DFT Transformation of an Image: Centering, Magnitude, and Phase Angle Computation

In this process, we perform a Discrete Fourier Transform (DFT) on an image. Initially, we shift the image to the center using frequency domain centering techniques (typically achieved by multiplying the image by (-1)^(x+y) before transformation) to better analyze its frequency characteristics. We then compute the magnitude and phase angle values of the transformed image to understand the strength and directional information of various frequency components. The magnitude spectrum reveals the amplitude distribution across frequencies, while the phase angle contains crucial spatial structure information. This approach enables deeper understanding of frequency domain features and facilitates extraction of valuable information for applications like image filtering, compression, and pattern recognition. Implementation typically involves using FFT algorithms (e.g., numpy.fft.fft2 in Python or fft2 in MATLAB) followed by magnitude calculation using abs() function and phase extraction via angle() or arctan2() functions.