Aliasing error in the design of multirate filters

A narrow-band filter is inherently of high order, and requires a high computation rate if implemented directly. A multirate implementation can offer the advantage of much reduced computation per output sample. This paper derives an expression for the system error of such an implementation. This error consists of two components, one due to the approximation of the desired filtering characteristics and the other due to aliasing. An expression for the fixed point multiplication roundoff error is also derived. Design rules are suggested which fix the aliasing error at a specified level. Examples are given.