Comparative Analysis of Fourier Transform Variants: Performance, Applications, and Efficiency

Abstract

This research undertakes a comparative analysis of the primary Fourier Transform (FT) variants to determine their performance metrics, applicable fields, and operational efficiencies. This paper evaluates the Continuous Fourier Transform (CFT), Discrete Fourier Transform (DFT), Fast Fourier Transform (FFT), Short-Time Fourier Transform (STFT), Fractional Fourier Transform (FrFT), Non-Uniform Fourier Transform (NUFT), and Sparse Fourier Transform (SFT). The study methodically compares each variant through a blend of empirical data analysis and theoretical review, highlighting specific advantages and limitations relative to various application requirements. Key findings demonstrate the FFT’s exceptional efficiency in digital signal processing and the adaptability of the STFT in time-frequency analysis, showcasing their pivotal roles in technological advancements. The outcome of this comparative study not only elucidates the optimal conditions for each FT variant's usage but also advances our understanding of their practical impacts, guiding future innovations in fields as diverse as telecommunications, medical imaging, and audio signal processing.