zerocrossings

Zerocrossings are the instants at which a signal changes sign, crossing the value zero. In a continuous-time signal x(t), a zerocrossing occurs at times t such that x(t) = 0. In a discrete-time signal x[n], zerocrossings are identified where consecutive samples have opposite signs or where a sample exactly equals zero. For a pure sinusoid, zerocrossings occur twice per period, spaced by half a cycle, assuming no DC offset or noise.

A common derived feature is the zero-crossing rate (ZCR), which counts the number of sign changes between consecutive samples within a frame and normalizes by the frame length. ZCR provides a coarse indication of a signal’s frequency content and is used in tasks such as voicing detection in speech, music onset detection, and simple pitch or tempo estimation. In practice, sign changes are usually computed with sign(x[n]) ≠ sign(x[n−1]), with special handling when samples are exactly zero.

Detection and analysis often require preprocessing. Removing DC offset and filtering to reduce noise can prevent spurious zero-crossings. Sub-sample timing can be estimated by linear interpolation around the crossing, improving accuracy for timing-based applications. Noise and high-frequency components can inflate ZCR and degrade reliability, so ZCR is typically used in combination with other features.

Limitations include sensitivity to noise, DC bias, and waveform shape; zero-crossings do not uniquely determine frequency content for complex signals. Variants include replacing the zero threshold with a small positive/negative level or using crossing-rate with slope constraints to improve robustness.