Applying a Technique of Identification for Estimating Definite Integrals

In this paper, we present a new approach which is based on the technique of parametric identification to estimate one-dimensional definite integrals. So we suppose a continuous function on the closed interval. This function can be represented at the points of continuity by Fourier series. A basic description of this method is that you take a number N of samples. For each sample, we estimate the function value for the considered function. We sum all of these values, and divide by N to get the mean value from our samples. We then multiply this value by the interval to get the integral. The method is implemented and tested on MATLAB for several examples. Simulations results confirmed the analytical methods, and the error of estimation can be more accurate. Furthermore, we give evidence that the method proposed here is much simpler and use less arithmetic operations, this method is especially suitable for digital signal processing.