FILTER FUNCTIONS WITH EXPONENTIAL CONVERGENCE ORDER

Oversampled functions can be evaluated using generalized sine-series a nd filter functions connected with these series. A standard filter fun ction is given by exp ((zeta(2) - 1)(-1)). We show that the Fourier tr ansform of this filter posseses the convergence order O(exp (- root x) ), improving an estimation given in [10]. Moreover, we define a family of filter functions with convergence order O(x . exp (- x(sigma))) wi th sigma arbitrary close to 1.