Topic
Non-uniform discrete Fourier transform
About: Non-uniform discrete Fourier transform is a research topic. Over the lifetime, 4067 publications have been published within this topic receiving 123952 citations.
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26 Apr 1985
TL;DR: A fast radix-2 two dimensional discrete cosine transform (DCT) is presented and a reduction of more than 50% in the number of multiplications and a comparable amount of additions is obtained in comparison to other algorithm.
Abstract: A fast radix-2 two dimensional discrete cosine transform (DCT) is presented. First, the mapping into a 2-D discrete Fourier transform (DFT) of a real signal is improved. Then an usual polynomial transform approach is used in order to map the 2-D DFT into a reduced size 2-D DFT and one dimensional odd DFT's. Finally, optimized odd DFT algorithms for real signals are developped. All together, a reduction of more than 50% in the number of multiplications and a comparable amount of additions is obtained in comparison to other algorithm.
117 citations
TL;DR: In this article, the authors compared the effectiveness of the discrete cosine and Fourier transforms in decorrelating sampled signals with Markov-1 statistics, and showed that the DCT offers a higher (or equal) effectiveness than the discrete Fourier transform for all values of the correlation coefficient.
Abstract: This correspondence compares the effectiveness of the discrete cosine and Fourier transforms in decorrelating sampled signals with Markov-1 statistics. It is shown that the discrete cosine transform (DCT) offers a higher (or equal) effectiveness than the discrete Fourier transform (DFT) for all values of the correlation coefficient. The mean residual correlation is shown to vanish as the inverse square root of the sample size.
116 citations
TL;DR: A watermarking method, which minimizes the impact of the watermark implementation on the overall quality of an image, is developed using a peak signal-to-noise ratio to evaluate quality degradation.
Abstract: In this paper, we evaluate the degradation of an image due to the implementation of a watermark in the frequency domain of the image. As a result, a watermarking method, which minimizes the impact of the watermark implementation on the overall quality of an image, is developed. The watermark is embedded in magnitudes of the Fourier transform. A peak signal-to-noise ratio is used to evaluate quality degradation. The obtained results were used to develop a watermarking strategy that chooses the optimal radius of the implementation to minimize quality degradation. The robustness of the proposed method was evaluated on the dataset of 1000 images. Detection rates and receiver operating characteristic performance showed considerable robustness against the print-scan process, print-cam process, amplitude modulated, halftoning, and attacks from the StirMark benchmark software.
115 citations
TL;DR: In this article, a unified and concise solution for inverse lattice problems is presented, which uses Ramanujan's sum rule, and a uniformly sampled arithmetic Fourier transform is presented in this work.
Abstract: The present work develops a unified and concise solution for inverse lattice problems. Also, a uniformly sampled arithmetic Fourier transform is presented in this work which uses Ramanujan's sum rule.
115 citations
TL;DR: In this article, a nonparametric method for the computation of instantaneous multivariate volatility for continuous semi-martingales, which is based on Fourier analysis, is presented. But the method is not suitable for the analysis of the entire market.
Abstract: We provide a nonparametric method for the computation of instantaneous multivariate volatility for continuous semi-martingales, which is based on Fourier analysis. The co-volatility is reconstructed as a stochastic function of time by establishing a connection between the Fourier transform of the prices process and the Fourier transform of the co-volatility process. A nonparametric estimator is derived given a discrete unevenly spaced and asynchronously sampled observations of the asset price processes. The asymptotic properties of the random estimator are studied: namely, consistency in probability uniformly in time and convergence in law to a mixture of Gaussian distributions.
114 citations