Frequency Synthesis Using Walsh Functions

Abstract
A new scheme for the programmable generation of either square or sine waves of a required frequency is proposed. It uses neither feedback, nor table lookup of stored values, but it derives the desired square wave from a Walsh function, fairly simple to select and to generate with digital circuits. For this purpose, the Walsh function is counted down in a binary counter, at whose output a function with clean spectrum results, whose spurious components can be bounded by a simple formula. This approach becomes the design principle for a programmable frequency synthesizer with phase-continuous output, practically instantaneous switching between frequencies, and no limit on the number of closely and evenly spaced frequencies that can be selected.

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