Application of the one-dimensional Fourier transform for tracking moving objects in noisy environments

1983 ◽  
Vol 21 (2) ◽  
pp. 280-293 ◽  
Author(s):  
Sarah A. Rajala ◽  
Alfy N. Riddle ◽  
Wesley E. Snyder

The structures of various ordered, but non-periodic, systems have been investigated and exhibit features which can be directly described by means of a construction which the authors call the shift lattice , which is a simple generalization of the concept of the lattice. This paper is devoted to a description of the properties of the one-dimensional shift lattice and its Fourier transform. Its applications to the phases related to L–Ta 2 O 5 and some Bi 2 TeO 5 -related systems are outlined and its relation to the theory of modulated structures and their Fourier transforms is briefly discussed.


2002 ◽  
Vol 11 (04) ◽  
pp. 405-426 ◽  
Author(s):  
JIUN-IN GUO ◽  
CHIEN-CHANG LIN ◽  
CHIH-DA CHIEN

This paper presents a new low-power parameterized hardware design for the one-dimensional (1D) discrete Fourier transform (DFT) of variable lengths. By combining the cyclic convolution formulation, block-based distributed arithmetic (BDA), and Cooley–Tukey decomposition algorithm together, we have developed a parameterized hardware design for the DFT of variable lengths ranging from 256 to 4096 points and with different modes of performance. The proposed design can perform different lengths of DFT computation through the configuration of parameters, which not only provides the flexibility in computing different length DFT but also facilitates the performance-driven design considerations in terms of power consumption and processing speeds, that is, we can configure the proposed design in different modes of performance by setting different parameters. This feature is beneficial to developing a parameterized DFT soft Intellectual Property (IP) core or hard IP core for meeting the system requirements of different silicon-on-a-chip (SOC) applications as compared with the existing fixed length DFT designs.


2014 ◽  
Vol 651-653 ◽  
pp. 2241-2244
Author(s):  
Ying Yu ◽  
Cai Lin Dong ◽  
Bo Wen Sheng ◽  
Wei Dan Zhong ◽  
Xiang Lin Zou

With the aim to meet the requirements of multi-directional choice, the paper raise a new approach to the invariant feature extraction of handwritten Chinese characters, with ridgelet transform as its foundation. First of all, the original images will be rotated to the Radon circular shift by means of Radon transform. On the basis of the characteristic that Fourier transform is row shift invariant, then, the one-dimensional Fourier transform will be adopted in the Radon domain to gain the conclusion that magnitude matrixes bear the rotation-invariance as a typical feature, which is pretty beneficial to the invariant feature extraction of rotation. When such is done, one-dimensional wavelet transform will be carried out in the direction of rows, thus achieving perfect choice of frequency, which makes it possible to extract the features of sub-line in the appropriate frequencies. Finally, the average values, standard deviations and the energy values will form the feature vector which is extracted from the ridgelet sub-bands. The approaches mentioned in the paper could satisfy the requirements from the form automatic processing on the recognition of handwritten Chinese characters.


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