Fourier methods give excellent frequency estimation performance with either single complex exponentials or long data lengths. For multiple exponentials parametric techniques offer superior resolution. This work examines the signal conditions which determine the choice of a particular method. Equations are developed that describe the Fourier performance with data length, SNR and relative frequen...

When unity reflectance is approached, the Fourier-transform method of calculating the reflectance spectrum of an optical grating modulated by a slowly varying envelope becomes unacceptably inaccurate. The modified Fourier transform method of Bovard [Appl. Opt. 29, 24 (1990)] can achieve complete accuracy for quarter-wave gratings. We report herein the extension of Bovard's method to non-quarter...

This work reports on investigation of the sensitivity of a Fourier-transform spectrometer to noise sources based on Monte-Carlo simulation of measurement of a single spectrum. Flexibility of this approach permits easily to imitate various noise contaminations of the interferograms and to obtain statistically reliable results for widely varying noise characteristics. More specifically, we evalua...

Because of mass assignment onto grid points in the measurement of the power spectrum using the Fast Fourier Transform (FFT), the raw power spectrum |δ f (k)| 2 estimated with FFT is not the same as the true power spectrum P (k). In this paper, we derive the formula which relates |δ

This papers deals with the analysis of shape and size of the debris particles obtained from wear experiments on polymers using image processing. Two analysis techniques that are very promising in this respect are the morphological pattern spectrum and the Fourier spectrum. They can be used to extract parameters that relate to particle size and shape. We experimentally compare different choices ...

The Fast Fourier Transform was applied to spatial spectrum modeling of a one-dimensional fractal (Cantor set), a two-dimensional fractal (Sierpinski carpet), and a three-dimensional fractal (Menger sponge). A spectrum is developed for different levels. The spatial spectrum was also obtained and modeled for various filling parameters. The ParaView software package was used for 3D modeling.

Because of mass assignment onto grid points in the measurement of the power spectrum using the Fast Fourier Transform (FFT), the raw power spectrum |δ f (k)| 2 estimated with FFT is not the same as the true power spectrum P (k). In this paper, we derive the formula which relates |δ