On the Interaction of Roundoff Noise and Dynamic Range in Digital Filters

With the rapid development of digital integrated circuits in the 1960's and the potential for large-scale integration (LSI) of these circuits in the 1970's, digital signal processing has become much more than a tool for the simulation of analog systems or a technique for the implementa* This paper is taken in part from a thesis submitted by Leland B. Jackson in partial fulfillment of the requirements for the degree of Doctor of Science in the Department of Electrical Engineering at Stevens Institute of Technology. 1 159 160 THE BELL SYSTEM TECHNICAL JOURNAL, FEBRUARY 1970 tion of very complex and costly one-of-a-kind systems alone. The traditional advantages of digital systems, such as high accuracy, stable parameter values, and straight-forward realization, have been supplemented through the use of integrated circuits by the additional advantages of high reliability, small circuit size, and ever-decreasing cost. As a result, it now appears that many signal processing systems which have been in the exclusive domain of analog circuits may in the future be implemented using digital circuits; while other proposed systems which could not be implemented at all because of the practical limitations of analog circuits may now be realized with digital circuits.2 The key element in most of these new signal-processing systems is the digital filter. The term "digital filter" here denotes a time-invariant, discrete or sampled-data filter with finite accuracy in the representation of all data and parameter values.