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: This work applies the language of the unified FT to develop FRT expressions for discrete and continuous signals, introducing a particular form of periodicity: chirp-periodicity.
Abstract: The fractional Fourier transform (FRT) is an extension of the ordinary Fourier transform (FT). Applying the language of the unified FT, we develop FRT expressions for discrete and continuous signals, introducing a particular form of periodicity: chirp-periodicity. The FRT sampling theorem is derived as an extension of its ordinary counterpart.
152 citations
TL;DR: The purpose of this paper is to introduce extensions of the FT¿s convolution theorem, dealing with the FRFT of a product and of a convolution of two functions.
Abstract: The fractional Fourier transform (FRFT) is a generalization of the classical Fourier transform (FT). It has recently found applications in several areas, including signal processing and optics. Many properties of this transform are already known, but an extension of the FT?s convolution theorem is still missing. The purpose of this paper is to introduce extensions of this theorem, dealing with the FRFT of a product and of a convolution of two functions.
150 citations
TL;DR: In this paper, the influence of time-domain noise on the results of a discrete Fourier transform (DFT) was studied and it was shown that the resulting frequency domain noise can be modeled using a Gaussian distribution with a covariance matrix which is nearly diagonal.
Abstract: An analysis is made to study the influence of time-domain noise on the results of a discrete Fourier transform (DFT). It is proven that the resulting frequency-domain noise can be modeled using a Gaussian distribution with a covariance matrix which is nearly diagonal, imposing very weak assumptions on the noise in the time domain.
150 citations
147 citations
06 Mar 2015
TL;DR: In this paper, the Fourier analysis of a continuous periodic signal in the time domain gives a series of discrete frequency components in the frequency domain, which is the sum of sinusoidal components of different frequencies.
Abstract: The French mathematician J. B. J. Fourier showed that arbitrary periodic functions could be represented by an infinite series of sinusoids of harmonically related frequencies. This chapter first defines periodic functions and orthogonal functions. A periodic function can be expanded in a Fourier series. The Fourier series of a periodic function is the sum of sinusoidal components of different frequencies. The chapter then illustrates the functions of odd or skew symmetry, even symmetry and half-wave symmetry. The odd and even symmetry has been obtained with the triangular function by shifting the origin. Fourier analysis of a continuous periodic signal in the time domain gives a series of discrete frequency components in the frequency domain. The chapter describes Dirichlet conditions and notion of power spectrum. Finally, it explains the function of convolution, which is generally carried out in the frequency domain.
147 citations