色导数与带权展开式
Chromatic Derivatives and Expansions with Weights
摘要：
色导数和带限函数的级数展开式最近被引入信号处理中，并且它们在实际应用中已被证明是有用的。我们扩展了色导数的概念，使用不同的权重。当积分算子的核函数为正时，这种扩张保证了每一点周围的色展开。除旧的例子外，还用Walsh-傅里叶变换、Poisson-小波变换等新的变换来说明这种改进方法。此外，还研究了函数在某些$L^p$ -空间中的色展开。
英文摘要：
Chromatic derivatives and series expansions of bandlimited functions have recently been introduced in signal processing and they have been shown to be useful in practical applications. We extend the notion of chromatic derivative using varying weights. When the kernel function of the integral operator is positive, this extension ensures chromatic expansions around every points. Besides old examples, the modified method is demonstrated via some new ones as Walsh-Fourier transform, and Poisson-wavelet transform. Moreover the chromatic expansion of a function in some $L^p$-space is investigated.
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