Fourier Analysis: Unveiling The Frequency Domain for Signal Deconstruction

Abstract

This paper explores the application of Fourier Transforms (FT) and series in signal analysis. FT decomposes a time-domain signal into its constituent frequency components in the frequency domain (j2?f plane), facilitating analysis unavailable in the s-plane of Laplace transforms. FT enables spectral analysis of signals and characterization of the response of Linear Time-Invariant (LTI) systems. Continuous-Time FT (CTFT) applies to analog signals, while Discrete-Time FT (DTFT) is used for discrete signals. The paper emphasizes the critical role of DTFT in digital signal processing (DSP), particularly for efficient convolution and various signal manipulations. It concludes by highlighting the transformative impact of FT on various scientific and engineering fields.