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.
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TL;DR: A transform coding scheme for closed image boundaries on a plane using a Gaussian circular autoregressive model to represent the boundary data and the variances of the Fourier coefficients and the MAX quantizer is implemented.
Abstract: A transform coding scheme for closed image boundaries on a plane is described The given boundary is approximated by a series of straight line segments Depending on the shape, the boundary is represented by the (x-y) coordinates of the endpoints of the line segments or by the magnitude of the successive radii vectors that are equispaced in angle around the given boundary Due to the circularity present in the data, the discrete Fourier transform is used to exactly decorrelate the finite boundary data By fitting a Gaussian circular autoregressive model to represent the boundary data, estimates of the variances of the Fourier coefficients are obtained Using the variances of the Fourier coefficients and the MAX quantizer, the coding scheme is implemented The scheme is illustrated by an example
114 citations
TL;DR: In this article, the authors propose to use multifractal analysis in reciprocal space as a tool to characterise, in a statistical and global sense, the nature of the Fourier transform of geometrical models for atomic structures.
Abstract: The authors propose to use multifractal analysis in reciprocal space as a tool to characterise, in a statistical and global sense, the nature of the Fourier transform of geometrical models for atomic structures. This approach is especially adequate for shedding some new light on a class of structures introduced recently, which exhibit 'singular scattering'. Using the language of measure theory, the Fourier intensity of these models is presumably singular continuous, and therefore represents an intermediate type of order, between periodic or quasiperiodic structures, characterised by Bragg peaks (atomic Fourier transform), and amorphous structures, which exhibit diffuse scattering (absolutely continuous Fourier transform). This general approach is illustrated in several examples of self-similar one-dimensional sequences and structures, generated by substitutions. A special emphasis is put on the relationship between the nature of the Fourier intensity of these models and the f( alpha ) spectrum obtained by multifractal analysis in reciprocal space.
113 citations
TL;DR: In this paper, two mathematical procedures of band narrowing using Fourier transforms are discussed and the methods of Fourier self-deconvolution and Fourier derivation are easier to use and to control than procedures which rely on the use of convolution functions.
113 citations
Book•
01 Jan 2006
TL;DR: Introduction Data Acquisition Noise Signal Averaging Real and Complex Fourier Series Continuous, Discrete, and Fast Fourier transform Fourier Transform Applications LTI systems, Convolution, Correlation, and Coherence Laplace and z-Transform.
Abstract: Introduction Data Acquisition Noise Signal Averaging Real and Complex Fourier Series Continuous, Discrete, and Fast Fourier Transform Fourier Transform Applications LTI systems, Convolution, Correlation, and Coherence Laplace and z-Transform Introduction to Filters: the RC-Circuit Filters: Analysis Filters: Specification, Bode plot, Nyquist plot Filters: Digital Filters Spike Train Analysis Wavelet Analysis: Time Domain Properties Wavelet Analysis: Frequency Domain Properties Nonlinear Techniques
112 citations
TL;DR: In this paper, the same rules can be applied to create a new type of fractional-order Fourier transform which results in a smooth transition of a function when transformed between the real and Fourier spaces.
112 citations