Generalized Regular Sampling of Trigonometric Polynomials and Optimal Sensor Arrangement
نویسندگان
چکیده
منابع مشابه
Random Sampling of Sparse Trigonometric Polynomials
We study the problem of reconstructing a multivariate trigonometric polynomial having only few non-zero coefficients from few random samples. Inspired by recent work of Candes, Romberg and Tao we propose to recover the polynomial by Basis Pursuit, i.e., by l-minimization. Numerical experiments show that in many cases the trigonometric polynomial can be recovered exactly provided the number N of...
متن کاملDeterministic Sampling of Sparse Trigonometric Polynomials
One can recover sparse multivariate trigonometric polynomials from few randomly taken samples with high probability (as shown by Kunis and Rauhut). We give a deterministic sampling of multivariate trigonometric polynomials inspired by Weil’s exponential sum. Our sampling can produce a deterministic matrix satisfying the statistical restricted isometry property, and also nearly optimal Grassmann...
متن کاملRandom Sampling of Multivariate Trigonometric Polynomials
We investigate when a trigonometric polynomial p of degree M in d variables is uniquely determined by its sampled values p(xj) on a random set of points xj in the unit cube (the “sampling problem for trigonometric polynomials”) and estimate the probability distribution of the condition number for the associated Vandermonde-type and Toeplitz-like matrices. The results provide a solid theoretical...
متن کاملRearrangements of Trigonometric Series and Trigonometric Polynomials
Abstract. The paper is related to the following question of P. L. Ul’yanov: is it true that for any 2π-periodic continuous function f there is a uniformly convergent rearrangement of its trigonometric Fourier series? In particular, we give an affirmative answer if the absolute values of Fourier coefficients of f decrease. Also, we study a problem how to choose m terms of a trigonometric polynom...
متن کاملImplicitization of Curves Parameterized by Generalized Trigonometric Polynomials
Consider a plane curve given parametrically by a generalized trigonometric polynomial, that is, x + iy = P n k=1 a k e ik. In this paper, we obtain an impliciti-zation of the curve, that is, an equation in x and y which captures all the points on the curve and, if any, only nitely many more points.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IEEE Signal Processing Letters
سال: 2010
ISSN: 1070-9908,1558-2361
DOI: 10.1109/lsp.2010.2041962