Macdonald's Evaluation Conjectures and Difference Fourier Transform

In the previous author's paper the Macdonald norm conjecture (including the famous constant term conjecture) was proved. This paper contains the proof of the remaining two (the duality and evaluation conjectures). The evaluation theorem is in fact a $q,t$-generalization of the classic Weyl dimension formula. As to the duality theorem, it states that the generalized trigonometric-difference zonal Fourier transform is self-dual (at least formally). We define this transform in terms of double affine Hecke algebras related to elliptic braid groups. The duality appeared to be directly connected with the transposition of the periods of an elliptic curve.Comment: 16 pg., AMSTe

Macdonald's Evaluation Conjectures, Difference Fourier Transform, and Applications

This paper contains the proof of Macdonald's duality and evaluation conjectures, the definition of the difference Fourier transform, the recurrence theorem generalizing Pieri rules, and the action of GL(2,Z) on the Macdonald polynomials at roots of unity.Comment: AMSTe

Sparse and Cosparse Audio Dequantization Using Convex Optimization

The paper shows the potential of sparsity-based methods in restoring quantized signals. Following up on the study of Brauer et al. (IEEE ICASSP 2016), we significantly extend the range of the evaluation scenarios: we introduce the analysis (cosparse) model, we use more effective algorithms, we experiment with another time-frequency transform. The paper shows that the analysis-based model performs comparably to the synthesis-model, but the Gabor transform produces better results than the originally used cosine transform. Last but not least, we provide codes and data in a reproducible way

About Calculation of the Hankel Transform Using Preliminary Wavelet Transform

The purpose of this paper is to present an algorithm for evaluating Hankel transform of the null and the first kind. The result is the exact analytical representation as the series of the Bessel and Struve functions multiplied by the wavelet coefficients of the input function. Numerical evaluation of the test function with known analytical Hankel transform illustrates the proposed algorithm.Comment: 5 pages, 2 figures. Some misprints are correcte

The FFX Correlator

We established a new algorithm for correlation process in radio astronomy. This scheme consists of the 1st-stage Fourier Transform as a filter and the 2nd-stage Fourier Transform for spectroscopy. The "FFX" correlator stands for Filter and FX architecture, since the 1st-stage Fourier Transform is performed as a digital filter, and the 2nd-stage Fourier Transform is performed as a conventional FX scheme. We developed the FFX correlator hardware not only for the verification of the FFX scheme algorithm but also for the application to the Atacama Submillimeter Telescope Experiment (ASTE) telescope toward high-dispersion and wideband radio observation at submillimeter wavelengths. In this paper, we present the principle of the FFX correlator and its properties, as well as the evaluation results with the production version.Comment: 20 figure

Corrections of the NIST Statistical Test Suite for Randomness

It is well known that the NIST statistical test suite was used for the evaluation of AES candidate algorithms. We have found that the test setting of Discrete Fourier Transform test and Lempel-Ziv test of this test suite are wrong. We give four corrections of mistakes in the test settings. This suggests that re-evaluation of the test results should be needed