单周正弦小波函数的性质

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关键词：傅里叶变换；小波变换；再生核函数；单周正弦小波；窗口函数DOI：10.15938/j. jhust.2025.06.014中图分类号：0175.14 文献标志码：A 文章编号：1007-2683（2025）06-0128-10

Abstract：Thesingle-cyclesiusoidalwaveletisa wavelet withacompactsupport intervalInorder tofurtherstudythepropertis ofthesingle-cyclesinusoidal wavelet，basedontheteoryofwaveletanalysis，thtime-frequencyanalysismethodisadoptedtoprove thatthesingle-cyclesinusoidalwaveletisabasic wavelet.Inthetime domain，ithaspropertiessuchascontinuity，symmetry， attenuationproprtyfiitedieretabilitylmosveryre，wdofuctioichanxpreedsivatiefst decayingfunctionByvirtueoftheinfinitediferentiabilityofthereproducingerelfunctionintePaleyWienersace，itisproved thatthesingle-cyclesinusoidalwaveletisinfinitelydiferentiableinthefrequencydomain.Byemployingthetheoryofrepoducing kernelHilbertspace，theanalyticalexpresioandpropertisfortereproducingkeelfunctiooftheimagesaceftesingle-cyle sinusoidalwaveletransfomhavebeenderived.ThisnotonlyenrichesthestudyofthetheoryofreproducingkeelHlbertspace，but alsoproviesatheoreticalbasisforsolvingngineringproblemsbyusing numericalcomputationmethods basedon waveletrasfors.

Keywords：Fourier transform；wavelet transform；reproducing kernelfunction；single-cyclesinusoidal wavelet；window function

0 引言

小波分析是一种时间－频率分析方法，主要用于分析非平稳信号。（剩余6064字）