The mutual evolving processes of signals' waveforms and their spectra were numerically analyzed in time and frequency domains. The purpose was to research the essential relation between the signals' waveforms and their spectra. Then, the mutual 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 waveform. 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 +infinity. For smart, quick, and easy implementation of discrete Fourier transforms to rectangular pulses and obtain signals' spectra, 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 waveform 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 +infinity. Signals' waveforms were in mutual transforms between the time and frequency domain. The transforming essence was considered as that the frequency component principle in Fourier series theory is reflected in the frequency domain. According to the principle of mutual transforms between 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 pattern should take on the sampling function model, which showed high contrast level. This new pattern was convenient for acquiring the phase information.