# acousticFluctuation

## Syntax

## Description

returns fluctuation strength in vacil based on Zwicker et al. [1] and ISO 532-1
time-varying loudness [2].`fluctuation`

= acousticFluctuation(`audioIn`

,`fs`

)

specifies a nondefault microphone calibration factor used to compute loudness.`fluctuation`

= acousticFluctuation(`audioIn`

,`fs`

,`calibrationFactor`

)

computes fluctuation using time-varying specific loudness.`fluctuation`

= acousticFluctuation(`specificLoudnessIn`

)

specifies options using one or more `fluctuation`

= acousticFluctuation(___,`Name,Value`

)`Name,Value`

pair arguments.

**Example: **```
fluctuation =
acousticFluctuation(audioIn,fs,'SoundField','diffuse')
```

returns fluctuation
assuming a diffuse sound field.

`[`

also returns specific fluctuation strength.`fluctuation`

,`specificFluctuation`

] = acousticFluctuation(___)

`[`

also returns the dominant modulation frequency.`fluctuation`

,`specificFluctuation`

,`fMod`

] = acousticFluctuation(___)

`acousticFluctuation(___)`

with no output arguments
plots fluctuation strength and specific fluctuation strength and displays the modulation
frequency textually. If the input is stereo, the 3-D plot shows the sum of both
channels.

## Examples

## Input Arguments

## Output Arguments

## Algorithms

Acoustic fluctuation strength is a perceptual measurement of slow modulations in amplitude
or frequency. The acoustic loudness algorithm is described in [1] and implemented in the
`acousticLoudness`

function. The acoustic fluctuation calculation is described in [2]. The algorithm for acoustic
fluctuation is outlined as follows.

$$fluctuation=\frac{0.008{\displaystyle \underset{z=0}{\overset{24}{\int}}\Delta L\text{\hspace{0.17em}}dz}}{\left(\frac{{f}_{\mathrm{mod}}}{4}\right)+\left(\frac{4}{{f}_{\mathrm{mod}}}\right)}$$

Where *f*_{mod} is the detected or
known modulation frequency and Δ*L* is the perceived modulation depth. If the
modulation frequency is not specified when calling `acousticFluctuation`

,
it is auto-detected by peak-picking a frequency-domain representation of the acoustic
loudness. The perceived modulation depth, Δ*L*, is calculated by passing
rectified specific loudness bands through ½ octave filters centered around
*f*_{mod}, followed by a lowpass filter to determine
the envelope.

## References

[1] ISO 532-1:2017(E). "Acoustics –
Methods for calculating loudness – Part 1: Zwicker method." *International
Organization for Standardization*.

[2] Zwicker, Eberhard, and H. Fastl.
*Psychoacoustics: Facts and Models*. 2nd updated ed,
Springer, 1999.

## Extended Capabilities

## Version History

**Introduced in R2020b**