Topic
Discrete-time Fourier transform
About: Discrete-time Fourier transform is a research topic. Over the lifetime, 5072 publications have been published within this topic receiving 144643 citations. The topic is also known as: DTFT.
Papers published on a yearly basis
Papers
More filters
40 citations
TL;DR: In this article, the authors generalize the definition of self-Fourier functions and show that any Fourier transformable function is the linear combination of four self Fourier functions whose explicit form can be found.
Abstract: By generalizing the definition of self-Fourier functions recently introduced by Caola (1991), the authors show that any Fourier transformable function is the linear combination of four self-Fourier functions whose explicit form can be found.
40 citations
TL;DR: In this paper, the authors derived a minimum sampling interval for the curvature parameter and a maximum curvature range for which stability is guaranteed for general (irregular) sampling for the parabolic Radon transform.
Abstract: A good choice of the sampling in the transform domain is essential for a successful application of the parabolic Radon transform. The parabolic Radon transform is computed for each temporal frequency and is essentially equivalent to the nonuniform Fourier transform. This leads to new and useful insights in the parabolic Radon transform. Using nonuniform Fourier theory, we derive a minimum sampling interval for the curvature parameter and a maximum curvature range for which stability is guaranteed for general (irregular) sampling. A significantly smaller sampling interval requires stabilization. If diagonal stabilization is used, no gain in resolution is obtained. In contrast to conventional implementations, the curvature sampling interval is proposed to be inversely proportional to the temporal frequency. This results in improved quality of the transform and yields significant savings in computation time.
40 citations
40 citations
TL;DR: In this article, the time variant discrete Fourier transform (TVDFT) was proposed as an alternative order tracking method for rotating machinery, which is a combination of the Fast Fourier Transform (FFT) and the resampling based methods.
40 citations