Couplets and Elementary Filters: Part I

Signal filtering is characterized by the "signal in-signal out" situation and the systems that generally perform this task are generally called filters. It is usually (but not always) a time-domain operation. Some of the applications are: removal of unwanted background noise, removal of interference, separation of frequency bands and shaping of the signal spectrum.

The mathematical machinery required to design and develop digital filters is quite intricate. In this feature we present a simple yet powerful approach to designing practical filters which requires just the knowledge of the z-transform, the discrete time counterpart of the Laplace transform.

The feature will take the reader through the frequency domain behaviour of the simple couplet, which is a binomial in z, its inverse, and the ratio of two couplets. These three elementary filters will then form a basis for the classification of most systems, according to the location of poles and zeros.

In part II of this article, we will see how these three elementary filters can be used to generate eight different kinds of practically useful filters.