INTERVAL PROPERTIES OF LATTICE ALLPASS FILTERS WITH APPLICATIONS

In practical applications of digital filters it is more realistic to t reat multiplier coefficients as finite intervals than restricting them to infinite or very long word-length representations. However, this c an not be done if the frequency response performance under interval as sumption is difficult to analyze. In this paper, it is proved that sta ble lattice allpass filters possess bounded continuous phase response when lattice parameters vary in bounded intervals. It is shown that sh arp bounds on the interval phase response can be computed easily at an arbitrary frequency using a simple recursive procedure. Application o f this property to the problem of finite word-length lattice allpass f ilter design is also discussed. By formulating this problem as an inte rval design it is possible to solve it efficiently independent of the number system used to represent multiplier coefficients.