Smoothing Minimally Supported Frequency (MSF) Wavelets : Part II
نویسندگان
چکیده
The main purpose of this paper is to give a procedure to “mollify” the low-pass filters of a large number of Minimally Supported Frequency (MSF) wavelets, so that the smoother functions obtained in this way are also low-pass filters for an MRA. Hence, we are able to approximate (in the L2-norm) MSF wavelets by wavelets with any desired degree of smoothness on the Fourier transform side. Although the MSF wavelets we consider are band-limited, this may not be true for their smooth approximations. This phenomena is related to the invariant cycles under the transformation x 7→ 2x (mod 2π). We also give a characterization of all low-pass filters for MSF wavelets. Throughout the paper new and interesting examples of wavelets are described.
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