Effects of ill-conditioned data on least squares adaptive filters

Abstract

An ill-conditioned least squares (LS) problem has a solution which may be highly sensitive to small perturbations in the data. This paper presents sensitivity results for the LS weight vector of an all-zero adaptive equalizer in an ill-conditioned signal environment. The ill-conditioned data results from severe amplitude distortion introduced by the data channel. Specifically, a theoretical upper bound for the relative change in the magnitude of the weight vector due to additive noise is derived as a function of the channel characteristics and equalizer order, and simulation results are presented which indicate the derived bound to be applicable over a wide range of equalizer orders.

A new Wiener filtering based detection scheme for time domain perceptual audio watermarking

“…Too large means roughly that log 10 (K) precision of matrix entries. numbers [5,6]. In this context, we introduce the spectrum flatness measure ν [7]:…”