Uncertainty relation for multidimensional discrete signals

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• 作者：Klaus Meerkoetter
• 关键词：Uncertainty relation ; MD discrete signals ; Spread in space ; Spread in frequency
• 刊名：Multidimensional Systems and Signal Processing
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：28
• 期：2
• 页码：389-406
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Circuits and Systems; Electrical Engineering; Signal,Image and Speech Processing; Artificial Intelligence (incl. Robotics);
• 出版者：Springer US
• ISSN：1573-0824
• 卷排序：28

文摘

It is well-known that the famous uncertainty relation between duration and bandwidth of continuous-time signals can be appropriately modified to be applicable also to discrete-time signals, i.e. to signals which are mathematically represented by sequences of real or complex numbers. While the generalization of the uncertainty relation to signals defined on the multidimensional (continuous) real space is quite obvious, this task is less trivial in the case of discrete signals. It is the purpose of this paper to show that an uncertainty relation can also be formulated for multidimensional (MD) discrete signals. The MD signals reaching the uncertainty limit are composed of binomial coefficients and generalizations thereof.