Time-Domain and Pitch Descriptors
Use this page for waveform and pitch-related descriptor definitions. These descriptors complement spectral features with noisiness, estimated fundamental frequency, and pitch confidence.
Reference Table
Variables
| Symbol | Meaning | Implementation |
|---|---|---|
| \(x[n]\) | Input audio sample at index \(n\). | In[n] |
| \(n\) | Time-domain sample index. | Loop variable i in ZeroCrossingRateExec, and input index in YINExec |
| \(N\) | Number of samples in the analysis frame. | m_Config.FFTSize; In.size() in YINExec |
| \(\mathbb{I}[\cdot]\) | Indicator function: 1 when the condition is true, otherwise 0. | Increment of local variable crossings |
| \(sign(x[n])\) | Sign of a sample after thresholding near-zero values. | std::signbit when ZCRZeroPos = true; explicit -1, 0, 1 sign otherwise |
| \(\tau\) | YIN lag, measured in samples. | Loop variable tau |
| \(\tau_{min}\) | Smallest lag searched by YIN. | minTau = SR / YINMaxFrequency |
| \(\tau_{max}\) | Largest lag searched by YIN. | maxTau, limited by frame size, YIN buffer size, and YINMinFrequency |
| \(d(\tau)\) | YIN difference function for lag \(\tau\). | Diff[tau], stored in m_YINDifference |
| \(d'(\tau)\) | Cumulative mean normalized difference function (CMNDF). | Cmnfg[tau], stored in m_YINCMNDF |
| \(j\) | Auxiliary summation index in the CMNDF denominator. | Iteration accumulated into local variable cumulative |
| \(\hat{\tau}\) | Selected pitch lag before interpolation. | tauEstimate |
| \(\tau_{refined}\) | Lag after parabolic interpolation. | refinedTau |
| \(SR\) | Sample rate in Hz. | m_Config.SR |
| \(Pitch\) | Estimated fundamental frequency in Hz. | Local variable Pitch, stored in Desc.Pitch |
| \(Confidence\) | Pitch confidence in the range \([0,1]\). | Local variable Confidence, stored in Desc.PitchConfidence |
Zero Crossing Rate
ID: zcr
1
Zero Crossing Rate counts how often the waveform crosses the zero-amplitude line, indicating noisiness or percussiveness.
The current implementation optionally pads the frame when ZCRCenter is enabled, applies the threshold ZCRThreshold, and then counts sign changes. With the default ZCRZeroPos = true, zero is treated as non-negative through std::signbit.
Pitch & PitchConfidence
ID: pitch
Estimated fundamental frequency and confidence are calculated using the YIN algorithm's cumulative mean normalized difference function (CMNDF).
The current implementation searches for the first CMNDF value below YINThreshold, refines the lag by parabolic interpolation, and reports confidence as \(1-d'(\tau)\) clamped to \([0,1]\).