| 書(shū)目名稱(chēng) | Information Theory | | 副標(biāo)題 | Three Theorems by Cl | | 編輯 | Antoine Chambert-Loir | | 視頻video | http://file.papertrans.cn/466/465749/465749.mp4 | | 概述 | Provides an introduction to information theory, fundamental to the digitized world.Accessible to mathematics and computer science undergraduates.Includes numerous exercises, with solutions | | 叢書(shū)名稱(chēng) | UNITEXT | | 圖書(shū)封面 |  | | 描述 | .This book provides an introduction to information theory, focussing on Shannon’s three foundational theorems of 1948–1949. Shannon’s first two theorems, based on the notion of entropy in probability theory, specify the extent to which a message can be compressed for fast transmission and how to erase errors associated with poor transmission. The third theorem, using Fourier theory, ensures that a signal can be reconstructed from a sufficiently fine sampling of it. These three theorems constitute the roadmap of the book.?.The first chapter studies the entropy. .of a discrete random variable and related notions. The second chapter, on compression and error correcting, introduces the concept of coding, proves the existence of optimal codes and good codes (Shannon‘s first theorem), and shows how information can be transmitted in the presence of noise (Shannon‘s second theorem). The third chapter proves the sampling theorem (Shannon‘s third theorem) and looks at its connections with other results, such as the Poisson summation formula. Finally, there is a discussion of the uncertainty principle in information theory..Featuring a good supply of exercises (with solutions), and an introdu | | 出版日期 | Textbook 2022 | | 關(guān)鍵詞 | Information entropy; Coding; Sampling theory; Random variables; Fourier series and Fourier transform | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-031-21561-2 | | isbn_softcover | 978-3-031-21560-5 | | isbn_ebook | 978-3-031-21561-2Series ISSN 2038-5714 Series E-ISSN 2532-3318 | | issn_series | 2038-5714 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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