VLSI Digital Signal Processing Systems: Design and Implementation

10.8    PIPELINED ADAPTIVE DIGITAL FILTERS

Adaptive digital filters are difficult to pipeline due to the presence of long feedback loops. Techniques such as look-ahead computation can be used to pipeline these filters but the resulting systems are not practical for integrated circuit implementations due to the large increase in hardware [14]. The lookahead computations maintain exact input-output mapping in frequency shaping filters (such as IIR digital filters), but such exact input-output mapping is not necessary in an adaptive filter, since the coefficients continue to adapt until they converge. However, analysis of the adaptation behavior in adaptive filters as measured by the misadjustment error and adaptation time constant is important. The misadjustment error is an indication of the error between the solution achieved by the adaptive filter and the optimal solution. The adaptation time constant is an indicator of the speed of convergence; the lower the time constant, the faster the convergence.

In this section, relaxed look-ahead transformation technique is used to pipeline the adaptive filters with little or no increase in hardware at the expense of marginal degradation in the adaptation behavior. The relaxed look-ahead transformation is based on certain relaxations or approximations of the look-ahead representation. Three forms of relaxed look-ahead are introduced including product, sum, and delay relaxations. Different types of relaxed look-ahead lead to different forms ...