Fourier Transform and Inverse Transform Implementation Example

This is a MATLAB implementation example demonstrating Fourier transform and inverse transform operations. Fourier transform is a crucial mathematical tool widely applied in signal processing, image processing, audio analysis, and communication systems. In this example, we utilize MATLAB to understand Fourier transform concepts and implement both forward and inverse transformations. The implementation employs MATLAB's built-in functions: fft() for forward Fourier transform and ifft() for inverse transform, accompanied by MATLAB's plotting functions (such as plot(), stem(), and subplot()) for result visualization. Key implementation aspects include signal preprocessing, frequency domain analysis, and verifying transform reversibility by comparing original and reconstructed signals. Through this example, you will learn how to implement Fourier transforms in MATLAB and understand their practical applications in signal processing, including frequency component extraction and signal reconstruction techniques.