Discrete-Fourier-Transform-DFT
This is the second project of the computer vision course (Spring 2022).
Discrete Fourier Transform (Spring 2022)
The project studies the representation and analysis of images in the frequency domain. Two important examples of such representations use the Discrete Cosine Transform, which plays a role in JPEG, and the Discrete Fourier Transform. The focus in this project is on the Discrete Fourier Transform, which uses a decomposition of a grayscale image into specific sine and cosine functions using a discrete version of the so-called Fourier transform. The resulting representation of an image in the frequency domain is also an image itself. This image contains valuable structural information about the original grayscale image. The mappings from grayscale to frequency domain image and vice versa are uniquely defined, allowing to move back and forth between both representations. This is a short report (approximately 1500 words) explaining the principle on which the Discrete Fourier Transform is based, how the frequency domain image is obtained from a grayscale image (and vice versa), and what information the frequency domain image reveals.