Fourier Transform of Images: Spectrum Swapping Implementation

This discussion explores the Fourier transform of images through practical code implementation. Our program performs spectral swapping operations by exchanging the magnitude and phase spectra between two distinct images. The implementation involves decomposing each image into its frequency domain components using fast Fourier transform (FFT) algorithms, then systematically interchanging their spectral characteristics. The magnitude spectrum represents the intensity distribution of various frequency components within an image, while the phase spectrum captures the relative positioning and phase relationships between these components. Through spectral swapping, we can observe how modifications to frequency intensity distributions and component alignments affect image reconstruction. This approach provides valuable insights into fundamental image processing principles and visual representation mechanisms. The code typically utilizes functions like fft2() for transformation, abs() for magnitude extraction, and angle() for phase calculation, followed by reconstruction using inverse FFT operations.