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Basic Details:

  • Course Code: EM 5060
  • Credits: 3
  • Pre-requisites: None
  • Compulsory/Optional: Optional

Aim :

To provide a thorough knowledge of fundamental and advanced concepts in Fourier analysis and applications.

Intended Learning Outcomes:

On successful completion of the course, the students should be able to;

  • ILO 1: Construct the trigonometric Fourier series as applied to real periodic functions.
  • ILO 2: Formulate the complex Fourier series through an orthonormal sequence of complex exponentials.
  • ILO 3: Compute Fourier transforms and inverse Fourier transforms as applied to nonperiodic functions.
  • ILO 4: Analyze and solve specific problems in harmonic analysis and spectral theory.
  • ILO 5: Compute Discrete Fourier Transform (DFT), and use Fast Fourier Transform (FFT) algorithm to find the DFT.

Couse Content:

Fourier approximation, Half Fourier development, Parseval's theorem, Amplitude, Phase & Energy spectrums, Complex form of Fourier series

Numerical techniques for integration, Computation of Fourier coefficients, Least squares method to compute Fourier coefficients

Continuous spectrums, sine & cosine integral transforms

Properties & theorems of Laplace transform

Time Allocation (Hours):

Lecture hrs
0
Tutorial hrs
0
Assignment hrs
0
Independent Learning & Assessment hrs
0

Recommended Texts:

  • Gerald B. Folland, “Fourier Analysis and Its Applications” (1992), American Mathematical Society.
  • K.W. Korner, “Fourier Analysis”, Revised Edition (2022), Cambridge University Press.

Assessment:

In - course:

Tutorials/Assignments/Quizzes
20%
Mid Semester Examination
30%

End-semester:

50%