Frequency Analysis of Digital Computers Operating in Real Time

When used in a control system, the digital computer operates in real time and interacts dynamically with other parts of the system. It is desirable to examine its effect by the use of conventional techniques of servo-mechanism design, namely, frequency analysis. An important feature of most digital computers is that the data passing through them are in sampled form. Frequency analysis has already been applied to the process of sampling and sampled-data systems. The present paper extends this approach to operations performed on the data in sampled form, such as by a digital computer. A real-time linear digital-computer program can be represented by a transfer function. Thus, the computer with its program is a filter whose analysis and design can proceed along lines familiar in network theory and servo design. The error analysis of familiar numerical formulas is illustrated. Various properties of programs are studied in both the s-domain (complex frequency) and the z-domain (complex delay). Tests for stability (or convergence) are described and illustrated. Programming is discussed from a new point of view, and a new programming method is developed. It is indicated how such studies could conceivably affect the logical design or instruction code of a computer.