Second-order Recursive Oscillators for Musical Additive Synthesis Applications on SIMD and VLIW Processors.
Todd D. Hodes, Adrian Freed · 1999
This paper summarizes our work adapting a recursive digital resonator for use on sixteen-bit fixed-point hardware. The modified oscillator is a two-pole filter with error properties expressly matched to use in the range of frequencies relevant to additive synthesis of digital audio. We present the algorithm, error analysis, performance analysis, and measurements of an implementation on a fixed-point vector microprocessor system. 1. INTRODUCTION The most widely used digital sinusoidal oscillator structure employs a first order recursion to accumulate and wrap a phasor, followed by a sinusoidal functional evaluation --- usually by indexing precomputed tables. Second order recursions are an attractive alternative because the sinusoid is computed within the structure, avoiding the need for a large table or specialized hardware function evaluator. Unfortunately, numerous theoretical and practical challenges have to be overcome to use second order structures. We are motivated to overcome th...