Analysis and Emulation of Early Digitally-Controlled Oscillators Based on the Walsh-Hadamard Transform

Early analog synthesizer designs are very popular nowadays, and the discrete-time emulation of voltage-controlled oscillator (VCO) circuits is covered by a large number of virtual analog (VA) textbooks, papers and tutorials. One of the issues of well-known VCOs is their tuning instability and sensitivity to environmental conditions. For this reason, digitally-controlled oscillators were later introduced to provide stable tuning. Up to now, such designs have gained much less attention in the music processing literature. In this paper, we examine one of such designs, which is based on the Walsh-Hadamard transform. The concept was employed in the ARP Pro Soloist and in the Welson Syntex, among others. Some historical background is provided, along with a discussion on the principle, the actual implementation and a band-limited virtual analog derivation.