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 article, the authors develop and study two conceptually new ways to define convolution products for hypercomplex Fourier transforms, which will enable the development and fast implementation of new filters for quaternionic signals and systems, as well as for their higher dimensional counterparts.
Abstract: Hypercomplex Fourier transforms are increasingly used in signal processing for the analysis of higher-dimensional signals such as color images. A main stumbling block for further applications, in particular concerning filter design in the Fourier domain, is the lack of a proper convolution theorem. The present paper develops and studies two conceptually new ways to define convolution products for such transforms. As a by-product, convolution theorems are obtained that will enable the development and fast implementation of new filters for quaternionic signals and systems, as well as for their higher dimensional counterparts.
35 citations
TL;DR: In this article, it was shown that the most natural extension of the DHT to two dimensions fails to be separate in two dimensions, and is therefore inefficient, and an alternative separable form is considered, corresponding convolution theorem is derived.
Abstract: Bracewell has proposed the Discrete Hartley Transform (DHT) as a substitute for the Discrete Fourier Transform (DFT), particularly as a means of convolution. Here, it is shown that the most natural extension of the DHT to two dimensions fails to be separate in the two dimensions, and is therefore inefficient. An alternative separable form is considered, corresponding convolution theorem is derived. That the DHT is unlikely to provide faster convolution than the DFT is also discussed.
35 citations
35 citations
TL;DR: In this paper, the authors apply techniques from non-commutative harmonic analysis to the development of fast algorithms for the computation of convolution integrals on motion groups, in particular on the group of rigid-body motions in 3-space, denoted here as SE(3).
35 citations
TL;DR: An optical system is used to provide the transform of the input image in this design and a digital postprocessor performs a differentiation process on these Fourier magnitude samples to obtain a vector of values which are combined in a predetermined fashion to provided the geometric moments of the original input function.
Abstract: A new system for calculating the geometric moments of an input image is presented. The system is based on a mathematical derivation that relates the geometric moments of the input image to the intensity of the Fourier transform of the image. Since optical systems are very efficient at obtaining Fourier transforms, an optical system is used to provide the transform of the input image in this design. An array of detectors is then used to sample the Fourier plane, and a digital postprocessor performs a differentiation process on these Fourier magnitude samples to obtain a vector of values which are combined in a predetermined fashion to provide the geometric moments of the original input function.
35 citations