Implementation of Fourier Transform in Image Processing

Abstract

For a realistic radio interferometer for flat-sky approximation, the basic observation is a set of complex visibilities, which is defined in 2D Fourier Transform (FT) as Radio Measurement Interferometer Measurement Equation (RIME). The Discrete Fourier Transform (DFT) is a specific form of Fourier analysis that is widely employed in signal processing and related fields to analyze frequencies contained in a sample signal to solve partial differential equations and to perform other operations such as convolutions. The presentation will focus on the implementation of the algorithm of Fast Fourier Transform (FFT) by converting a 2D image to the frequency domain and back to the image domain (Inverse FFT). The technique will then be related to RIME.