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 new approach for image encryption based on the real-valuedness of the reality-preserving multiple-parameter fractional Fourier transform and the decorrelation property of chaotic maps is proposed in order to meet the requirements of the secure image transmission.
62 citations
TL;DR: It is shown that it is possible to define the autocorrelation function of symbolic data, assuming only that the authors can compare any two symbols and decide if they are equal or distinct, and another interpretation of the spectrum is given, borrowing from the spectral envelope concept.
61 citations
TL;DR: Empirically evaluate a recently proposed Fast Approximate Discrete Fourier Transform (FADFT) algorithm, FADFT-2, for the first time and it is shown that FAD FT-2 not only generally outperforms F ADFT-1 on all but the sparsest signals, but is also significantly faster than FFTW 3.1 on large sparse signals.
Abstract: In this paper we empirically evaluate a recently proposed Fast Approximate Discrete Fourier Transform (FADFT) algorithm, FADFT-2, for the first time. FADFT-2 returns approximate Fourier representations for frequency-sparse signals and works by random sampling. Its implemen- tation is benchmarked against two competing methods. The first is the popular exact FFT imple- mentation FFTW Version 3.1. The second is an implementation of FADFT-2’s ancestor, FADFT-1. Experiments verify the theoretical runtimes of both FADFT-1 and FADFT-2. In doing so it is shown that FADFT-2 not only generally outperforms FADFT-1 on all but the sparsest signals, but is also significantly faster than FFTW 3.1 on large sparse signals. Furthermore, it is demonstrated that FADFT-2 is indistinguishable from FADFT-1 in terms of noise tolerance despite FADFT-2’s better execution time.
61 citations
TL;DR: A maximum-likelihood estimation method is presented which in parallel with the system transfer function also estimates a parametric noise transfer function, leading to a consistent and efficient estimator.
61 citations
TL;DR: This work shows that the original bulk-optics configuration for performing the fractional-Fourier-transform operation provides a scaled output using a fixed lens and suggests an asymmetrical setup for obtaining a non-scaled output.
Abstract: Recently two optical interpretations of the fractional Fourier transform operator were introduced. We address implementation issues of the fractional-Fourier-transform operation. We show that the original bulk-optics configuration for performing the fractional-Fourier-transform operation [J. Opt. Soc. Am. A 10, 2181 (1993)] provides a scaled output using a fixed lens. For obtaining a non-scaled output, an asymmetrical setup is suggested and tested. For comparison, computer simulations were performed. A good agreement between computer simulations and experimental results was obtained.
61 citations