CAJ | 학술논문

数值解析信号波形时频域对易演变过程，研究任意信号波形与频率组分的内在联系，并将该对易原理应用于莫尔条纹相位分析，提取相位信息。采用矩形窗模拟冲激波形和直流波形的变换过程，通过控制矩形窗函数窗宽，获得各种宽度矩形脉冲，窗宽趋于零情况下获得冲激波形，趋于∞获得直流波形。自开发快速傅里叶变换（fast Fourier transform ，FFT ）系统，对矩形脉冲实施离散傅里叶变换，方便快捷获得相应频谱数值解析波形，分析波形与频谱对易关系。结果发现，矩形窗函数频谱是 Sa函数，窗宽变化导致 Sa函数波形变化。窗宽减小时，Sa函数波形展宽，振动舒缓，趋于零极限时，变成直流波形。窗宽增大时，Sa函数波形紧缩，振动加剧，趋于∞的极限时，演变成δ冲激波形，信号波形时频域是对易的。根据时频域波形与频谱对易关系，在分析莫尔条纹时，将莫尔条纹的一级谱滤出并归一，由波谱对易原理，时域信号将体现Sa函数，使条纹对比分明，便于提取相位信息。
수치해석신호파형시빈역대역연변과정，연구임의신호파형여빈솔조분적내재련계，병장해대역원리응용우막이조문상위분석，제취상위신식。채용구형창모의충격파형화직류파형적변환과정，통과공제구형창함수창관，획득각충관도구형맥충，창관추우령정황하획득충격파형，추우∞획득직류파형。자개발쾌속부리협변환（fast Fourier transform ，FFT ）계통，대구형맥충실시리산부리협변환，방편쾌첩획득상응빈보수치해석파형，분석파형여빈보대역관계。결과발현，구형창함수빈보시 Sa함수，창관변화도치 Sa함수파형변화。창관감소시，Sa함수파형전관，진동서완，추우령겁한시，변성직류파형。창관증대시，Sa함수파형긴축，진동가극，추우∞적겁한시，연변성δ충격파형，신호파형시빈역시대역적。근거시빈역파형여빈보대역관계，재분석막이조문시，장막이조문적일급보려출병귀일，유파보대역원리，시역신호장체현Sa함수，사조문대비분명，편우제취상위신식。
The mutual evolving processes of signals’ waveforms and their spectra were numerically analyzed in time and frequen-cy domains .The purpose was to research the essential relation between the signals ’ waveforms and their spectra .Then ,the mu-tual transform principle was applied to analyze moiré pattern spectra ,acquiring phase distribution information of the pattern . The rectangular window function was used to simulate the mutual transform between the impulse signal and direct-current wave-form .Many rectangular window signals with deferent widths were obtained by changing the window width .The unit impulse signal was obtained by changing the width down to zero ,and the direct-current waveform obtained by changing the width up to+ ∞ .For smart ,quick ,and easy implementation of discrete Fourier transforms to rectangular pulses and obtain signals ’ spec-tra ,a simple FFT system was worked out .With its calculating ,the mutual evolving processes of signals’ waveforms and their spectra were tracked deeply .All signals here were transformed with it .As the result ,first ,the spectra of rectangular window signals were in the form of sampling function [Sa(x)=sin(x)/x] .Second ,with the change in the window’s width ,the wave-form of Sa(x) changed .Third ,when the width decreased ,the waveform of Sa(x) extended ,and vibrated more slowly .It changed into direct-current waveform when the width decreased to zero .Last ,when the width increased ,the waveform of Sa(x) shranked ,and vibrated faster .It changed into impulse waveform when the width increased to + ∞ .Signals’ waveforms were in mutual transforms between the time and frequency domain .The transforming essence was considered as that the frequency com-ponent principle in Fourier series theory is reflected in the frequency domain .According to the principle of mutual transforms be-tween signals’ waveforms and their spectra ,the first order spectrum of the moiré pattern was extracted out and normalized to a constant one when the moiré patterns were analyzed for acquiring their phase information .By the normalization ,the moiré pat-tern should take on the sampling function model ,which showed high contrast level .This new pattern was convenient for acqui-ring the phase information .