The Fourier Transform and its Applications
The Fourier Transform and its Applications
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DOI：
10.1049/ep.1965.0268
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发表时间：
1965
期刊：
影响因子：
--
通讯作者：
K. W. Cattermole
中科院分区：
文献类型：
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作者：
K. W. Cattermole
关于这一主题的书有很多，任何增加的数量都需要有特殊的卓越性或一些有价值的新奇来证明：这本书在第一个分数上应该得到一半，在第二个分数上应该得到满分。作者解释其成因作为一个评论的图片字典的转变。几乎所有的定理和具体的转换引用了大量的说明清楚的图表和讨论的物理意义。抽象的分析方法，图形表示，和几个应用程序之间的关系被清楚地阐明。事实上，我自己在浏览文本时的第一反应是承认：在这里，在一个连贯的介绍中，有几个主题，我第一次孤立地学习，多年来，我慢慢意识到它们的相似之处，我希望自己也能这样解释。离散项被表示为脉冲，这通过“广义函数”方法来证明。由于后者是如此基本，遗憾的是，它的论述是最薄弱的部分的工作，既不清晰，也不严格的莱特希尔的书，其中布雷斯韦尔引用作为一个权威。所有通常性质的傅立叶变换在一个和两个维度，重点是卷积和使用重复脉冲序列和其他理想化的波形;特殊符号用于这些是有帮助的。其他积分变换被解释为傅立叶变换的相对物。处理的应用程序是信号表示和滤波，天线辐射模式，扩散和统计。有许多问题，其中一些异常精心设计，发人深省。总的来说，这是一本清晰而有用的书。KW卡特莫尔
There are many books on this subject, and any addition to their number needs to be justified either by special excellence or by some worthwhile novelty of approach: this one deserves halfmarks on the first score, and full marks on the second. The author explains its genesis as a commentary to a pictorial dictionary of transforms. Virtually all the theorems and specific transforms cited are abundantly illustrated by clear diagrams and discussion of physical significance. The relations between the abstract analytic approach, the graphical representation, and several applications are clearly expounded. Indeed, my own first reaction on scanning the text was one of recognition: here, in a coherent presentation, were several topics that I had first learnt in isolation, whose similarities had slowly dawned on me through the years, and which I should wish to explain in just this way myself.The treatment is founded on the Fourier integral rather than the series; discrete terms are represented as impulses, which are justified by the'generalised-function'approach. As the latter is so fundamental, it is a pity that its exposition is the weakest part of the work, neither as lucid nor as rigorous as LighthilPs book which Bracewell cites as an authority. All the usual properties of Fourier transforms in one and two dimensions are given, with emphasis on convolution and on the use of repeated impulse trains and other idealised waveforms; the special notations used for these are helpful. Other integral transforms are explained as relatives of the Fourier transform. The applications treated are to signal representation and filtering, antenna radiation patterns, diffusion and statistics. There are many problems, some of them unusually well contrived to be thoughtprovoking. On the whole, it is a clear and useful volume. KW CATTERMOLE