Design of linear-phase adaptive heterodyne filters

Modern broad-band communications systems as well as complex control systems and high-quality audio often require the removal of narrow-band interference through an adaptive band-stop filter with highly linear phase throughout its pass-band. High-Quality fixed linear phase filters can be designed using the Parks-McClellan technique, but these filters require a large number of coefficients and thus are difficult to make tunable or adaptive. Through the use of a new heterodyne approach involving complex heterodyne signals it is possible to take any linear-phase filter and make it adaptive. The process requires a new Nyquist filter that removes signals from the lower half of the z-plane (negative frequencies) and two heterodyne operations that shift the signal to the fixed linear-phase filter and back. Detailed designs are developed for adaptive center-frequency band-stop filters. These filters retain the linear-phase property of the original filter yet are fully adaptive over the range from DC to the Nyquist frequency.