Bounds on Truncation Error for the Cardinal Sampling Expansion

摘要

It is well-known that a function bandlimited to (-pi, pi) and having a Fourier transform which is either square integrable or absolutely integrable can be represented exactly for all time by an infinite series involving the sample values of the function at the integer points. If the summation involves only a finite number of terms, then an approximation to the bandlimited function is obtained. We define the difference between the given function and the finite approximation to it as a truncation error. Studies concerning bounds on the magnitude of the truncation error are reported here. (Author)