Band-limited signal extrapolation by truncated Bernstein polynomials
نویسندگان
چکیده
منابع مشابه
On the Extrapolation of Band-Limited Functions with Energy Constraints
Abstruct-A modification of the algorithm proposed by Papoulis and Gerchberg for extrapolating band-limited functions’ is suggested to extend its applicability over data corrupted by noise. We assume that energy constraints are known either for the band-limited signal or for the noise. In addition, the discrete formulation of the iterative algorithm is derived, and the transition from the con...
متن کاملJacobi polynomials in Bernstein form
The paper describes a method to compute a basis of mutually orthogonal polynomials with respect to an arbitrary Jacobi weight on the simplex. This construction takes place entirely in terms of the coefficients with respect to the so–called Bernstein–Bézier form of a polynomial.
متن کاملBernstein Polynomials and Brownian Motion
One of the greatest pleasures in mathematics is the surprising connections that often appear between apparently disconnected ideas and theories. Some particularly striking instances exist in the interaction between probability theory and analysis. One of the simplest is the elegant proof of the Weierstrass approximation theorem by S. Bernstein [2]: on the surface, this states that if f : [0, 1]...
متن کاملApproximation with Bernstein-Szegö polynomials
We present approximation kernels for orthogonal expansions with respect to Bernstein-Szegö polynomials. The construction is derived from known results for Chebyshev polynomials of the first kind and does not pose any restrictions on the Bernstein-Szegö polynomials.
متن کاملBernstein polynomials and learning theory
When learning processes depend on samples but not on the order of the information in the sample, then the Bernoulli distribution is relevant and Bernstein polynomials enter into the analysis. We derive estimates of the approximation of the entropy function x log x that are sharper than the bounds from Voronovskaja’s theorem. In this way we get the correct asymptotics for the Kullback-Leibler di...
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: Journal of Mathematical Analysis and Applications
سال: 1984
ISSN: 0022-247X
DOI: 10.1016/0022-247x(84)90047-7