ZwickerLoudness.jl

Zwicker loudness calculation for stationary sounds per ISO 532-1:2017 (Method 1).

Converts 28 one-third-octave band SPL values into perceptual loudness in sones and phons, with 240-bin specific loudness at 0.1 Bark resolution.

Installation

using Pkg
Pkg.add(url="https://github.com/slink/ZwickerLoudness.jl")

Quick Start

using ZwickerLoudness

# 28 one-third-octave band SPL values [dB], 25 Hz to 12.5 kHz
spl = [60, 62, 65, 68, 70, 72, 74, 75, 73, 71,
       69, 67, 65, 63, 61, 59, 57, 55, 53, 50,
       47, 44, 41, 38, 35, 32, 29, 26.0]

result = zwicker_loudness(spl)

result.loudness           # total loudness [sone]
result.loudness_level     # loudness level [phon]
result.specific_loudness  # N'(z) at 0.1 Bark resolution [sone/Bark] (240 values)

# Diffuse field listening condition
result_diffuse = zwicker_loudness(spl; field_type=:diffuse)

Also accepts 31-band input (standard 20 Hz -- 20 kHz); bands 2--29 are extracted automatically.

How It Works

The ISO 532-1:2017 pipeline:

28 one-third-octave bands (25 Hz -- 12.5 kHz)
    |
    v
Low-frequency correction (DLL table, equal-loudness contours)
    |
    v
20 critical band excitation levels (energy summation + ear transmission)
    |
    v
Core specific loudness (Zwicker power-law, s=0.25, korry correction)
    |
    v
240-bin spreading (USL/RNS slope tables, 0.1 Bark resolution)
    |
    v
Integration --> total loudness [sone] --> loudness level [phon]

Key psychoacoustic effects modeled:

• Low-frequency correction -- equal-loudness contour weighting for bands below 315 Hz
• Threshold in quiet -- frequency-dependent minimum audibility per critical band
• Ear transmission -- outer/middle ear transfer function (A0 correction)
• Loudness growth -- power-law compression with critical band adaptation (DCB)
• Spreading function -- upward spread of masking via tabulated upper slopes (USL)
• Free/diffuse field -- selectable listening condition (DDF correction)

API

zwicker_loudness(spl; field_type=:free) -> ZwickerResult

Compute Zwicker loudness from one-third-octave band SPL values.

Input: Vector of SPL values [dB] for 28 bands (25 Hz -- 12.5 kHz). Also accepts 31 bands (20 Hz -- 20 kHz), shorter vectors (padded with silence), or longer vectors (truncated).

Keyword arguments:

Argument	Default	Description
field_type	:free	Listening condition: :free or :diffuse

Returns a ZwickerResult:

Field	Type	Description
loudness	Float64	Total loudness [sone]
loudness_level	Float64	Loudness level [phon]
specific_loudness	Vector{Float64}	N'(z) at 0.1 Bark resolution [sone/Bark], 240 values

Conformance

Validated against ISO 532-1:2017 Annex B test signals and cross-checked with the MoSQITo Python reference implementation.

Test Signal	Expected [sone]	Result [sone]	Tolerance
Annex B Signal 1 (broadband)	83.296	83.296	+/-5%

References

• ISO 532-1:2017 -- Acoustics: Methods for calculating loudness, Part 1: Zwicker method
• Zwicker, E. (1991). "Program for calculating loudness according to DIN 45631 (ISO 532B)". J. Acoust. Soc. Jpn. (E) 12, 1.
• Zwicker, E. & Fastl, H. (2007). Psychoacoustics: Facts and Models. Springer.

License

MIT