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.
Papers published on a yearly basis
Papers
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TL;DR: The computer simulation results show that the proposed image encryption algorithm is feasible, secure and robust to noise attack and occlusion.
32 citations
01 Jan 2001
TL;DR: The Nonuniform Discrete Fourier Transform (NDFT) is provided, which can be used to obtain frequency domain information of a finite-length signal at arbitrarily chosen frequency points and its applications in the design of 1-D and 2-D FIR digital filters are discussed.
Abstract: In many applications, when the representation of a discrete-time signal or a system in the frequency domain is of interest, the Discrete-Time Fourier Transform (DTFT) and the z-transform are often used. In the case of a discrete-time signal of finite length, the most widely used frequency-domain representation is the Discrete Fourier Transform (DFT), which is simply composed of samples of the DTFT of the sequence at equally spaced frequency points, or equivalently, samples of its z-transform at equally spaced points on the unit circle. A generalization of the DFT, introduced in this chapter, is the Nonuniform Discrete Fourier Transform (NDFT), which can be used to obtain frequency domain information of a finite-length signal at arbitrarily chosen frequency points. We provide an introduction to the NDFT and discuss its applications in the design of 1-D and 2-D FIR digital filters. We begin by introducing the problem of computing frequency samples of the z-transform of a finite-length sequence. We develop the basics of the NDFT, including its definition, properties and computational aspects. The NDFT is also extended to two dimensions. We propose NDFT-based nonuniform frequency sampling techniques for designing 1-D and 2-D FIR digital filters, and present design examples. The resulting filters are compared with those designed by other existing methods.
32 citations
Book•
10 Oct 2014
TL;DR: In this paper, the Fourier transform of an oscillating function has been studied in the context of radial functions and Oscillatory Integral Integrals and Fourier Transform in one variable.
Abstract: Foreword.- Introduction.- Chapter 1. Basic properties of the Fourier transform.- Chapter 2. Oscillatory integrals and Fourier transforms in one variable.- Chapter 3. The Fourier transform of an oscillating function.- Chapter 4. The Fourier transform of a radial function.- Chapter 5. Multivariate extensions.- Appendix.- Bibliography.
32 citations
TL;DR: In this article, a generalized convolution theorem in the fractional Fourier domain was proposed and generalized sampling expansion was shown to be a special case of the generalized Papoulis sampling expansion, and its application in the context of image superresolution was discussed.
32 citations