筑波大学教育課程編成支援システム(EN)

0AL0303 Modern Information Theory

2.0 Credits, 1, 2 Year, SprAB Tue3,4
Kazuki Katagishi

Course Overview

This cource provides distributions(hyperfunctions)-based complete proof of Shannon's sampling theory and then "Fluency information theory" which can be considered as a generalization of Shannon's sampling theory

Remarks

Identical to 01CF202 and 01CH102.

Course Type

lectures

Relation to Degree Program Competences

Course Objectives(Learning Outcomes)

This cource provides distributions(hyperfunctions)-based complete proof for Shannon's sampling theory and "Fluency information theory" as post Shannon.
(1)Students should understand the mathematical relation between Fourier transform and Fourier series in waveform(singnal) analysis.
(2)Students should understand importance of distributions(hyperfunctions) in modern waveform analysis.
(3)Students should understand complete proof for Shannon's sampling theory based on distributions(hyperfunctions).
(4)Students should understand Fluency sampling theory as a generalization of Shannon's sampling theory.
(5)Students should understand Fluency information theory as modern information theory.

Course Keywords

Distributions(Hyperfunctions), δ-functions, Shannon's sampling theory, Fluency sampling theory, Fluency information theory

Class Schedule

(1)Fourier transform and Fourier series
(2)Distributions(Hyperfunctions) for waveform(signal) analysis
(3)Distributions-based complete proof of Shannon's sampling theory
(4)Fluency sampling theory as generalized Shannon's sampling theory
(5)Fluency information theory as a pair of Fluency sampling functions(DA functions) and their biorthogonal sampling functions(AD functions)

Course Prerequisites

Nothing special

Grading Philosophy

Comprehensively evaluate 20 points for the report and 80 points for the final examination, and pass 60 points or more.

Course Hours Breakdown and Out-of-Class Learning

Questions will be asked in class, so please submit a report in the next class.

Textbooks, References,and Supplementary Materials

Distribute materials that summarize the contents of the lecture every time.
<references>
1. A. Papoulis, "Signal Analysis", McGraw-Hill, New York, NY, 1977.
2. E.O. Brigham, "The Fast Fourier Transform", Englewood Cliffs, NJ, Prentice-Hall, 1974.

Office Hours and Contact Information

17:30-18:30 after this class, Academic Computing and Communications Center (room number 404)
E-mail: katagisi@cc.tsukuba.ac.jp

Other(Behavioral expectations and points to note for students during coursework)

It is desirable to have prior knowledge of under graduated level "linear algebra" and "analysis" in math, but consider so that you can understand the contents of the class without prior knowledge.

シラバス参照