帯域制限波形空間多重解像度解析のよるシャノンウェーブレットフレーム

概要

論文の詳細を見る
Multiresolution analysis played an important role in constructing a wavelet frame. However,any wavelet frame via multiresolution analysis was limited to being dyadic dilations and regular translations of a single function so far. As the results,such a wavelet frame can only represent signals using details of sizes and positions specified by dyadic dilations and regular translations, respectively. We proposed a concept of general frame multiresolution analysis, which enables us to construct wavelet frames with irregular translations. However, dilations are still dyadic. Dyadic dilations have a shortcoming that they give low resolutions of higherfrequency components of a function in frequency domain. In order to overcome this shortcoming, wavelet packets were used and functions were redecomposed to specified resolutions. However, re-decompositions were still dyadic. More flexible realizations of multiresolution analysis and wavelet frames are needed. In this paper we propose a theory of Shannon wavelet frame. A Shannon wavelet frame is an extension of Shannon wavelet basis which only consider a basis generate by dyadic dilations and regular translations of a single function. Whereas a Shannon wavelet frame is extended to a more general case which is not limited to being dyadic dilations and regular translations. Details having any size and position in a function can be accurately represented by some Shannon wavelet frames. A method for constructing a dual frame of such a wavelet frame is also proposed.
1996-03-11

帯域制限波形空間多重解像度解析のよるシャノンウェーブレットフレーム

スポンサーリンク

概要

著者

関連論文

スポンサーリンク