Perceived fluctuation strength of acoustic signal
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
Measure Acoustic Fluctuation
Fluctuation Measurements Using Calibrated Microphone
Set up an experiment as indicated by the diagram.
fs = 48e3; deviceReader = audioDeviceReader(fs,"SamplesPerFrame",2048); deviceWriter = audioDeviceWriter(fs);
audioOscillator object to generate a 1 kHz sinusoid.
osc = audioOscillator("sine",1e3,"SampleRate",fs,"SamplesPerFrame",2048);
dsp.AsyncBuffer object to buffer data acquired from the microphone.
dur = 5; buff = dsp.AsyncBuffer(dur*fs);
For five seconds, play the sinusoid through your speaker and record using your microphone. While the audio streams, note the loudness as reported by your SPL meter. Once complete, read the contents of the buffer object.
numFrames = dur*(fs/osc.SamplesPerFrame); for ii = 1:numFrames audioOut = osc(); deviceWriter(audioOut); audioIn = deviceReader(); write(buff,audioIn); end SPLreading = 60.4; micRecording = read(buff);
To compute the calibration factor for the microphone, use the
calibrationFactor = calibrateMicrophone(micRecording(fs+1:end,:),deviceReader.SampleRate,SPLreading);
You can now use the calibration factor you determined to measure the fluctuation of any sound that is acquired through the same microphone recording chain.
Perform the experiment again, this time, add 100% amplitude modulation at 4 Hz. To create the modulation signal, use
audioOscillator and specify the amplitude as
0.5 and the DC offset as
0.5 to oscillate between 0 and 1.
mod = audioOscillator("sine",4,"SampleRate",fs, ... "Amplitude",0.5,"DCOffset",0.5,"SamplesPerFrame",2048); dur = 5; buff = dsp.AsyncBuffer(dur*fs); numFrames = dur*(fs/osc.SamplesPerFrame); for ii = 1:numFrames audioOut = osc().*mod(); deviceWriter(audioOut); audioIn = deviceReader(); write(buff,audioIn); end micRecording = read(buff);
acousticFluctuation with the microphone recording, sample rate, and calibration factor. The fluctuation reported from
acousticFluctuation uses the true acoustic loudness measurement as specified by 532-1. Display the average fluctuation strength over the 5 seconds.
fluctuation = acousticFluctuation(micRecording,deviceReader.SampleRate,calibrationFactor); fprintf('Average fluctuation = %d (vacil)',mean(fluctuation(501:end,:)))
Average fluctuation = 1.413824e+00 (vacil)
Measure Fluctuation from Specific Loudness
Read in an audio file.
[audioIn,fs] = audioread("Engine-16-44p1-stereo-20sec.wav");
acousticLoudness to calculate the specific loudness.
[~,specificLoudness] = acousticLoudness(audioIn,fs,'TimeVarying',true);
acousticSharpness without any outputs to plot the acoustic sharpness.
acousticFluctuation without any outputs to plot the acoustic fluctuation.
Effect of Frequency Modulation on Acoustic Fluctuation
Generate a pure tone with a 1500 Hz center frequency and approximately 700 Hz frequency deviation at a modulation frequency of 0.25 Hz.
fs = 48e3; fMod = 0.25; dur = 20; numSamples = dur*fs; t = (0:numSamples-1)/fs; tone = sin(2*pi*t*fMod)'; fc = 1500; excursionRatio = 0.47; excursion = 2*pi*(fc*excursionRatio/fs); audioIn = modulate(tone,fc,fs,'fm',excursion);
Listen to the first 5 seconds of the audio and plot the spectrogram.
acousticFluctuation with no output arguments to plot the acoustic fluctuation strength.
Specify Known Modulation Frequency
acousticFluctuation function enables you to specify a known fluctuation frequency. If you do not specify a known fluctuation frequency, the function auto-detects the fluctuation.
fileReader = dsp.AudioFileReader('Engine-16-44p1-stereo-20sec.wav'); fmod = 10.8; amplitude = 0.15; osc = audioOscillator('sine',fmod, ... "DCOffset",0.5, ... "Amplitude",amplitude, ... "SampleRate",fileReader.SampleRate, ... "SamplesPerFrame",fileReader.SamplesPerFrame); testSignal = ; while ~isDone(fileReader) x = fileReader(); testSignal = [testSignal;osc().*fileReader()]; end
Listen to two seconds of the test signal and plot its waveform.
samplesToView = 1:2*fileReader.SampleRate; sound(testSignal(samplesToView,:),fileReader.SampleRate); plot(samplesToView/fileReader.SampleRate,testSignal(samplesToView,:)) xlabel('Time (s)')
Plot the acoustic fluctuation. The detected frequency of the modulation is displayed textually.
