Digital filters - a case study

The purpose of this case study is to present a development of the step-invariant approach to highpass digital filter design. It will be shown that the transfer function,G(z) obtained via the step invariant design method, may be made to approximate closely to the transfer function, G(z) obtained via the bilinear z-transform method. The analysis presented justifies this step-invariant design method, and shows that it is possible to convert a time domain (step-invariant) filter, G(z) to one that satisfies a frequency domain specification,G(z) . This is achieved by observing certain conditions and by employing a suitable gain term. The validity of the method is demonstrated using a practical example of a simple highpass filter and a digital phase-advance network.