Apparatus and method of additive synthesis of digital audio signals using a recursive digital oscillator

A computer readable medium encoded with computer executable instructions comprising:

• a first set of executable instructions to receive digital audio signal frames wherein each digital audio signal frame has a set of specified frequency values expressed as a bit sequence;
• a second set of executable instructions to Re-Map said bit sequence to represent lower frequencies with more significant bits and higher frequencies with less significant bits;
• and
• a third set of executable instructions to facilitate additive synthesis of said digital audio signal frames in a reduced-precision recursive digital oscillator
• wherein said recursive digital oscillator generates frequency f lying in the range from zero to one-half of a sampling frequency fs including recursion coefficients xn given by xn=2xn−1−εxn−1−xn−2, wherein ε=2−2 cos(ω) and wherein ω=2πf/fs, and
• and wherein said Re-Mapping biases the generating frequency of said oscillator, whereby ε is represented by an unsigned mantissa, m, combined with an unsigned exponent, e, biased so that the actual represented value is ε=22−em.