This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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....
View
Full
Document
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
 rao

Click to edit the document details