There are various methodologies and techniques for analyzing data collected via measurements and observations. Among them, this course focuses on the analysis of time series. Mathematical theory and technique are covered through the lectures, and practical data analyses are executed through computer programming.
Students will acquire the knowledge and skills on the discrete Fourier transform method for characterizing temporal variation in the data, and on various techniques to reduce or eliminate noise superimposed on the data.
By the end of this course, students will be able to:
1) Program a simple data analysis code in MATLAB.
2) Determine an appropriate interval for the sampling of continuously-changing physical quantities.
3) Derive correlation and frequency spectrum of time series data.
4) Extract the meaningful part of the data by removing the noise.
random process, discrete Fourier transform, sampling theorem, Wiener-Khintchin theorem, spectrogram, noise, moving average, filter, singular value decomposition, singular spectrum analysis
|Intercultural skills||Communication skills||Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
Theory is taught in the class and exercises are occasionally given. Students may be asked to explain the assumptions made in the preparation.
Practices on MATLAB programming are conducted in the computer room of IDE Lounge.
Lecture and practice are provided in turns.
|Course schedule||Required learning|
|Class 1||Orientation. Signals (1): sampling theorem, Fourier transform||Find signals within daily life|
|Class 2||Signals (2): random process, autocorrelation, ergodicity, Wiener-Khinchin theorem|
|Class 3||Practice (1): MATLAB||Matrix programming in MATLAB|
|Class 4||Frequency analysis (1): discrete Fourier transform|
|Class 5||Practice (2): discrete Fourier transform||Sampling and discrete Fourier transform of sinusoidal wave|
|Class 6||Frequency analysis (2): uncertainty principle, window function, short time Fourier transform|
|Class 7||Practice (3): short time Fourier transform||Spectrogram of chirp signal|
|Class 8||Noise elimination (1): white noise, moving average|
|Class 9||Practice (4): moving average||Moving average of white noise|
|Class 10||Noise elimination (2): filter|
|Class 11||Practice (5): filter||Noise elimination by filtering|
|Class 12||Signal separation (1): singular value decomposition theorem, singular value decomposition of data|
|Class 13||Signal separation (2): singular spectrum analysis|
|Class 14||Practice (6): singular spectrum analysis||Signal separation and noise elimination by singular spectrum analysis|
|Class 15||Wrap up. Final report assignment.||Processing of voice data|
Masao MASUGI, Signal Analysis, Morikita Pub., 2013 (in Japanese).
Materials for practices are distributed via OCW-i.
Knowledge and applied skill of signals, frequency analysis, noise elimination, signal separation and MATLAB programming will be assessed.
Reports for practice sssions 30%, final report 35%, and final exam 35%.
Students are assumed to have successfully completed Engineering Mathematics A/C, and Theory of Information Processing. Students are also recommended to take Engineering Measurement.
Only students in the Department of International Development Engineering can take this course.