On the origins of DSP

Abstract

SUMMARY We tend to think of digital signal processing as one of the recent high technologies that have emerged as a consequence of Moore's law but its roots go back the 16th century and beyond. The two most fundamental processes in DSP, namely, sampling; and interpolation, go back to Gregory (1 638- 1675), Newton (1 642- 1727), and Stirling (1692-1770), even to the great Archimedes of Syracuse (287-212 B.C). As will be demonstrated, by the lecture, when Archimedes derived a practical value of pi, he actually used sampling and interpolation. Interpolation is, in effect, a filtering process since it involves fitting a smooth curve through a number of data points, and by using Stirling's interpolation formula, quite unexpectedly; a good quality low-pass filter can be designed. The lecture will show also that, contrary to popular belief, Babbage (1791-1871) did not invent computers. What he was actually trying to construct was a discrete-time system that could perform interpolation. Thus if Babbage was successful with his difference engine, and programmed it to perform interpolation based on Stirling's formula, he would have constructed the first digital filter, alas in mechanical form. The lecture will trace the origins and evolution of the underlying mathematical principles of DSP starting with Archimedes and ending with the prophetic statement of Moore about the number of transistors that can be manufactured on a single VLSI chip.