In mathematics, discrete Chebyshev polynomials, or Gram polynomials, are a type of discrete orthogonal polynomials used in approximation theory, introduced...

The Chebyshev polynomials are two sequences of orthogonal polynomials related to the cosine and sine functions, notated as T n ( x ) {\displaystyle T_{n}(x)}...

include the discrete Chebyshev polynomials, Charlier polynomials, Krawtchouk polynomials, Meixner polynomials, dual Hahn polynomials, Hahn polynomials, and Racah...

coefficients of Chebyshev polynomials of the first kind. Other discrete Chebyshev transforms involve related grids and coefficients of Chebyshev polynomials of the...

Gegenbauer polynomials form the most important class of Jacobi polynomials; they include the Chebyshev polynomials, and the Legendre polynomials as special...

named after Pafnuty Chebyshev because its mathematical characteristics are derived from Chebyshev polynomials. Type I Chebyshev filters are usually referred...

Hermite polynomials were defined by Pierre-Simon Laplace in 1810, though in scarcely recognizable form, and studied in detail by Pafnuty Chebyshev in 1859...

form" Chebyshev norm Discrete Chebyshev polynomials Discrete Chebyshev transform Chebyshev rational functions Chebyshev–Gauss quadrature Chebyshev–Markov–Stieltjes...

Chebyshev polynomials, and fast DCT algorithms (below) are used in Chebyshev approximation of arbitrary functions by series of Chebyshev polynomials,...

multiple dimensions Discrete Chebyshev polynomials — polynomials orthogonal with respect to a discrete measure Favard's theorem — polynomials satisfying suitable...

4}\delta ^{-2}n^{-1}.} (Chebyshev's inequality) It follows that the polynomials fn tend to f uniformly. Bernstein polynomials can be generalized to k...

fast algorithms for discrete cosine or sine transforms (e.g. fast DCT used for JPEG and MPEG/MP3 encoding and decoding), fast Chebyshev approximation, solving...

wavelets are examples of orthogonal functions with discrete ranges. Legendre and Chebyshev polynomials provide orthogonal families for the interval [−1...

a polynomial of degree N. One can obtain polynomials very close to the optimal one by expanding the given function in terms of Chebyshev polynomials and...

than fixed in advance. Discrete Chebyshev transforms (on the 'roots' grid and the 'extrema' grid of the Chebyshev polynomials of the first kind). This...

derived at the Chebyshev Gauss–Lobatto collocation points by using the discrete orthogonal relationship of the Chebyshev polynomials. Then, using two...

{\displaystyle s_{n}} . The polynomials are normalized by setting ω c = 1 {\displaystyle \omega _{c}=1} . The normalized Butterworth polynomials then have the general...

terms of Chebyshev polynomials. Equivalently, they employ a change of variables x = cos ⁡ θ {\displaystyle x=\cos \theta } and use a discrete cosine transform...

parameter α sets the Chebyshev norm of the sidelobes to −20α decibels. The window function can be calculated from W0(k) by an inverse discrete Fourier transform...

Chebyshev polynomials. Linear interpolation uses a linear function for each of intervals [xk,xk+1]. Spline interpolation uses low-degree polynomials in...

non-uniform discrete Fourier transform (NUDFT or NDFT) of a signal is a type of Fourier transform, related to a discrete Fourier transform or discrete-time Fourier...

Chebyshev space is the subspace of Chebyshev polynomials of order n in the space of real continuous functions on an interval, C[a, b]. The polynomial...

Hahn polynomials are a family of orthogonal polynomials in the Askey scheme of hypergeometric orthogonal polynomials, introduced by Pafnuty Chebyshev in...

polynomials in r1, r2, r3, and a. The proof then results in the verification of the equality of two polynomials. If the coefficients of a polynomial are...

Thomas Parks in 1972, is an iterative algorithm for finding the optimal Chebyshev finite impulse response (FIR) filter. The Parks–McClellan algorithm is...

Detector used in image processing. Butterworth filter Comb filter Chebyshev filter Discrete Gaussian kernel Elliptic filter Gaussian blur Gaussian pyramid...

It is one of several graph polynomials studied in algebraic graph theory. Several different types of matching polynomials have been defined. Let G be...

mathematics, the dual Hahn polynomials are a family of orthogonal polynomials in the Askey scheme of hypergeometric orthogonal polynomials. They are defined on...

discrete Chebyshev polynomial, and the corresponding eigenvalue, P ℓ ( cos ⁡ β ) {\displaystyle P_{\ell }(\cos \beta )} , is the Legendre polynomial....

scaling the H ( s ) {\displaystyle H(s)} polynomials to the inverse of that frequency. To scale the polynomials, simply append ω c {\displaystyle \omega...