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.

Incoherent fractional Fourier transform and its optical implementation

Abstract: The fractional Fourier transform is redefined for working with incoherent light. As a real transformation, the incoherent fractional Fourier transform overcomes coherent system disadvantages such as the speckle effect and the need for incoherent–coherent conversion. It also might have some applications for digital image and signal processing owing to its decreased computing complexity. An incoherent optical implementation of the new transform based on the shearing interferometer is suggested. Laboratory experimental results are given.

Invariant pattern recognition for range images using the phase Fourier transform and a neural network

Abstract: A method for invariant pattern recognition of range images by means of the phase Fourier transform is introduced. The phase Fourier transform may be used for the segmentation of connected planar and quadric surfaces. The method is generalized to nonconnected planar surfaces through the use of the concept of the characteristic normal. An invariant representation under changes of position, scale, and orientation for the characteristic normals is defined. This representation is used as the input for a feedforward neural network. Examples of applications are given, and finally the method is applied to the problems of classification and occlusion.

Generation of all radix-2 fast Fourier transform algorithms using binary trees

Abstract: In this work a systematic method to generate all possible fast Fourier transform (FFT) algorithms is proposed based on the relation to binary trees. The binary tree is used to represent the decomposition of a discrete Fourier transform (DFT) into sub-DFTs. The radix is adaptively changed according to compute sub-DFTs in proposed decomposition. In this work we determine the number of possible algorithms for 2n-point FFTs with radix-2 butterfly operation and propose a simple method to determine the twiddle factor indices for each algorithm based on the binary tree representation.

Non-linear wave propagation solutions by Fourier transform perturbation

Abstract: A Fourier transform perturbation method is developed and used to obtain uniformly valid asymptotic approximations of the solution of a class of one-dimensional second order wave equations with small non-linearities. Multiple time scales are used and the initial-value problem on the infinite line is solved by Fourier transforming the wave equation and expanding the Fourier transform in powers of the small parameter. The non-linearity involves only the first partial derivatives of the dependent variable and the determination of the leading approximation is reduced to the solution of a pair of coupled non-linear ordinary differential equations in Fourier space. Examples are given involving a convolution non-linearity and a Van-der-Pol non-linearity.