## This note was uploaded on 06/18/2010 for the course DSP 5 taught by Professor Rao during the Spring '10 term at Asia University, Tokyo.

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bandlimited wavelets - Bandlimited Wavelets The orthonormal...

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