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Unformatted text preview: Meyer wavelet The first orthonormal wavelets were constructed by Meyer and they were bandlimited. Let ( ) t be a real valued function with a Fourier transform ( ) that satisfies the following: 1. It is real and positive in the range 4 /3 and is zero at frequencies outside this range. Because ( ) has been assumed to be real, ( ) t is symmetric about the origin. It also follows that ( ) is itself symmetric about 2. It is smooth in the sense that ( ) is differentiable. 3. This type of function satisfies the Poisson summation formula. Thus, ( ) t and its integer translates form an orthonormal set. It can be shown that any bandlimited scaling function necessarily satisfies the Meyer bandlimit. The function ( ) H obtained by substituting such a ( ) in is the frequency response of an LPF with cutoff frequency 2 /3 rad. Furthermore, it is real valued and satisfies the PRQMF property. Thus, ts impulse response serves as the coefficient sequence of the and satisfies the PRQMF property....
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This note was uploaded on 06/18/2010 for the course DSP 4 taught by Professor Rao during the Spring '10 term at Asia University, Tokyo.
- Spring '10