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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
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Journal ArticleDOI
TL;DR: A new linear integral transform is defined, which is called the exponential chirp transform, which provides frequency domain image processing for space-variant image formats, while preserving the major aspects of the shift-invariant properties of the usual Fourier transform.
Abstract: Space-variant (or foveating) vision architectures are of importance in both machine and biological vision. In this paper, we focus on a particular space-variant map, the log-polar map, which approximates the primate visual map, and which has been applied in machine vision by a number of investigators during the past two decades. Associated with the log-polar map, we define a new linear integral transform, which we call the exponential chirp transform. This transform provides frequency domain image processing for space-variant image formats, while preserving the major aspects of the shift-invariant properties of the usual Fourier transform. We then show that a log-polar coordinate transform in frequency provides a fast exponential chirp transform. This provides size and rotation, in addition to shift, invariant properties in the transformed space. Finally, we demonstrate the use of the fast exponential chirp algorithm on a database of images in a template matching task, and also demonstrate its uses for spatial filtering.

51 citations

Book ChapterDOI
01 Jan 1982
TL;DR: In this article, the main properties of the discrete Fourier transform (DFT) are summarized and various fast DFT computation techniques known collectively as the Fast Fourier Transform (FFT) algorithm are presented.
Abstract: The object of this chapter is to briefly summarize the main properties of the discrete Fourier transform (DFT) and to present various fast DFT computation techniques known collectively as the fast Fourier transform (FFT) algorithm. The DFT plays a key role in physics because it can be used as a mathematical tool to describe the relationship between the time domain and frequency domain representation of discrete signals. The use of DFT analysis methods has increased dramatically since the introduction of the FFT in 1965 because the FFT algorithm decreases by several orders of magnitude the number of arithmetic operations required for DFT computations. It has thereby provided a practical solution to many problems that otherwise would have been intractable.

50 citations

Journal ArticleDOI
TL;DR: A new method for the discrete fractional Fourier transform (DFRFT) computation is given and the DFRFT of any angle can be computed by a weighted summation of the D FRFTs with the special angles.
Abstract: A new method for the discrete fractional Fourier transform (DFRFT) computation is given in this paper. With the help of this method, the DFRFT of any angle can be computed by a weighted summation of the DFRFTs with the special angles.

50 citations

Journal ArticleDOI
TL;DR: In this article, a regular acquisition grid that minimizes the mixing between the unknown spectrum of the well-sampled signal and aliasing artifacts is proposed to recover 2D signals that are band-limited in one spatial dimension.
Abstract: Random sampling can lead to algorithms in which the Fourier reconstruction is almost perfect when the underlying spectrum of the signal is sparse or band-limited. Conversely, regular sampling often hampers the Fourier data recovery methods. However, 2D signals that are band-limited in one spatial dimension can be recovered by designing a regular acquisition grid that minimizes the mixing between the unknown spectrum of the well-sampled signal and aliasing artifacts. This concept can be easily extended to higher dimensions and used to define potential strategies for acquisition-guided Fourier reconstruction. The wavenumber response of various sampling operators is derived and sampling conditions for optimal Fourier reconstruction are investigated using synthetic and real data examples.

50 citations

Journal ArticleDOI
TL;DR: A more efficient algorithm is presented, based on the properties of the Radon transform and the two-dimensional (2-D) fast Fourier transform, which can sacrifice little performance for significant computational savings.
Abstract: In this work, we describe a frequency domain technique for the estimation of multiple superimposed motions in an image sequence. The least-squares optimum approach involves the computation of the three-dimensional (3-D) Fourier transform of the sequence, followed by the detection of one or more planes in this domain with high energy concentration. We present a more efficient algorithm, based on the properties of the Radon transform and the two-dimensional (2-D) fast Fourier transform, which can sacrifice little performance for significant computational savings. We accomplish the motion detection and estimation by designing appropriate matched filters. The performance is demonstrated on two image sequences.

50 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202318
202233
20213
20201
20191
20189