: 10.62796/pijst
Pratima Gurung, PhD (Physics), Pokhara University, Pokhara, Nepal.
Published Date: 02-08-2025 Issue: Vol. 2 No. 8 (2025): August 2025 Published Paper PDF: Download
Abstract- The Fourier Transform (FT) stands as one of the most foundational tools in modern physics for analyzing signals, decomposing functions, and interpreting time-dependent phenomena. This research paper presents a conceptual exploration of the Fourier Transform with a focus on its role in signal analysis within the broader context of physics. Rather than emphasizing mathematical formalism, this study aims to provide an accessible understanding of how the Fourier Transform operates across multiple domains, including engineering, medicine, quantum mechanics, and audio processing. Beginning with a historical overview, the paper revisits the ground-breaking contributions of Joseph Fourier in the 19th century, where his insight into representing heat equations through trigonometric series laid the groundwork for contemporary signal theory. The study then moves to explore fundamental principles, highlighting how the transformation enables the conversion of time-domain functions into their frequency-domain counterparts, offering deep insights into the spectral composition of physical systems. A key emphasis of the paper is on real-life applications of Fourier Transform in various scientific and technological fields. The transform’s use in medical imaging (such as MRI and CT scans), digital audio analysis, and structural engineering underscores its interdisciplinary significance. In the context of quantum mechanics, the FT serves as a bridge between position and momentum representations, revealing the underlying duality in wave functions. The paper also presents a comparative analysis of FT with other transform methods such as the Wavelet and Gabor transforms, discussing their respective advantages and limitations. Challenges related to sampling, resolution, and spectral leakages are briefly addressed, alongside recent advancements in discrete and fast Fourier Transform algorithms. By synthesizing theoretical insights with practical applications, this paper seeks to make Fourier analysis approachable for scholars from both scientific and non-scientific backgrounds. The aim is to inspire a deeper appreciation of how a single mathematical tool continues to shape our understanding of physical reality across disciplines.
Keywords-Fourier Transform, Signal Analysis, Frequency Domain, Quantum Mechanics, Interdisciplinary Applications, Conceptual Physics.
Published Date: 02-08-2025 Issue: Vol. 2 No. 8 (2025): August 2025 Published Paper PDF: Download
Abstract- The Fourier Transform (FT) stands as one of the most foundational tools in modern physics for analyzing signals, decomposing functions, and interpreting time-dependent phenomena. This research paper presents a conceptual exploration of the Fourier Transform with a focus on its role in signal analysis within the broader context of physics. Rather than emphasizing mathematical formalism, this study aims to provide an accessible understanding of how the Fourier Transform operates across multiple domains, including engineering, medicine, quantum mechanics, and audio processing. Beginning with a historical overview, the paper revisits the ground-breaking contributions of Joseph Fourier in the 19th century, where his insight into representing heat equations through trigonometric series laid the groundwork for contemporary signal theory. The study then moves to explore fundamental principles, highlighting how the transformation enables the conversion of time-domain functions into their frequency-domain counterparts, offering deep insights into the spectral composition of physical systems. A key emphasis of the paper is on real-life applications of Fourier Transform in various scientific and technological fields. The transform’s use in medical imaging (such as MRI and CT scans), digital audio analysis, and structural engineering underscores its interdisciplinary significance. In the context of quantum mechanics, the FT serves as a bridge between position and momentum representations, revealing the underlying duality in wave functions. The paper also presents a comparative analysis of FT with other transform methods such as the Wavelet and Gabor transforms, discussing their respective advantages and limitations. Challenges related to sampling, resolution, and spectral leakages are briefly addressed, alongside recent advancements in discrete and fast Fourier Transform algorithms. By synthesizing theoretical insights with practical applications, this paper seeks to make Fourier analysis approachable for scholars from both scientific and non-scientific backgrounds. The aim is to inspire a deeper appreciation of how a single mathematical tool continues to shape our understanding of physical reality across disciplines.
Keywords-Fourier Transform, Signal Analysis, Frequency Domain, Quantum Mechanics, Interdisciplinary Applications, Conceptual Physics.
