Inverting the sign of a waveguide's reflected wave drops the pitch an octave and cancels DC buildup

A useful trick in feedback waveguide/Karplus-Strong models is to invert the sign of the reflected portion of the loop relative to the input. Two things happen. First, the sign inversion means the loop repeats every two passes rather than every pass, effectively doubling the delay-line period, so the perceived pitch drops by one octave — letting a short delay line reach very low notes. Second, inversion cancels any DC (zero-frequency) offset that would otherwise accumulate as the signal feeds back on itself; without this, a nonzero average could grow until the delay line overflows and the model becomes unstable. So the same inverter both extends the low-pitch range and keeps the feedback loop numerically safe. This is why waveguide string terminations use a reflection coefficient of r=-1 (an inverter) rather than r=+1.

Examples

Nord Modular: invert the feedback path so a 256-sample delay line reaches an octave lower without a longer line, while preventing runaway DC overflow.

Assessment

Explain why inverting the reflected wave halves the effective loop frequency. Describe the failure mode (overflow) that DC buildup causes in a non-inverting feedback delay.