Exploring fourier transformations: benefits, limitations, and applications in analyzing two-dimensional right rectangular prism’s magnetic field

Abstract

Fourier Transformations are crucial in signal processing, offering a unique approach for complex data analysis. This paper explores their advantages and limitations, explaining key concepts like Fourier Transformation, Fourier series, Discrete Fourier Transform, and Continuous Fourier Transform, focusing on practical applications. The strengths, such as signal decomposition into frequency components, are exemplified through a case study on the total magnetic field of two-dimensional right rectangular prisms. However, limitations arise with non-stationary signals due to the assumption of stationarity. Alternative methods like the Wavelet Transformation and Short-Time Fourier Transformation are briefly discussed. Serving as a practical guide, this paper aids researchers in utilizing Fourier Transformations while recognizing scenarios where alternative techniques may be more suitable.