Fourier Transforms in Digital Image Processing Courses

Abstract

To help teaching and learning of Fourier transforms in digital image processing courses, an approach to the Fourier transforms from a standpoint of linear algebra is presented. After representing a periodic sequence by a circulant matrix, the periodic convolution can be formulated in terms of matrix multiplication, and finally, the Fourier transform is written in a form of matrix diagonalization. As a comparison, summation formulas are prevalent in traditional courses on signals and systems and matrices are scarcely found in textbooks of digital signal processing. We hope that this approach will make the Fourier transform easier to teach and learn in digital image processing courses.