System modeling using an adaptive delay filter

In this paper, we present a special technique for modeling an unknown system. This technique requires a type of adaptive filter called an Adaptive Delay Filter [1]-[3]. This filter structure includes variable delay taps in addition to variable gains. The Adaptive Delay Filter is especially applicable to system modeling problems in which the system to be modeled has a sparse impulse response [4]-[7]. Using the standard adaptive filter to model a sparse system could require a very large filter [8], while an Adaptive Delay Filter could model the sparse impulse response with very few elements in the filter since the delay taps spread out to adapt to the unknown system. An analysis of the mean-squared error surface using this technique is included, along with the computer simulation results of the performance in modeling both the delay taps and the gains of an unknown system. A comparison of this technique with the conventional approach using Widrow's LMS algorithm will be addressed.