Adaptive filtering using quantized output measurements

A normalized stochastic gradient adaptive filtering algorithm based on a finite impulse response (FIR) model is discussed. The algorithm identifies the system exactly, given only coarsely quantized output measurements. A description of the quantizer is included in the overall input-output model, and the scheme exploits an approximation of the derivative of the quantizer. Using an associated differential equation, global convergence is established to a zero output error (except for possible colored measurement disturbances) parameter setting or to the boundary of the model set.