Topic
Discrete sine transform
About: Discrete sine transform is a research topic. Over the lifetime, 3269 publications have been published within this topic receiving 73181 citations.
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TL;DR: In this paper, a new realized volatility estimator based on a combination of the multi-scale regression and discrete sine transform (DST) approaches is presented, which can be constructed within a simple regression-based approach by exploiting the linear relation existing between the market microstructure bias and the realized volatilities computed at different frequencies.
Abstract: In this study we present a new realized volatility estimator based on a combination of the multi-scale regression and discrete sine transform (DST) approaches. Multi-scale estimators similar to that recently proposed by Zhang (2006) can, in fact, be constructed within a simple regression-based approach by exploiting the linear relation existing between the market microstructure bias and the realized volatilities computed at different frequencies. We show how such a powerful multi-scale regression approach can also be applied in the context of the Zhou [Nonlinear Modelling of High Frequency Financial Time Series, pp. 109–123, 1998] or DST orthogonalization of the observed tick-by-tick returns. Providing a natural orthonormal basis decomposition of observed returns, the DST permits the optimal disentanglement of the volatility signal of the underlying price process from the market microstructure noise. The robustness of the DST approach with respect to the more general dependent structure of the microstruct...
37 citations
TL;DR: This work compares the fidelity in reproducing the classical harmonic motion of discrete coherent states of the N x N Fourier matrix with several options considered in the literature.
Abstract: The N×N Fourier matrix is one distinguished element within the group U(N) of all N×N unitary matrices. It has the geometric property of being a fourth root of unity and is close to the dynamics of harmonic oscillators. The dynamical correspondence is exact only in the N→∞ contraction limit for the integral Fourier transform and its fractional powers. In the finite-N case, several options have been considered in the literature. We compare their fidelity in reproducing the classical harmonic motion of discrete coherent states.
37 citations
07 Jun 1988
TL;DR: An efficient method for computing the discrete Fourier transform when only a few output points are needed is described, based on a novel factorization of the DFT, where one part is computed using standard power-of-two FFTs and the other uses a technique similar to the Goertzel algorithm.
Abstract: The authors describe an efficient method for computing the discrete Fourier transform (DFT) when only a few output points are needed. The method is shown to be more efficient than either Goertzel's method or pruning, and it allows any band in the output to be computed. It is based on a novel factorization of the DFT, where one part is computed using standard power-of-two FFTs (fast Fourier transforms) and the other uses a technique similar to the Goertzel algorithm. >
37 citations
19 Apr 2015
TL;DR: Objective results indicate that this representation of f0 improves f0 prediction over traditional short-term approaches and is comparable to the recently proposed CWT-HMM, while using less parameters.
Abstract: We propose a representation of f0 using the Continuous Wavelet Transform (CWT) and the Discrete Cosine Transform (DCT). The CWT decomposes the signal into various scales of selected frequencies, while the DCT compactly represents complex contours as a weighted sum of cosine functions. The proposed approach has the advantage of combining signal decomposition and higher-level representations, thus modeling low-frequencies at higher levels and high-frequencies at lower-levels. Objective results indicate that this representation improves f0 prediction over traditional short-term approaches. Subjective results show that improvements are seen over the typical MSD-HMM and are comparable to the recently proposed CWT-HMM, while using less parameters. These results are discussed and future lines of research are proposed.
37 citations
TL;DR: The numerical simulations have demonstrated the validity and high security level of the image cryptosystem based on the novel transform which is similar to fractional Fourier transform and gyrator transform to some extent.
37 citations