Specify the known modulation frequency and then plot the acoustic fluctuation again.
audioIn — Audio input
column vector | two-column matrix
Audio input, specified as a column vector (mono) or matrix with two columns (stereo).
To measure fluctuation strength given any modulation frequency, the recommended minimum signal duration is 10 seconds.
fs — Sample rate (Hz)
Sample rate in Hz, specified as a positive scalar. The recommended sample rate for new recordings is 48 kHz.
The minimum acceptable sample rate is 8 kHz.
calibrationFactor — Microphone calibration factor
sqrt(8) (default) | positive scalar
Microphone calibration factor, specified as a positive scalar. The default
calibration factor corresponds to a full-scale 1 kHz sine wave with a sound pressure
level of 100 dB (SPL). To compute the calibration factor specific to your system, use
specificLoudnessIn — Specific loudness (sones/Bark)
Specific loudness in sones/Bark, specified as a T-by-240-by-C array, where:
T is one per 2 ms of the time-varying signal.
240 is the number of Bark bins in the domain for specific loudness. The Bark bins are
C is the number of channels.
You can use the
acousticLoudness function to calculate time-varying specific loudness
[~,specificLoudness] = acousticLoudness(audioIn,fs,'TimeVarying',true);
Specify optional pairs of arguments as
the argument name and
Value is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name in quotes.
ModulationFrequency — Known modulation frequency (Hz)
'auto-detect' (default) | scalar or two-element vector with values in the range
Known modulation frequency in Hz, specified either
'auto-detect' or as a scalar or two-element vector with values in
'auto-detect', then the function limits the search range to
between 0.2 and 64 Hz. If the input is mono, then the modulation frequency must be
specified as a scalar. If the input is stereo, then the modulation frequency can be
specified as either a scalar or two-element vector.
SoundField — Sound field
'free' (default) |
Sound field of audio recording, specified as
PressureReference — Reference pressure (Pa)
20e-6 (default) | positive scalar
Reference pressure for dB calculation in pascals, specified as a positive scalar. The default value, 20 micropascals, is the common value of air.
fluctuation — Fluctuation strength (vacil)
K-by-1 | K-by-2
Fluctuation strength in vacil, returned as a K-by-1 column vector or K-by-2 matrix of independent channels. K corresponds to the time dimension.
specificFluctuation — Specific fluctuation strength (vacil/Bark)
K-by-47 matrix | K-by-47-by-2 array
Specific fluctuation strength in vacil/Bark, returned as a
K-by-47 matrix or a K-by-47-by-2 array. The first
specificFluctation, K, corresponds
to the time dimension and matches the first dimension of
fluctuation. The second dimension of
specificFluctation, 47, corresponds to bands on the Bark scale,
with centers from 0.5 to 23.5, inclusive, in 0.5 increments. The third dimension of
specificFluctation corresponds to the number of channels and
matches the second dimension of
fMod — Dominant modulation frequency (Hz)
scalar (mono input) | 1-by-2 vector (stereo input)
Dominant modulation frequency in Hz, returned as a scalar for mono input or a 1-by-2 vector for stereo input.
Acoustic fluctuation strength is a perceptual measurement of slow modulations in amplitude
or frequency. The acoustic loudness algorithm is described in  and implemented in the
function. The acoustic fluctuation calculation is described in . The algorithm for acoustic
fluctuation is outlined as follows.
Where fmod is the detected or
known modulation frequency and ΔL is the perceived modulation depth. If the
modulation frequency is not specified when calling
it is auto-detected by peak-picking a frequency-domain representation of the acoustic
loudness. The perceived modulation depth, ΔL, is calculated by passing
rectified specific loudness bands through ½ octave filters centered around
fmod, followed by a lowpass filter to determine
 ISO 532-1:2017(E). "Acoustics – Methods for calculating loudness – Part 1: Zwicker method." International Organization for Standardization.
 Zwicker, Eberhard, and H. Fastl. Psychoacoustics: Facts and Models. 2nd updated ed, Springer, 1999.