Source: https://docs.jmrp.io/phonometry/signals/filters/ # Octave filtering Acoustic analysis rarely wants a raw FFT: standards, ratings and human hearing all work in **fractional octave bands**, frequency intervals whose width grows proportionally with frequency. phonometry implements them as banks of recursive filters whose designs are verified against the class tolerances of **IEC 61260-1:2014**. The default Butterworth bank, and the Chebyshev II and Bessel alternatives, put their **-3 dB points exactly on the ANSI S1.11 band edges**, so their band levels are directly comparable; the two equiripple architectures (Chebyshev I, Elliptic) place their ripple edge there instead and consequently read a few tenths of a decibel high in every band, which is why a campaign should fix one architecture and keep it. The foundation page is [Filter Banks](https://docs.jmrp.io/phonometry/signals/filter-banks/). It covers the band mathematics, how a signal is decomposed into 1/1, 1/3 or arbitrary 1/b octave bands, the parametric EQ and the zero-phase offline mode for analysis where filter delay must not smear the result. Under the hood every bank is a cascade of second-order sections with multirate decimation, which is what keeps low-frequency bands numerically stable. Choosing among the five architectures (Butterworth, Chebyshev I/II, Elliptic and Bessel) is the job of the [Filter Architecture Gallery](https://docs.jmrp.io/phonometry/signals/filter-gallery/): what their frequency responses trade against each other, the full response gallery and per-architecture usage, plus the Linkwitz-Riley crossover. Proving a designed bank against those tolerances is the job of [Filter Class Verification (IEC 61260-1)](https://docs.jmrp.io/phonometry/signals/filter-compliance/): the Table 1 acceptance mask band by band, the effective bandwidth and the summation of outputs as IEC 61260-2 tests them, the swept time-invariance test, the stricter class 0 of the withdrawn 1995 edition, what a performance class buys in a measurement, and the accredited one-page compliance fiche. The same guide grades a laboratory's IEC 61260-3 periodic test results. The other two pages scale that foundation along two independent axes. [Block Processing](https://docs.jmrp.io/phonometry/signals/block-processing/) scales it in *time*: signals that never fit in memory (hour-long recordings, live monitoring, embedded loggers) are processed buffer by buffer with carried filter state, so the result is bit-identical to a single pass *through the same bank*: streaming rules out both the multirate decimation and the per-block detrending an offline bank uses by default, so the offline pass a streamed result is compared against has to be built the same way. [Multichannel and Performance](https://docs.jmrp.io/phonometry/signals/multichannel/) scales it in *channels*: microphone arrays and multichannel recordings are analysed vectorized, one call for all channels, with notes on where the computation time actually goes. Read them in that order. Everything downstream (levels, loudness, room parameters) consumes the band signals or band levels these pages produce. ## Pages in this section - [Filter Banks](https://docs.jmrp.io/phonometry/signals/filter-banks/): the band mathematics, bank parameters, parametric EQ, band decomposition and zero-phase filtering. - [Filter Architecture Gallery](https://docs.jmrp.io/phonometry/signals/filter-gallery/): the five architectures compared, the response gallery and per-architecture usage. - [Filter Class Verification (IEC 61260-1)](https://docs.jmrp.io/phonometry/signals/filter-compliance/): the Table 1 acceptance mask, effective bandwidth, summation and swept test, periodic-test grading, class 0 and the compliance fiche. - [Block Processing](https://docs.jmrp.io/phonometry/signals/block-processing/): stateful streaming workflows with carried filter state. - [Multichannel and Performance](https://docs.jmrp.io/phonometry/signals/multichannel/): vectorized multichannel analysis and performance notes. ## What this section does not cover `verify_filter_class` checks a designed digital response against Table 1 of IEC 61260-1 and grades the effective bandwidth (5.12) and the summation of outputs (5.16) on it as IEC 61260-2 computes them, and `verify_time_invariance` runs the swept test of 5.14 through the bank itself; a class verdict here is a statement about the design and not about a device. The tests IEC 61260-2 and IEC 61260-3 run on a physical filter (overload, linearity, self-generated noise, the environmental influence quantities) need the instrument in a laboratory and are not run here; `verify_filter_periodic` grades the results a laboratory brings back from the periodic tests, and says what they cannot show. Near Nyquist the bilinear transform warps the frequency axis and the bank carries no correction for it, unlike the fitted `high_accuracy` design of the weighting filters: `verify_filter_class` grades every band up to half the input rate, the alias images a decimated band reads included, and reports the stopband beyond it as `range_limited` rather than verified, so keep the top band edge comfortably below Nyquist or raise `fs`. Two operations do not stream: zero-phase forward-backward filtering needs the whole signal, and rank statistics such as L90 have to be computed once on the pooled envelope. And the per-channel path never mixes channels: delay between two microphones, or how much of one channel a second explains, is [Correlation and delay](https://docs.jmrp.io/phonometry/spectra/correlation-delay/) and [Multiple and partial coherence](https://docs.jmrp.io/phonometry/spectra/miso-coherence/).