A tracking analysis of the adaptive filters equipped with the sign algorithm and operating in nonstationary environments is presented. Under the assumption that the nonstationary can be modeled using a random disturbance, it is shown that the long-term time average of the mean-absolute error is bounded, and that there exists an optimal choice of the convergence constant mu which minimizes this quality. Applying the commonly used independence assumption, and under the assumption that the nonstationarity is solely due to the time-varying behavior of the optimal coefficients, it is shown that the distributions of the successive coefficient misalignment vectors converge to a limiting distribution when the adaptive filter is used in the system identification mode. Finally, under the additional assumption that the signals involved are zero mean and Gaussian, a set of nonlinear difference equations is derived that characterizes the mean and mean-squared behavior of the filter coefficients and the mean-squared estimation error during adaptation and tracking. Results of several experiments that show very good correlation with the theoretical analyses are presented. >

Tracking analysis of the sign algorithm in nonstationary environments

An adaptive filter structure that requires zero multiplications for its implementation is introduced. The primary input signal is quantized using differential pulse code modulation (DPCM), and the DPCM outputs are processed by a conventional adaptive filter. The filter coefficients are updated using the sign algorithm. Under the assumption that the primary and reference input signals to the adaptive filter are zero-mean, wide-sense stationary, and Gaussian, theoretical results for the mean and mean-squared behaviour of the filter are also derived. A simulation example demonstrating the usefulness of the filter, as well as verifying the theoretical results and comparing the multiplication-free adaptive digital filter to the sign algorithm, is also presented. >

An efficient FIR adaptive filter using DPCM and the sign algorithm

This paper presents a multiplierless realization structure for the implementation of adaptive digital filters. Multiplierless realization is achieved by quantizing input signals in such way that each input sample is expressed as a sum of a fixed number of signed power-of-two (SPT) terms. This simplifies all multiplications involving input signal data. Simulation results for suppressing a narrow-band interference in a direct-sequence spread-spectrum communication system show that the performance of our technique with input signal quantized to 2 SPT terms is comparable to a conventional filter with input uniformly quantized to 10 bits. However, our technique reduces the number of transistors required for realization in a custom VLSI circuit to about 1/3 of that required by conventional realization. >

http://ieeexplore.ieee.org/iel2/3224/9170/00409001.pdf

Multiplierless realization of adaptive filters by nonuniform quantization of input signal

In order to detect a precise pulse waveform, we have developed a pulse diagnostic system using the multiplication free adaptive digital filter (MADF) algorithm. The MADF algorithm is used to reduce intersymbol interference (ISI) in the data channel. The application of the apparatus has important significance in ensuring the objectivity of clinical information and in promoting the representation and stability.

Convergence characteristics of MADF algorithm in the pulse diagnostic apparatus

Convergence analyses of two adaptive filter structures that require no multiplications for their implementation are presented. Under the assumption that primary and reference inputs to the adaptive filters are zero mean, wide-sense stationary, and Gaussian random processes, expressions are derived for the mean and mean-squared behavior of the filter weight vector using a variety of simplifying assumptions. Results of some computer simulation experiments are presented. >

Multiplication-free adaptive filters

The authors update delta modulation digital filter weights using the LMS (least-mean-squares) and the SIGN algorithms to realize an adaptive digital filter without multiplication operations. It is shown that using the SIGN algorithm results in an adaptive filter that can be implemented using the simple up/down counting operations. Learning curves demonstrating convergence properties of the algorithms for a system identification problem are presented. >

D.H. Youn

Papers

Multiplication-free adaptive digital filters