Skip to content
phonometry

Core signal analysis

By José M. Requena Plens · Published , updated

Everything in phonometry starts here. This section covers the chain that turns a raw digital signal into standards-compliant acoustic numbers: split it into fractional octave bands (ANSI S1.11 / IEC 61260-1), shape it with the frequency weightings of IEC 61672-1, smooth it with the Fast/Slow/Impulse time ballistics, and integrate it into Leq and statistical levels. It is, in effect, a sound level meter decomposed into composable functions, and every other section of the documentation builds on it: a loudness model consumes calibrated band levels, a room parameter starts from a filtered impulse response, an environmental rating is an adjusted Leq. Build a sound level meter assembles that chain end to end on a single runnable page; it is the best starting point if you want to see the whole area at work before opening the deep guides.

Around the level chain sit the general signal-analysis tools: calibrated spectral estimates (Welch PSD and cross-spectral density with confidence intervals), correlation and time-delay estimation and the Hilbert envelope, all stated with the Bendat & Piersol error analysis. And two transversal concerns complete the core. Calibration decides what the digital samples mean physically: results can be referenced to a measured calibrator tone or a known sensitivity (dB SPL), or stay in digital full scale (dBFS). Measurement uncertainty (the GUM and its Monte Carlo supplement) qualifies any result computed from uncertain inputs, which is what makes a number defensible in a report.

If you are new to the library, read Filter Banks first: it introduces the band decomposition every other page assumes. Then Integrated and Statistical Levels shows the metrics most measurements end in, and Calibration and dBFS anchors them to physical units.

Octave filtering

Section titled “Octave filtering”

Fractional octave band decomposition and the two ways to scale it: streaming blocks and multichannel arrays.

  • Filter Banks: the five filter architectures, their frequency responses, band decomposition and zero-phase offline filtering.
  • Block Processing: stateful streaming analysis that carries filter state across buffers, for signals that never fit in memory.
  • Multichannel and Performance: vectorized analysis of many channels at once, with performance notes.

Levels and weighting

Section titled “Levels and weighting”

From weighted signal to reported level: the frequency weightings, the time ballistics and the integrated, statistical and rating levels.

Signals and spectra

Section titled “Signals and spectra”

Fine-grained frequency- and time-domain analysis, every estimate calibrated and carrying its statistical quality.

  • Calibrated spectral analysis: the Bendat & Piersol Welch estimators with their statistical quality: PSD and cross-spectral density with chi-square confidence intervals, the coherent output spectrum with the spectral SNR, 1/n-octave smoothing and exact-slope colored-noise generators.
  • Multiple and partial coherence: the multiple-input/output coherence functions for multiple correlated sources and one output, with the conditioning that tells a genuine cause from a source that merely correlates with it, and the partial coherent output spectra that say which source dominates each band.
  • Time-frequency analysis: the calibrated STFT spectrogram in absolute units (dB SPL for pascals) and the zoom FFT that resolves tones closer than a practical FFT bin.
  • Cepstrum, echoes and the envelope spectrum: the power, real and complex cepstrum with quefrency analysis, echo detection with the reflection coefficient read off the cepstral peak, lowpass/highpass liftering of a log spectrum, and the envelope spectrum that turns amplitude modulations into discrete lines.
  • Time synchronous averaging: extraction of a periodic waveform of known period by time domain averaging, the comb filter that describes it in the frequency domain, the square-root noise-reduction law, and the choice of the number of averages that places a comb node on an interfering order (McFadden 1987).
  • Correlation, time delay and envelope: correlation estimates with the Bendat & Piersol random errors, time-delay estimation by direct correlation, cross-spectrum phase slope and the Knapp & Carter GCC weightings, sub-sample impulse-response delay and alignment, and the Hilbert envelope.
  • Test signals and sample-rate tools: IEC 60268-1 tone bursts with exact gating, resampling with a stated anti-alias specification, and band-limited fractional delay.
  • System measurement: complementary Golay pairs, sweeps with an arbitrary target magnitude spectrum by group-delay shaping, and the Kirkeby-regularized inversion of a measured response.

Calibration and uncertainty

Section titled “Calibration and uncertainty”

What the numbers mean and how much to trust them.

  • Calibration and dBFS: physical SPL calibration from a calibrator tone (IEC 60942) or a known sensitivity, and the digital dBFS mode.
  • Measurement uncertainty (GUM and Monte Carlo): the law of propagation of uncertainty and the Monte Carlo method of ISO/IEC Guide 98-3, with expanded uncertainty and coverage intervals.
  • Data qualification: the reverse arrangement and runs stationarity tests on segment statistics, and the Rice level-crossing and peak statistics with the irregularity factor.
Created and maintained by· GitHub· PyPI· All projects