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
TL;DR: In this paper, two matched chirps propagating through each other behave as a narrowband filter in wave vector space, with the filter centre moving at a rate proportional to the acoustic velocity and the chirp rate.
Abstract: The generation of Fourier transforms of electronic signals in real time with an acoustic-surface-wave convolver is demonstrated. Two matched chirps propagating through each other behave as a narrowband filter in wavevector space, with the filter centre moving at a rate proportional to the acoustic velocity and the chirp rate.
26 citations
DOI•
30 Dec 1899TL;DR: The Cooley-Tukey Algorithm as discussed by the authors was developed to compute the Discrete Fourier Transform for a large number of input points in relatively reasonable times, however, for certain uses a demand developed for computing the Fourier transform in a very short time or even in real time.
Abstract: With the advent of digital computers it became possible to compute the Discrete Fourier Transform for a large number of input points in relatively reasonable times. However, for certain uses a demand developed to compute the Discrete Fourier Transform in a very short time or even in real time. Also, a demand developed for computing the Fourier Transform for a very large number of input points. These demands resulted in a requirement for computing the Fourier Transform in the fastest time possible. A very economical way for computing the Fourier Transform was developed a few years ago and is known as the Cooley-Tukey Algorithm. This article describes another algorithm for computing the Discrete Fourier Transform where the required number of additions and subtractions is the same as in the Cooley-Tukey Algorithm; but the required number of multiplications is only one half of that in the Cooley-Tukey Algorithm.
26 citations
TL;DR: The algorithm is based on the Lagrange interpolation formula and the Green's theorem, which are used to preprocess the data before applying the fast Fourier transform, and readily generalizes to higher dimensions and to piecewise smooth functions.
26 citations
TL;DR: In this paper, the discrete inverse Radon transform of a function sampled on the product space of two two-dimensional spheres is determined as the solution of a minimization problem, which is iteratively solved using fast Fourier techniques for and SO(3).
Abstract: The inversion of the one-dimensional Radon transform on the rotation group SO(3) is an ill-posed inverse problem which applies to x-ray tomography with polycrystalline materials. This paper presents a novel approach to the numerical inversion of the one-dimensional Radon transform on SO(3). Based on a Fourier slice theorem the discrete inverse Radon transform of a function sampled on the product space of two two-dimensional spheres is determined as the solution of a minimization problem, which is iteratively solved using fast Fourier techniques for and SO(3). The favorable complexity and stability of the algorithm based on these techniques has been confirmed with numerical tests.
26 citations
TL;DR: A large interval can be selected as the threshold to obtain almost optimal filtering results and once the selected threshold is suitable, it is almost optimal.
Abstract: A simple phase unwrapping approach based on windowed Fourier filtering was proposed recently [K. Qian et al. A simple phase unwrapping approach based on filtering by windowed Fourier transform. Opt Laser Technol 2005;37:458–62]. The windowed Fourier filtering algorithm is an essential ingredient that suppresses the noise effectively and makes the phase unwrapping trivial. This paper adds a note on the threshold selection in the windowed Fourier filtering algorithm. A large interval can be selected as the threshold to obtain almost optimal filtering results. Once the selected threshold is suitable, it is almost optimal. This makes the threshold selection in the windowed Fourier filtering algorithm extremely easy.
26 citations