Implementation of Fast Fourier Transform in image processing, signal processing and acoustics

Since its introduction in 1965 by Cooley and Tukey, the Fast Fourier Transform (FFT) has revolutionized signal processing, converting time domain data into frequency domain data with unprecedented efficiency. Compared to the Discrete Fourier Transform (DFT), the FFT significantly reduces computational complexity, enabling many complex data processing tasks. This paper explores the cutting-edge applications of the FFT in three important areas, i.e., signal processing, image processing, and acoustics. In signal processing, FFT enhances the analysis of ground vibration, which helps to detect and avoid natural disasters such as earthquakes, and in communication technology, simultaneous signal capture in the highly dynamic environment of a supersonic vehicle. In image processing, FFT enables image patching, resolution enhancement, and image compression and decompression. The FFT improves the global perception of image complementation through frequency domain transformation, which makes it more efficient and stable in processing high-resolution images. In acoustics, the detailed division of tones is achieved by FFT, which facilitates the development of fibre optic acoustic sensors. Despite the limitations of the FFT in dealing with non-periodic and non-stationary signals, its significance for signal transformation and the contributions it generates to various fields remain invaluable, and the future direction of the FFT is shown through the introduction of its cutting-edge technologies in various fields.