解析信号韵定义及瞬时频率、瞬时幅值的算法在信号处理的时频分析领域有着重要意义.四元数解析信号是1维解析信号的定义在2维上的合理延伸,但是现有的四元数解析信号的相位定义不适合分析2维信号的瞬时频率.为此根据四元数解析信号的自身特点提出了一种新颖的四元数解析信号相位定义,并应用两种2维信号分解工具验证了该定义的适用性.合成与自然纹理的试验结果表明,该相位定义更加符合信号的内在性质,更有利于对图像解析特征的提取与分类.

The definition of analytic signal and the computation algorithm for instantaneous frequencies and instantaneous amplitudes have important significance in signal processing domain.The quaternionic analytic signal is an appropriate extension of 1D analytic signal to 2D case.Whereas,the existing phase definition of quaternionic analytic signal isn't fit for extracting instantaneous frequencies of images.According to the properties of quaternionic analytic signal,a novel phase definition of quaternionic analytic signal is proposed in this paper and two decomposition tools are utilized to test the effectiveness of the definition.The experimental results of synthetic and natural textures indicate that the new definition is more coincident with image intrinsic characters and advantageous for image analytic feature extraction and classification.