Source: https://jmrplens.github.io/phonometry/guides/sections/core-signal-analysis/ 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](/phonometry/guides/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](/phonometry/guides/filter-banks/) first: it introduces the band decomposition every other page assumes. Then [Integrated and Statistical Levels](/phonometry/guides/levels/) shows the metrics most measurements end in, and [Calibration and dBFS](/phonometry/guides/calibration/) anchors them to physical units. ## [Octave filtering](/phonometry/guides/sections/octave-filtering/) Fractional octave band decomposition and the two ways to scale it: streaming blocks and multichannel arrays. - [Filter Banks](/phonometry/guides/filter-banks/): the five filter architectures, their frequency responses, band decomposition and zero-phase offline filtering. - [Block Processing](/phonometry/guides/block-processing/): stateful streaming analysis that carries filter state across buffers, for signals that never fit in memory. - [Multichannel and Performance](/phonometry/guides/multichannel/): vectorized analysis of many channels at once, with performance notes. ## [Levels and weighting](/phonometry/guides/sections/levels-weighting/) From weighted signal to reported level: the frequency weightings, the time ballistics and the integrated, statistical and rating levels. - [Frequency Weighting (A, C, G, Z)](/phonometry/guides/weighting/): the IEC 61672-1 ear-response curves and the ISO 7196 infrasound G-weighting. - [Time Weighting](/phonometry/guides/time-weighting/): Fast, Slow and Impulse exponential ballistics per IEC 61672-1. - [Integrated and Statistical Levels](/phonometry/guides/levels/): Leq and LAeq, percentile levels L10/L50/L90, LCpeak and SEL, noise dose (IEC 61252), Lden and rating levels (ISO 1996-1), and octave spectrograms. ## [Signals and spectra](/phonometry/guides/sections/signals-spectra/) Fine-grained frequency- and time-domain analysis, every estimate calibrated and carrying its statistical quality. - [Calibrated spectral analysis](/phonometry/guides/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](/phonometry/guides/miso-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](/phonometry/guides/time-frequency/): 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](/phonometry/guides/cepstrum-echoes/): 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](/phonometry/guides/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](/phonometry/guides/correlation-delay/): 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](/phonometry/guides/test-signals/): IEC 60268-1 tone bursts with exact gating, resampling with a stated anti-alias specification, and band-limited fractional delay. - [System measurement](/phonometry/guides/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](/phonometry/guides/sections/calibration-uncertainty/) What the numbers mean and how much to trust them. - [Calibration and dBFS](/phonometry/guides/calibration/): physical SPL calibration from a calibrator tone (IEC 60942) or a known sensitivity, and the digital dBFS mode. - [Measurement uncertainty (GUM and Monte Carlo)](/phonometry/guides/gum-uncertainty/): 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](/phonometry/guides/data-qualification/): the reverse arrangement and runs stationarity tests on segment statistics, and the Rice level-crossing and peak statistics with the irregularity factor.