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Research Paper | Mathematics | Volume 15 Issue 7, July 2026 | Pages: 308 - 312 | India
Fourier Transform: Principles, Properties, and Real-Life Applications with Emphasis on Signal Processing and Mobile Communications
Abstract: The Fourier Transform (FT) is a basic mathematical tool for converting signals from the time/spatial domain to the frequency domain. Its discrete and fast versions (DFT/FFT) allow to efficiently analyse and process complex signals. This review concerns the principles of the Fourier transform, its important properties and wide practical applications with particular emphasis on signal processing in mobile communications and power systems. There is a technique called Fourier Transform (FT for short) in wireless networks. This is what allows things like Orthogonal Frequency Division Multiplexing. This is what allows 4G and 5G systems to send data quickly and efficiently, reducing interference. But that?s not all-FT is also used in power quality management to identify and correct problems such as harmonics and transients quickly. However, the basic FT method has its limitations, especially when dealing with signals that change over time, so scientists have developed more advanced versions like the Short-Time FT, Stockwell transform, and wavelets to handle these tricky signals. You'll also see FT in medical imaging like MRI scans and in the compression of audio and image files like MP3s and JPEGs. It is even employed in vibration analysis and is starting to be employed in machine learning, which is a pretty exciting area of research. Overall, FT is a very powerful tool that helps us to make sense of complex signals and has many different applications. This paper reviews the basic mathematics, historical development, and changing role of Fourier analysis in modern technology. It focuses on strengths, recent progress and future directions and discusses computational implementations for practical problem solving. The book closes the gap between theory and applications and emphasises the relevance of Fourier methods to science and engineering.
Keywords: Fourier Transform, FFT, OFDM, Power Quality, MRI, Signal Processing, Mobile Communications
How to Cite?: Dr. Shally Gupta, "Fourier Transform: Principles, Properties, and Real-Life Applications with Emphasis on Signal Processing and Mobile Communications", Volume 15 Issue 7, July 2026, International Journal of Science and Research (IJSR), Pages: 308-312, https://www.ijsr.net/getabstract.php?paperid=SR26701190323, DOI: https://dx.doi.org/10.21275/SR26701190323