Thomas A. Brubaker

Multiplication Using Logarithms Implemented with Read-Only Memory

A method for designing the read-only memories (ROMs) needed for multiplication using logarithms is developed. By defining the word length of the multiplicand, multiplier, and product as n bits and the word length of -the rounded logarithms as m bits, design curves are given that allow various values of n and m to be selected for a given multiplier accuracy. Then a table is used to determine, which combination results in an implementation with the least number of bits.

Implementation of digital controllers

Abstract The variance of error at the output of a digital control system due to input data quantization and product rounding in a digital controller is derived. Two forms of controller implementations are considered. Then an expression for the word length that yields a specified variance of error is determined. Scaling is then discussed and an example consisting of a discrete integral plus proportional controller is presented.

Limit cycles in digital filters

A study is made of the nonlinear phenomenon of limit cycles in digital filters implemented using fixed point arithmetic with product rounding. By investigating individually the different types of limit cycles, bounds are derived on the coefficients for second-order filters in the direct and canonic form that are more efficient than earner bounds. Then the results are extended to filters connected in cascade.

Time-domain synthesis of recursive digital filters†

The synthesis of infinite memory digital filters for the operations of smoothing, filtering, prediction and differentiation is described. In the design, constraints are developed using a polynomial approximation to the signal. The noise is then minimized subject to the constraints using the method of Lagrangian multipliers.

Computation of the discrete autocovariance

Given an Nth-order discrete system, the autocovariance sequence is formulated as a set of recursive and non-recursive difference equations. Application of the final value theorem for a z transform then permits the first N terms of the steady-state autocovariance sequence to be computed via one matrix inversion. The remaining terms are calculated using a simple recursive relationship.

Fault detection in digital filter systems

The use of a parameter identification procedure to detect faults in hardware used to implement a broad class of linear algorithms defined as digital filters is presented. Using the filter coefficient estimates produced by the identifier, a method of measuring the acceptability of the filtering algorithm is suggested and a numerical example is given.

A strategy for coefficient quantization in digital control algorithms

Abstract A strategy for quantizing the coefficients in a general second order digital control algorithm is presented. First, the errors in the magnitude and phase functions for the algorithm are derived in terms of the filter coefficients. By specifying a maximum allowable error for each function over a given frequency range, quantization regions can then be established. An example consisting of a lag-lead digital control algorithm is included to illustrate the procedure.

Energy distributions for sampled and reconstructed periodic signals

By using Parsevals theorm for almost periodic functions an expression for the energy distribution in a sampled and reconstructed sinusoidal waveform is derived. The expression is then evaluated for zero- and first-order hold systems through use of the psi function and its derivatives.

Steady-state design of second-order digital filters using the Kalman formulation

Abstract A design methodology for second-order digital band-pass filters is described based on the Kalman filter formulation with a sinusoidal signal model. When driver noise is included, steady-state relationships between the Kalman gain, the coefficients of the covariance matrix and the coefficients of the driver-noise covariance matrix are derived. Then, expressions for the steady-state filter, discrete-time transfer function, magnitude and phase functions, pole-zero locations and −3dB frequencies are derived. Finally, a procedure for selecting the driver-noise covariance matrix based on the desired frequency domain characteristics is developed. A design example illustrates the procedure.

Development of adaptive instrumentation for process control

This abstract describes the operation of an automated electrochemical cell that utilizes an ion selective electrode (ISE) as the detector. The instrument can rapidly and automatically generate on-line estimates of the concentration of an ion, thus providing chemical information useful for controlling a chemical process. A typical application might be the monitoring of a sewage treatment plant to facilitate control of the concentration of a contaminant in discharged water.