Fourier Analysis in Signal Processing

Abstract

Fourier analysis is one of the pillars of modern signal processing methods, making it possible to transform complex signals into basic sinusoidal signals. This mathematical framework makes it easy to analyze, synthesize and transform signals in both the time and frequency domains. The applications of Fourier analysis are in a variety of fields such as telecommunications, audio processing, image processing, biomedical engineering, and radar systems. This research is based on the theoretical basis of Fourier series and Fourier transform, the practical realization of Fourier series and Fourier transform in digital signal processing (DSP), and its performance in noise reduction, filtering and spectrum analysis. The study also addresses the progress made in the field of fast Fourier transform (FFT) algorithms and its effect with the computational efficiency. By combining advances in Fourier analysis with new digital signal processing methods, engineers can achieve the following: Clear up signals Optimal data transmission and performance improvements. The results indicate the critical importance of Fourier methods in the design, implementation, and optimization of analog and digital signal processing information systems. Furthermore, the research highlights that computational techniques have continued to evolve and there are newer and newer applications of Fourier analysis in large signal processing situations and in real-time signal processing situations.