In this paper a new digital audio watermarking algorithm is proposed based on B-spline approximation. The algorithm takes the advantage of non-uniform B-spline wavelet, namely, the number of low-frequency components can be arbitrarily selected, so, it is very flexible. Meanwhile, it avoids the complex calculations of non-uniform B-spline wavelets. The simulation experiments show that this algor...

A diierential equation of the form Dp(x)Du(x) = f(x; u(x)) is solved by collocation, using a class of spline functions of order 3. A restriction of each spline function to any subinterval of the partition is piecewisely in the kernel of the operator DDp(x)D. A coeecient p(x) may be singular. An algorithm is described by means of which a B-spline basis could be eeciently constructed. Some numeri...

in this paper, we use a third degree b-spline function to construct an approximate solution forthird order linear and nonlinear boundary value problems coupled with the least square method. severalexamples are given to illustrate the efficiency of the proposed technique.

The application of collocation methods using spline basis functions to solve differential model equations has been in use for a few decades. However, the application of spline collocation to the solution of the nonlinear, coupled, partial differential equations (in primitive variables) that define the motion of fluids has only recently received much attention. The issues that affect the effecti...

The matrix forms for curves and surfaces were largely promoted in CAD. These formulations are very compact to write, simple to program, and clear to understand. They manifest the desired basis as a matrix transformation of the common power basis. Furthermore, this implementation can be made extremely fast if appropriate matrix facilities are available in either hardware or software. Derivatives...