On the uniqueness of weights in single-layer perceptrons

In this paper the geometric formulation of the single layer perceptron weight optimization problem previously described by Coetzee et al. (1993, 1996) is combined with results from other researchers on nonconvex set projections to describe sufficient conditions for uniqueness of weight solutions. It is shown that the perceptron data surface is pseudoconvex and has infinite folding, allowing for the specification of a region of desired vectors having unique projections purely in terms of the local curvature of the data surface. No information is therefore required regarding the global curvature or size of the data surface. These results in principle allow for a posteriori evaluation of whether a weight solution is unique or globally optimal, and for a priori scaling of desired vector values to ensure uniqueness, through analysis of the input data. The practical applicability of these results from a numerical perspective is evaluated on some carefully chosen examples.     

An adaptive PAM-4 5-Gb/s backplane transceiver in 0.25-/spl mu/m CMOS

This paper describes a backplane transceiver, which uses pulse amplitude modulated four-level (PAM-4) signaling and continuously adaptive transmit-based equalization to move 2.5-GBd/s symbols totalling 5 Gb/s across typical FR-4 backplanes for total distances of up to 50 inches through two sets of backplane connectors. The 17-mm/sup 2/ device is implemented in a 0.25-/spl mu/m CMOS process, operates off of 2.5- and 3.3-V supply voltages, and consumes 1 W.     

High-speed ΔΣ ADC with error correction

A digital error correction scheme is described for ΔΣ ADCs with multibit quantisers. It operates in the background and remains effective even for very low oversampling ratios     

Time-varying performance surfaces for adaptive IIR filters:geometric properties and implications for filter stability

We present a new framework for understanding the performance of adaptive IIR filters which enhances the understanding of filter stability during on-line operation. This new understanding arises from examining geometric properties of time-varying performance surfaces which are defined by the data, rather than the standard steady-state error surfaces as defined by statistics of the data. Data-dependent descent directions used in adaptive algorithms to update filter coefficients typically are viewed as functions of gradients defined on fixed performance surfaces, and data is used to approximate these gradients at each iteration. In contrast, we view data-dependent descent directions at each iteration as functions of exact gradients on time-varying performance surfaces. By examining the shape of these time-varying performance surfaces near filter stability boundaries, we are able to identify the origin of on-line stability problems associated with existing adaptive IIR filtering formulations, and suggest corrective measures. Specifically, by using exact z-domain methods, we define time-varying performance surfaces which geometrically enforce filter stability, and maintain the geometric and physical properties of the “true” error surface at each iteration. Development of adaptive algorithms based on this measure is expected to result in adaptive filters having improved stability performance during on-line operation