论文标题
基于卷积的特殊仿射小波变换和相关的多分辨率分析
Convolution Based Special Affine Wavelet Transform and Associated Multi-resolution Analysis
论文作者
论文摘要
在本文中，我们研究了特殊仿射傅立叶结构域中的卷积结构，以结合众所周知的特殊仿射傅立叶和小波的优势，变成了一种新型的积分变换，形成了特殊的仿射小波变换，并研究了关节频率范围内相关的恒定Q-property。初步分析涵盖了基本属性，正交关系，反转公式和范围定理的推导。最后，我们通过引入与特殊仿射小波变换和正交特殊仿射小波相关的多分辨率分析的概念来扩展本研究的范围。我们称其为特殊的仿射多分辨率分析。与特殊仿射傅里叶域有关的必要条件，在该域中建立了CHIRP调制函数的整数移动构成RIESZ的基础或正常基础的多分辨率子空间基础。
In this paper, we study the convolution structure in the special affine Fourier domain to combine the advantages of the well known special affine Fourier and wavelet transforms into a novel integral transform coined as special affine wavelet transform and investigate the associated constant Q-property in the joint time-frequency domain. The preliminary analysis encompasses the derivation of the fundamental properties, orthogonality relation, inversion formula and range theorem. Finally, we extend the scope of the present study by introducing the notion of multi-resolution analysis associated with special affine wavelet transform and the construction of orthogonal special affine wavelets. We call it special affine multi-resolution analysis. The necessary and sufficient conditions pertaining to special affine Fourier domain under which the integer shifts of a chirp modulated functions form a Riesz basis or an orthonormal basis for a multi-resolution subspace is established.
