2008•Journal of Neijiang Normal UniversityRequires access

The Limitation of Fourier Transform in Practice and the Methods of Solution

Shao Yi-quan

Abstract

Fourier transform is a whole transform.It can not denote the partial characteristic of the signal in both time and frequency domain.The paper makes a detailed analysis of the limitations of Fourier transform and gives the method of how to overcome the limitations.Finally,it compares the noise reduction effects in signal noise reduction application between Fourier transform and wavelet transform with experimental simulation.It proves the superiority of wavelet transform.

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Key concepts: Harmonic wavelet transform, Fractional Fourier transform, Constant Q transform, Short-time Fourier transform, Fourier transform, Non-uniform discrete Fourier transform, Wavelet transform, Discrete Fourier transform (general)