2016 Fourier and Laplace Transforms

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Academic unit or major
Computer Science
Nagahashi Hiroshi  Obi Takashi 
Class Format
Media-enhanced courses
Day/Period(Room No.)
Tue7-8(W631)  Fri7-8(W631)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
Access Index

Course description and aims

The instructor will lecture on complex function theory and basic signal processing methods (Fourier analysis and Laplace transforms).

Student learning outcomes

The aim of this course is for students to derive solutions of definite integrals with residue theorem and solutions of partial differential equations by using Laplace transforms.


- Complex function theory
- Linear system
- Fourier analysis
- Laplace transform

Competencies that will be developed

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

Class flow


Course schedule/Required learning

  Course schedule Required learning
Class 1 Complex numbers: Four arithmetic operations, Euler's formula
Class 2 Complex functions: continuity, differentiability, holomorphic functions
Class 3 Holomorphic function and complex integral
Class 4 Cauchy's integral theorem/formula
Class 5 Taylor expansion and Laurent expansion
Class 6 Residue
Class 7 Residue theorem
Class 8 Applications to definite integral
Class 9 Fourier series and its properties 1
Class 10 Fourier series and its properties 2
Class 11 Fourier series and its properties 3
Class 12 Fourier transform and its properties 1
Class 13 Fourier transform and its properties 2
Class 14 Laplace transform and its properties
Class 15 Applying the Laplace transform to solve linear differential equations

Assessment criteria and methods

Students will be assessed on their understanding of Fourier series, Fourier transform and Laplace transform.
Students' course scores are based on exercise problems (20%) and midterm and final exams (80%).

Related courses

  • ZUS.F301 : Foundations of Functional Analysis
  • ZUS.C301 : Signal Processing
  • ZUS.M303 : Digital Communications

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