2021 Spectral Analysis

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Academic unit or major
Undergraduate major in Mechanical Engineering
Okuma Masaaki 
Course component(s)
Lecture / Exercise    (ZOOM)
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Academic year
Offered quarter
Syllabus updated
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Course description and aims

Spectral analysis plays a basic and important technique to analyze the data of dynamic phenomena such as vibration. This course aims to lecture the fundamental theories and knowledges of the specialized technique with exercise using some case-studies in structural dynamics.
An emphasized aim is to lecture for students to gain deep understanding of the theory of Fourier Transformation from the viewpoints of both physics and mathematics and to be able to use the theory for analyzing various actual data.

Student learning outcomes

At the end of this course, students will be able to :
1) understand fundamental theories of dynamics for spectral analysis
2) understand the methods from data acquisition to spectral analysis concretely for practical use


Dynamic Phenomena, Spectrum, Random Vibration, Correlation

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Lecturing and exercise using PC to concretely understand the lectured theories and practical usage.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Brief introduction of the history of spectral analysis, and basics of random vibration and spectrum Realize the research history of spectral analysis, and enhance academic interest in it
Class 2 Relationship of autocorrelation and spectrum Understand autocorrelation and spectrum.
Class 3 Relationship of crosscorrelation, crossspectrum and transfer function Understand relationship of crosscorrelation, crossspectrum and transfer function
Class 4 Stationary and ergodic Understand "stationary" and "ergodic" conditions.
Class 5 Data acquisition and treatment Understand basic and standard methods of data acquisition and treatment.
Class 6 Programing Make programming codes to understand the theories deeply.
Class 7 Applications of spectral analysis in mechanical engineering Think the applicability of the analysis.

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.


Several materials are provided based on the study-aid books listed below by lecturer.

Reference books, course materials, etc.

Structural Dynamics, written by Masaaki Okuma, Asakura
Spectral analysis, written by Mikio Hino, Asakura.

Assessment criteria and methods

The course scores are basically determined by integrating final examination (approximately 70%) and exercises (approximately 30%). However, this course must be provided online due to COVID-19 in this academic year. Therefore, the scores are determined by some exercises and reports. No final exam is planned.

Related courses

  • MEC.D201 : Mechanical Vibrations
  • MEC.D311 : Vibration Analysis
  • MEC.D531 : Experimental Modal Analysis for Structural Dynamics
  • MEC.D431 : Advanced Sound and Vibration Measurement
  • CVE.A210 : Structural Dynamics in Civil Engineering
  • MEC.D431 : Advanced Sound and Vibration Measurement
  • SCE.I432 : Acoustic measurement engineering

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Bring a note-PC in which Matlab and/or some programing software is available.


Each student is required to attend with his/her note-PC in which Matlab software is installed.
This course is to be provided for fourth grade students. Only fourth-grade students are permitted to take this course in 2021 under the consideration of a new infectious disease and online style of the lecture.

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