Extensions of the weighted-sample method for digitizing continuous-time filters

Methods continue to improve for taking the transfer function of a stable, continuous-time, single-input single-output system or filter and converting it to an "equivalent" discrete-time filter, The weighted-sample (WS) method of carrying out the digitizing process, described in recent literature, is one such method. It is a higher order method, compared with the first-order Tustin's method, so it usually achieves a smaller error for a given system, input, and sample time. Like the Tustin method, but unlike some recent, higher order digitization methods, it allows the sample time to be selected without being constrained by stability considerations. This paper describes two extensions to the weighted-sample method. The first provides the ability to handle cases in which the continuous filter contains one or more series integrators. The second extension modifies the WS filter to a new form, termed the WS' filter, which turns out to be the same as the MSRP filter recently described. Several examples are given, and accuracy is assessed.