Abstract :
The well-known Bernstein polynomials are frequently used in signal representation, finite impulse response filter realization, computer-aided geometric design, and B-spline techniques. In this letter, a refinement of the Bernstein approximation scheme for complex exponentials, by making use of a judicious Lagrange interpolation scheme, is proposed. Applied to a general function, this approach leads to a new polynomial approximant, termed a multinomial Lagrange-Bernstein approximant, that performs better than the usual Bernstein approximant.
Keywords :
CAD; FIR filters; engineering graphics; polynomial approximation; signal representation; splines (mathematics); B-spline technique; Bernstein approximation scheme; Lagrange interpolation scheme; computer-aided geometric design; finite impulse response filter; polynomial approximant; signal representation; Chebyshev approximation; Digital filters; Finite impulse response filter; H infinity control; Interpolation; Lagrangian functions; Polynomials; Signal design; Signal representations; Spline; Approximation of exponentials; Bernstein polynomials; Lagrange interpolation; multinomials; signal representation;
