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A Fourier Transform is a mathematical technique that converts a function of time, f(t), into a frequency function, \(\hat{f}(\omega )\) . The Fourier Series is closely related to it. One of the main disadvantages of Fourier series is that they can only be applied to periodic signals. Several naturally occurring signals cannot be represented by Fourier series due to their non-periodicity or aperiodicity. Fourier developed a mathematical model to solve this problem called ‘Fourier transform’, which transforms signals from the time (or spatial) domain to the frequency domain. The Fourier transform is widely used in physics and engineering, for example in LTI systems, RADAR systems, astronomy, and signal processing.

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  • 发表日期：

    2025年

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  • Santosh Kumar Upadhyay,
  • Jay Singh Maurya

摘要

A Fourier Transform is a mathematical technique that converts a function of time, f(t), into a frequency function, \(\hat{f}(\omega )\) . The Fourier Series is closely related to it. One of the main disadvantages of Fourier series is that they can only be applied to periodic signals. Several naturally occurring signals cannot be represented by Fourier series due to their non-periodicity or aperiodicity. Fourier developed a mathematical model to solve this problem called ‘Fourier transform’, which transforms signals from the time (or spatial) domain to the frequency domain. The Fourier transform is widely used in physics and engineering, for example in LTI systems, RADAR systems, astronomy, and signal processing.