Fourier transforms, analysis using periodicity requirement

Figure 3.48 shows the fibril organization on the micrometer scale. The fibril possesses a random orientation. Already at this magnification, a periodic pattern on top of the fibril is discernible. For a quantitative analysis, higher resolution images are required. As described in [102], the analysis of the pitch of the periodic pattern can be performed using fast Fourier transform procedures. Dehydration leads to an alteration of the observed structure, thus suggesting the need for studies in liquid... 

This expression covers two methods, Fourier analysis and Fourier synthesis. In almost all cases, it is used to mean Fourier analysis, whereby a periodic function is transformed into the sum of a series of sine waves with different frequencies. The result of the transformation consists of intensities and phases of sine waves. Fourier analysis is widely used in nuclear magnetic resonance and infrared spectroscopy to evaluate the intensities and frequencies of the absorbed waves while the sample is irradiated with equal intensities of all frequencies in a specified range. In such applications, the fast Fourier transformation (FFT) algorithm is most commonly used. The frequencies of the sine waves are harmonic and have a base frequency whose period is the measured time of the periodic function. Use of the FFT requires the values of the periodic function at several times in equal intervals. The number of data points has to be a power of two. 

---