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From Fourier Transform to Wavelet Transform

Shihong Huang

Open publisher page 8 citations

Abstract

The Fourier transform and the wavelet transform are two important mathematical transforms used in industry.The applications of Fourier transform have more localizations because it can not obtain the precise time localization of the spectral frequency.The wavelet transform is more flexible in the choosing variable of the window function,so it is used in industry more and more.This article introduces the Fourier transform first,analyses its deficiencies,than introduce the concept of the wavelet transform and uses the multiresolution analysis to analyse the non-stationary signal.

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What this paper is about

The Fourier transform and the wavelet transform are two important mathematical transforms used in industry.The applications of Fourier transform have more localizations because it can not obtain the precise time localization of the spectral frequency.The wavelet transform is more flexible in the choosing variable of the window function,so it is used in industry more and more.This article introduces the Fourier transform first,analyses its deficiencies,than introduce the concept of the wavelet transform and uses the multiresolution analysis to analyse the non-stationary signal.

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OpenAlex reports 8 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

The Fourier transform and the wavelet transform are two important mathematical transforms used in industry.The applications of Fourier transform have more localizations because it can not obtain the precise time localization of the spectral frequency.The wavelet transform is more flexible in the choosing variable of the window function,so it is used in industry more and more.This article introduces the Fourier transform first,analyses its deficiencies,than introduce the concept of the wavelet transform and uses the multiresolution analysis to analyse the non-stationary signal.

Key concepts: Harmonic wavelet transform, Constant Q transform, Fractional Fourier transform, Wavelet transform, Short-time Fourier transform, S transform, Fourier transform, Wavelet

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