Aliasing error in the multirate implementation of narrowband filters

Narrowband filters are inherently of high order, so they require a high computation rate if implemented directly Multirate filters are capable of effectively approximating narrowband characteristics. Such an implementation may require a much reduced rate of computation. This paper derives an expression for the system error of this approach. This error consists of two components, one due to the filter approximation and the other due to aliasing. The role of aliasing error in the design of multi-rate filters is then considered. Examples are presented.