On the design of gradient algorithms for digitally implemented adaptive filters

摘要: The effect of digital implementation on the gradient (steepest descent) algorithm commonly used in mean-square adaptive equalization pulse-amplitude modulated data signals is considered. It shown that digitally implemented algorithms can exhibit effects which are significantly different from those encountered analog (infinite precision) algorithms. This illustrated by considering often quoted result stochastic approximation to achieve optimum rate convergence an step size should be proportional 1/n , where n number iterations. On closer examination one finds this applies only when large and relevant for as iterations becomes not continually decrease a algorithm. manifestation quantization inherent any system. A surprising these produce residual error minimized making possible. Since taking small sizes, step-size sequence reflects compromise between competing goals. performance time-varying gain suggested contrasted with constant sequence. environment latter capable attaining smaller error.