Topic
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.
Papers published on a yearly basis
Papers
More filters
TL;DR: Effective methods are proposed for calculating a multidimensional discrete Fourier transform based on a new representation of it and their application to discrete number theory is proposed.
Abstract: Effective methods are proposed for calculating a multidimensional discrete Fourier transform based on a new representation of it.
39 citations
01 Jan 1986
TL;DR: It is concluded that the fast Fourier transform still has the advantage of speed, but the chirp-z transform offers some additional flexibility that makes it more useful in many applications.
Abstract: The advantages and disadvantages of three different algorithms for transforming frequency-domain data to the time domain are reviewed The algorithms are a direct computation of the Fourier series, the fast Fourier transform, and the chirp-z transform It is concluded that the fast Fourier transform still has the advantage of speed, but the chirp-z transform offers some additional flexibility that makes it more useful in many applications
39 citations
TL;DR: An algorithm called the quick Fourier transform (QFT) is developed that reduces the number of floating-point operations necessary to compute the DFT by a factor of two or four over direct methods or Goertzel's method for prime lengths.
Abstract: This paper looks at an approach that uses symmetric properties of the basis function to remove redundancies in the calculation of the discrete Fourier transform (DFT). We develop an algorithm called the quick Fourier transform (QFT) that reduces the number of floating-point operations necessary to compute the DFT by a factor of two or four over direct methods or Goertzel's method for prime lengths. By further application of the idea to the calculation of a DFT of length-2/sup M/, we construct a new O(NlogN) algorithm, with computational complexities comparable to the Cooley-Tukey algorithm. We show that the power-of-two QFT can be implemented in terms of discrete sine and cosine transforms. The algorithm can be easily modified to compute the DFT with only a subset of either input or output points and reduces by nearly half the number of operations when the data are real.
39 citations
TL;DR: In this paper, the exact expression for the discrete Fourier transform of a sum of exponentially damped sinusoids is derived, and its applicability for describing the general DFT spectrum is demonstrated.
39 citations
TL;DR: A new method of computing high-resolution narrow-band spectra faster than the chirp z transform and direct computation of discrete Fourier transform and in combination with Skinner's pruning algorithm for the decimation-in-time FFT formulation is presented.
Abstract: A new method of computing high-resolution narrow-band spectra faster than the chirp z transform (CZT) and direct computation of discrete Fourier transform (DFT) is presented. This is achieved by a generalization of Markel's pruning algorithm and in combination with Skinner's pruning algorithm for the decimation-in-time FFT formulation. However, for very high resolutions it is shown that the CZT is selectively superior to the new method.
39 citations