The polynomial of degree n which is the best approximation of the sinc function on the interval 0, π/2 with the square norm is considered. By using Lagrange's method of multipliers, we construct the polynomial explicitly. This method is also generalized to the continuous function on the closed interval a, b. Numerical examples are given to show the effectiveness.

– Filter, any modification of the signal according to design specifications. – Frequency selectivity – Causal filters (real time without delay) – Note ideal filters are not realizable. We can’t have perfect magnitude response. For example, the ideal low pass filter is not realizable because it requires infinite length sinc function. We would like causal filters: – IIR ok – FIR sometimes even be...

− The comparison of three different algorithms for the estimation of parameters of two sine signals with common frequency is presented. The algorithms are the ellipse fit, the seven parameter sine fit and the spectral sinc fit. The comparison includes signal to noise ratio analysis, amplitude analysis and phase difference analysis.