Applications of Fourier Series in Signal & Image Processing System

The Fourier series and its extensions remain vital tools in modern signal and image processing, connecting the time (or spatial) domain with the frequency domain. Originating from Joseph Fourier's 19th-century work on heat conduction, the Fourier framework enables the decomposition of periodic and non-periodic signals into their harmonic components, supporting spectrum analysis, noise reduction, filtering, and data compression. In image processing, Fourier methods serve as the foundation for compression standards such as JPEG, as well as tasks like feature extraction, edge detection, and medical image reconstruction. Recent developments have expanded Fourier analysis into hybrid models that integrate wavelets and machine learning, with applications in emerging fields such as 5G, quantum computing, and AI-driven imaging. Although the Fourier series has limitations in handling non-stationary signals, it continues to evolve as a versatile analytical and computational tool, maintaining its significance in engineering, science, and technology.