Adaptive Matrix/Vector Gradient Algorithm for Design of IIR Filters and ARMA Models

Abstract

<p class="MsoNormal"> <span lang="EN-US">This work describes a novel adaptive matrix/vector gradient (AMVG) algorithm for design of IIR filters and ARMA signal models. The AMVG algorithm can track to IIR filters and ARMA systems</span><span lang="EN-US"> </span><span lang="EN-US">having poles also outside the unit cir</span><span lang="EN-US">cle. The time reversed filtering procedure was used to treat the unstable conditions. The SVD-based null space solution was used for the initialization of the AMVG algorithm. We demonstrate the feasibility of the method by designing a digital phase shifter, which adapts to complex frequency carriers in the presence of noise. We implement the half-sam</span><span lang="EN-US">ple delay filter and describe the envelope detector based on the Hilbert transform filter.</span><span lang="EN-US"><o:p></o:p></span> </p

Gamma Splines and Wavelets

“…Hence, we may easily construct adaptive gamma spline wavelets, where and parameters are self-adjusting according to some cost criteria or error function. Recently our research group introduced an adaptive matrix-vector gradient algorithm [12], which can be used for optimization of the and parameters to match for special signal features. Our preliminary results in wireless transmission of the ambulatory ECG indicate that the adaptive gamma spline wavelets improved compression performance compared with the static B-spline wavelets.…”

“…The B-spline approximation transfers the information to the next subscale via the two-scale equation (6). The wavelet , ( ) behaves like the B-spline via the dilation and translation equation (12). If we keep the B-spline as a wavelet, the binomial kernel [ ] works as a scaling filter in the wavelet analysis.…”

Cost-Sensitive Estimation of ARMA Models for Financial Asset Return Data

“…Among those, the autoregressive moving average (ARMA) model [1] is the simplest while essential in the sense that most other models are equipped with at least the basic ARMA components. The ARMA models appear in a wide spectrum of applications recently including filter design in signal processing [11], time-series analysis and model selection in computational statistics [12], and jump (large changes) modeling for asset prices in quantitative finance [13], to name just a few. For a time-series y = 1 , .…”