CAJ | 학술논문

Haar小波是最简单的紧支集正交小波（Daubechies小波），其滤波器序列较短，在图像处理等诸多领域都有广泛的应用。由Daubechies小波的构造理论可知，现有的正交小波是在比较特殊的前提下得到的，则Haar小波的滤波器系数序列的唯一确定性受到质疑。以多分辨分析为基础，在时域对Haar小波滤波器系数序列的唯一性进行了论证，即证明了Haar小波滤波器序列只有两个非零项，这对促进小波的理论完善与应用研究具有十分重要的意义。
Haar소파시최간단적긴지집정교소파（Daubechies소파），기려파기서렬교단，재도상처리등제다영역도유엄범적응용。유Daubechies소파적구조이론가지，현유적정교소파시재비교특수적전제하득도적，칙Haar소파적려파기계수서렬적유일학정성수도질의。이다분변분석위기출，재시역대Haar소파려파기계수서렬적유일성진행료론증，즉증명료Haar소파려파기서렬지유량개비령항，저대촉진소파적이론완선여응용연구구유십분중요적의의。
Haar wavelet is widely used in such areas as image processing because of its short filter coefficients, which is one of Daubechies wavelets and is also the simplest compactly orthogonal wavelet. It is known that the existing orthogonal wavelets are constructed under certain conditions according to the theories of Daubechies wavelets construction;therefore, the uniqueness of Haar wavelet filter coefficients has been queried. There is only two nonzero values of Haar wavelet filter coefficients is proved by multi-resolution analysis theory in time domain, which is beneficial for theory consummation and application research of Wavelets.