W.M. Snelgrove

Continuous-time LMS adaptive recursive filters

An approach for implementing continuous-time adaptive recursive filters is presented. The resulting filters should be capable of operating on much higher signal frequencies than their digital counterparts since no sampling is required. With respect to implementation problems, the effects of DC offsets are investigated and formulas derived so that these effects can be estimated and reduced. It is shown that the DC offset performance is strongly affected by the choice of structure for the adaptive filter. Experimental results from a discrete prototype are given where accurate adaption is observed and DC offset effects are compared to theoretical predictions. >

Orthonormal ladder filters

A state-space structure for the realization of arbitrary filter transfer-functions is presented. This structure should prove useful where integrators are the basic building blocks such as in transconductance-C, MOSFET-C, or active-RC filters. The structure is derived from a singly terminated LC ladder and has the characteristics that it is always scaled for optimum dynamic range and its integrator outputs are orthogonal. For this reason, the resulting realizations are called orthonormal ladder filters. Since dynamic range scaling is inherent to the proposed structure, it is felt that this design technique may be most useful in programmable or adaptive filters. The sensitivity and dynamic range properties of an orthonormal ladder filter are shown to be comparable in performance to the equivalent properties obtained from a cascade of biquads. >

Comparison of DC offset effects in four LMS adaptive algorithms

It is well known that DC offsets degrade the performance of analog adaptive filters. In this paper, the effects of DC offsets on four variations of the stochastic gradient algorithm are analyzed. Assuming a Gaussian probability distribution for the input signal and error signal, the output mean squared error (MSE) performance in the presence of DC offsets is evaluated for each of the algorithms. The theoretical work is compared with computer simulations and the results, together with convergence properties of each of the algorithms and their respective hardware requirements, are used in selecting the most appropriate algorithm. Although a Gaussian input distribution is assumed, it may reasonably be inferred that the critical results obtained should also hold for other input distributions. >

Adaptive recursive state-space filters using a gradient-based algorithm

To aid in the search for better adaptive filter structures, a method is presented to obtain the gradients required to adapt general state-space filters. Unfortunately, the number of computations for this general case is quite high. To reduce the number of computations, two new state-space adaptive filters are introduced. One application where these new structures are shown to be useful is in oversampled filtering where an estimate of the final pole locations is known and the adaptive filter is required only to fine-tune the transfer function. It is shown that for this type of application, the new adaptive structures can have much improved adaptation rates and roundoff noise performance as compared to the corresponding direct-form realizations. >

Adaptive linearization schemes for weakly nonlinear systems using adaptive linear and nonlinear FIR filters

Three adaptive linearization schemes are proposed. In the first scheme, linearization is performed by canceling nonlinearity at the output of a physical system. In the second, a nonlinear postprocessor is employed to postdistort signals. In the third, a preprocessor is used. The schemes using a postprocessor and a preprocessor are designed for weakly nonlinear systems, whereas the scheme of linearization by cancellation at the output can be applied to problems with stronger nonlinearities. In all three methods, necessary estimates of linear and nonlinear operators are provided by adaptive linear and nonlinear filters. Typical simulation results for a physical system modeled by a Volterra series with a linear term, a quadratic term, and a cubic term are presented and are judged encouraging.<<ETX>>

Median-based offset cancellation circuit technique

A simple technique to compensate for DC offsets in many analog circuits is presented. An offset-free, infinite DC gain integrator is established in a feedback loop about the uncompensated circuit, resulting in a high-pass system output response. The ideal integrator is realized via the use of a counter resulting in the cancellation of the signals median rather than the usual case of the signals mean.<<ETX>>

Nonlinear IIR adaptive filtering using a bilinear structure

A nonlinear IIR (infinite-impulse-response) adaptive filter that is based on a Volterra polynomial realized by a set of bilinear systems is presented. Each bilinear system corresponds to a cascade connection of linear systems and multipliers. This allows the extension of some linear adaptive concepts. Nonlinear IIR adaptive filters have an advantage over FIR (finite-impulse-response) Volterra filters in that in some applications they may result in less computation. The results of a simulation example show the applicability and practical convergence rate of the nonlinear IIR adaptive filter presented.<<ETX>>

A novel self-calibrating scheme for video-rate 2-step flash analog-to-digital converter

The authors present an online trimming technique and an error-code self-trimming algorithm for video rate 2-step flash analog-to-digital converters (ADCs). The self-calibrating scheme, combining a digital error correction process and the self-trimming algorithm, dynamically maintains the random offsets of the comparators well within +or-0.6 LSB and counteracts the interstage gain error, while improving the design of a conventional 2-step ADC towards a higher speed, a smaller size, and a lower power dissipation. The technique is applicable to subranging ADCs of up to any accuracy. Results from simulation of a 10-bit ADC are given to illustrate the superior efficiency of the scheme and the simplicity of the corresponding circuitry.<<ETX>>

Continuous-time analog adaptive recursive filters

An approach is presented for implementing continuous-time analog adaptive recursive filters. The building blocks used to implement such filters are commonly used in integrated circuits, and thus the resulting filters can be fully integrated. Circuit details and experimental results for a discrete prototype are presented.<<ETX>>

State-space adaptive recursive filters

The authors propose an LMS (least-mean-squares) algorithm for adapting the poles and zeros of state-space IIR (infinite-impulse-response) filters. Recently presented state-space sensitivity formulae are used to obtain gradients which are required to adapt the filter coefficients. The number of computations for a general state-space adaptive filter is seen to be large, but a modified companion-form filter is shown to require much less computation. Also, it is shown that, in general, it is possible to efficiently adapt any state-space system by modifying any one column of its A matrix. This could prove useful where only small changes in coefficients are expected. Finally, simulation results are presented.<<ETX>>