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在图象传输和图象处理中,图象变换在理论研究以及实际工作方面都起了重要的作用。这里主要介绍二维离散沃尔什(Walsh)变换及其性质。我们知道,一个二维图象,在信道上传输的是用 Fourier 变换之后的代码,而不是图象本身,结果引进了图象编码的技术,因此,必然引进快速 Fourier 变换(简记 FFT)的计算法。本文所介绍的图象变换是用 Walsh 矩阵算子进行变换,在信道上传输的图象是 Walsh 变换后的代码,而不是空间图象。其快速计算法类似于 FFT,由于 Walsh 变换运算仅要求加法和减法,这就使得快速 Walsh 变换(记为 FWT)比 FFT 的运算速度要快得多。在一维情况下,做 N=2~n 点的信号变换时,FFT 需要进行 Nlog_2N 次乘法和
In image transmission and image processing, image transformation plays an important role in theoretical research and practical work. Here mainly introduces the two-dimensional discrete Walsh transform and its properties. We know that a two-dimensional image, transmitted on the channel after the Fourier transform code, rather than the image itself, the result of the introduction of the image encoding technology, therefore, the inevitable introduction of fast Fourier transform (abbreviated FFT) Calculation method. The image transformation introduced in this paper is transformed by Walsh matrix operator. The image transmitted on the channel is the Walsh transformed code, not the spatial image. The fast algorithm is similar to FFT, since Walsh transform requires only addition and subtraction, which makes fast Walsh transform (denoted as FWT) much faster than FFT. In a one-dimensional case, to do N = 2 ~ n point signal transformation, FFT need Nlog_2N multiplication and