Orthogonal sets of data windows constructed from trigonometric polynomials
نویسندگان
چکیده
منابع مشابه
Orthogonal sets of data windows constructed from trigonometric polynomials
In contrast to common practise in many other physical sciences, the statistical analysis of PTTI data is often based directly on time domain techniques rather than on frequency domain (spectral analysis) techniques. The predominant analysis technique in the PTTI community, namely, the two-sample (or Allan) variance, is often used to indirectly infer frequency domain properties under the assumpt...
متن کاملConnection of Semi-integer Trigonometric Orthogonal Polynomials with Szegö Polynomials
In this paper we investigate connection between semi-integer orthogonal polynomials and Szegő’s class of polynomials, orthogonal on the unit circle. We find a representation of the semi-integer orthogonal polynomials in terms of Szegő’s polynomials orthogonal on the unit circle for certain class of weight functions.
متن کاملOrthogonal trigonometric polynomials: Riemann-Hilbert analysis and relations with OPUC
Abstract. In this paper, we study the theory of orthogonal trigonometric polynomials (OTP). We obtain asymptotics of OTP with positive and analytic weight functions by Riemann-Hilbert approach and find they have relations with orthogonal polynomials on the unit circle (OPUC). By the relations and the theory of OPUC, we also get four-terms recurrent formulae, ChristoffelDarboux formula and some ...
متن کاملReconstructing hyperbolic cross trigonometric polynomials by sampling along generated sets
The evaluation of multivariate trigonometric polynomials at the nodes of a rank-1 lattice leads to a onedimensional discrete Fourier transform. Often, one is also interested in the reconstruction of the Fourier coefficients from their samples. We present necessary and sufficient conditions on rank-1 lattices allowing a stable reconstruction of trigonometric polynomials supported on hyperbolic c...
متن کاملMinimizing trigonometric matrix polynomials over semi-algebraic sets
This paper addresses the problem of minimizing the minimum eigenvalue of a trigonometric matrix polynomial. The contribution is to show that, by exploiting Putinar’s Positivstellensatz and introducing suitable transformations, it is possible to derive a nonconservative approach based on semidefinite programming (SDP) whose computational burden can be significantly smaller than that of an existi...
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 Transactions on Acoustics, Speech, and Signal Processing
سال: 1990
ISSN: 0096-3518
DOI: 10.1109/29.56034