Non-uniform discrete Fourier transform

About: Non-uniform discrete Fourier transform is a research topic. Over the lifetime, 4067 publications have been published within this topic receiving 123952 citations.

Method for continuing Fourier spectra given by the fast Fourier transform

Abstract: A new method for continuing the Fourier spectrum of data of finite extent has been developed. Almost perfect restoration was obtained for noise-free data. Much improved resolution was obtained for error-laden data. Many forms of peak data lend themselves easily to the application of additional constraints that further enhance resolution almost to the theoretical limit.

The discrete fractional Fourier transformation

Abstract: Based on the fractional Fourier transformation of sampled periodic functions, the discrete form of the fractional Fourier transformation is obtained. It is found that for a certain dense set of fractional orders it is possible to define a discrete transformation. Also, for its efficient computation a fast algorithm, which has the same complexity as the FFT, is given.

Robust color texture features based on ranklets and discrete Fourier transform

Abstract: We present a set of multiscale, multidirectional, rotation-invariant features for color texture characterization. The proposed model is based on the ranklet transform, a technique relying on the calculation of the relative rank of the intensity level of neighboring pixels. Color and texture are merged into a compact descriptor by computing the ranklet transform of each color channel separately and of couples of color channels jointly. Robustness against rotation is based on the use of circularly symmetric neighborhoods together with the discrete Fourier transform. Experimental results demonstrate that the approach shows good robustness and accuracy.

Fast Fourier Transform for Step-Like Functions: The Synthesis of Three Apparently Different Methods

Abstract: In 1965 Cooley and Tukey published an algorithm for rapid calculation of the discrete Fourier transform (DFT), a particularly convenient calculating technique, which can well be applied to impulse-like functions whose beginning and end lie at the same level. Independently, various propositions were made to overcome the truncation error which arises, if a step-like function, i.e. one whose end level differs from its starting level, is treated in the same way. It was argued that they behave differently under the influence of noise, band-limited violation, and other experimental inconveniences. The aim of this paper is to show that the three widely and satisfactorily used techniques of Samulon, Nicolson, and Gans, which originate from apparently different ideas, are exactly the same. An extended DFT and fast Fourier transform (FFT) formula is deduced which is adapted as well to impulse-like as to step-like functions.