Calculation of upper bounds for errors of an approximate sampled frequency response

The sampled frequency response of a continuous system can be represented by an infinite series which is truncated for practical application. In utilizing the truncated series, it is desirable to retain the fewest number of terms and still keep the error between the actual sampled frequency response and the approximated sampled frequency response below a specified tolerance. In this correspondence a technique is presented for calculating an upper bound on the amount of this error, and serendipituously, an error estimating procedure is provided.