Sentence examples for form a complete basis from inspiring English sources

The uniformly spaced infinite length sinc functions form a complete basis for the space of band-limited signals.

The Bernstein polynomials of th degree form a complete basis over, and they are defined by (2.1).

Bernoulli polynomials form a complete basis over the interval [0, 1] [30] and are defined by [31] begin{aligned} beta _m(t)=sum limits _{i = 0}^{m}{left( begin{array}{c} m i end{array}right) } alpha _{m-i} t^{i}, end{aligned} (2.1 that (alpha _i,i=0,1,.....,m) are Bernoulli numbers.

If we compute the electron scattering for a set of plane waves that forms a complete basis, these waves can each be multiplied by a complex scalar value and summed to give a desired electron probe.

The set of orthonormal column vectors u j (j = 1, ···, NSV) constituting (i.e. ] and forms a complete basis for an arbitrary SV coefficient vector. Hence, it is expanded uniquely as. The scalar coefficients ß j are obtained by. Similarly, a flow coefficient vector m is expanded as, where V i is the orthonormal column vector of dimension NFL constituting V (i.e. and ).

Zernike moments are constructed by a set of complex polynomials which form a complete orthogonal basis set defined on the unit disk x 2 + y 2 ≤ 1.

It is well known that for the self-adjoint compact operators the eigenvalues are real, and the corresponding eigenfunctions form a complete orthogonal basis on (L^{2}).

Knowing that the spherical harmonics form a complete orthonormal basis over allows the expansion of any square-integrable function (i.e., vMF) as a linear combination of these (4).

By definition of, it is not difficult to see that and form a complete set of basis for an -dimensional linear space.

EMD is a method of breaking down the signal without leaving the time domain; it filters out functions which form a complete and nearly orthogonal basis for the signal being analyzed [1].

The basis functions in this method form a complete orthonormal set and are expressible in terms of spherical harmonics and spherical Bessel functions.