Haar小波滤波器序列只有两个非零项的论证

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。

Demonstration of only two nonzero coefficients of Haar wavelet filter

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.