spectralFlux

Spectral flux for audio signals and auditory spectrograms

Syntax

flux = spectralFlux(x,f)

flux = spectralFlux(x,f,initialCondition)

flux = spectralFlux(___,Name=Value)

[flux,finalCondition] = spectralFlux(___)

spectralFlux(___)

Description

flux = spectralFlux(x,f) returns the spectral flux of the signal, x, over time. Spectral flux is a measure of the variability of the spectrum over time. How the function interprets x depends on the shape of f.

flux = spectralFlux(x,f,initialCondition) specifies the previous spectral state. This syntax is supported only for frequency-domain inputs.

flux = spectralFlux(___,Name=Value) specifies options using one or more name-value arguments.

For example, flux = spectralFlux(x,f,NormType=1) calculates spectral flux using norm type 1.

[flux,finalCondition] = spectralFlux(___) also returns the final spectral state. You can specify an input combination from any of the previous syntaxes.

spectralFlux(___) with no output arguments plots the spectral flux.

• If the input is in the time domain, the spectral flux is plotted against time.

• If the input is in the frequency domain, the spectral flux is plotted against frame number.

Examples

Spectral Flux of Time-Domain Audio

Read in an audio file and calculate the flux using default parameters.

[audioIn,fs] = audioread("Counting-16-44p1-mono-15secs.wav");
flux = spectralFlux(audioIn,fs);

Plot the spectral flux against time.

spectralFlux(audioIn,fs)

Spectral Flux of Frequency-Domain Audio Data

Read in an audio file and then calculate the mel spectrogram using the melSpectrogram function. Calculate the flux of the mel spectrogram over time.

[audioIn,fs] = audioread("Counting-16-44p1-mono-15secs.wav");

[s,cf,t] = melSpectrogram(audioIn,fs);

flux = spectralFlux(s,cf);

Plot the spectral flux against the frame number.

spectralFlux(s,cf)

Specify Nondefault Parameters

Read in an audio file.

[audioIn,fs] = audioread("Counting-16-44p1-mono-15secs.wav");

Calculate the flux of the power spectrum over time. Calculate the flux for 50 ms Hamming windows of data with 25 ms overlap. Use the range from 62.5 Hz to fs/2 for the flux calculation.

flux = spectralFlux(audioIn,fs, ...
                    Window=hamming(round(0.05*fs)), ...
                    OverlapLength=round(0.025*fs), ...
                    Range=[62.5,fs/2]);                 

Plot the spectral flux.

spectralFlux(audioIn,fs, ...
             Window=hamming(round(0.05*fs)), ...
             OverlapLength=round(0.025*fs), ...
             Range=[62.5,fs/2])

Calculate Spectral Flux of Streaming Audio

Spectral flux measures the change in consecutive spectra. To calculate spectral flux of streaming audio, you can pass the state in and out of the function.

Create a dsp.AudioFileReader object to read in audio data frame-by-frame. Create a dsp.AsyncBuffer object to buffer the audio input into overlapped frames. Create a second dsp.AsyncBuffer object to log the spectral flux calculation.

fileReader = dsp.AudioFileReader('Counting-16-44p1-mono-15secs.wav');
inputBuffer = dsp.AsyncBuffer;
logger = dsp.AsyncBuffer;

In an audio stream loop:

1. Read in a frame of audio data from your source.

2. Write the audio data to the input buffer.

3. If a hop of data is available from the buffer, read a frame of data with overlap.

4. Calculate the one-sided magnitude short time Fourier transform.

5. Calculate the spectral flux.

6. Log the spectral flux for later plotting.

fs = fileReader.SampleRate;

samplesPerFrame = round(fs*0.05);
samplesOverlap = round(fs*0.025);

samplesPerHop = samplesPerFrame - samplesOverlap;

win = hamming(samplesPerFrame,'periodic');

Sprev = [];
while ~isDone(fileReader)
    audioIn = fileReader();
    write(inputBuffer,audioIn);
    
    while inputBuffer.NumUnreadSamples >= samplesPerHop
        audioBuffered = read(inputBuffer,samplesPerFrame,samplesOverlap);
        [S,f] = stft(audioBuffered,fs,"Window",win,"OverlapLength",samplesOverlap,"FrequencyRange","onesided");
        [flux,Sprev] = spectralFlux(abs(S),f,Sprev);
        write(logger,flux);
    end
    
end
release(fileReader)

Plot the logged data.

plot(read(logger))
ylabel('Flux')

Input Arguments

x — Input signal

column vector | matrix | 3-D array

Input signal, specified as a vector, matrix, or 3-D array. How the function interprets x depends on the shape of f.

Data Types: single | double

f — Sample rate or frequency vector (Hz)

scalar | vector

Sample rate or frequency vector in Hz, specified as a scalar or vector, respectively. How the function interprets x depends on the shape of f:

• If f is a scalar, x is interpreted as a time-domain signal, and f is interpreted as the sample rate. In this case, x must be a real vector or matrix. If x is specified as a matrix, the columns are interpreted as individual channels.

• If f is a vector, x is interpreted as a frequency-domain signal, and f is interpreted as the frequencies, in Hz, corresponding to the rows of x. In this case, x must be a real L-by-M-by-N array, where L is the number of spectral values at given frequencies of f, M is the number of individual spectra, and N is the number of channels.

Data Types: single | double

initialCondition — Previous spectral state

[] (default) | matrix

Previous spectral state, specified as an L-by-N matrix, where:

• L is the number of bins in the one-sided spectral representation, equal to numel(f).

• N is the number of channels of audio data, equal to size(x,3).

If initialCondition is unspecified, or specified as an empty, spectralFlux considers the first spectrum as repeating. That is, the first flux output is zero.

Dependencies

This input argument is only valid if the input, x, is a frequency-domain representation of audio. The spectralFlux function interprets the domain of the input x based on the size of f.

Data Types: single | double

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is 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.

Example: Window=hamming(256)

NormType — Norm type

2 (default) | 1

Norm type used to calculate flux, specified as 2 or 1.

Data Types: single | double

Note

The following name-value arguments apply if x is a time-domain signal. If x is a frequency-domain signal, the following name-value arguments are ignored.

Window — Window applied in time domain

rectwin(round(f*0.03)) (default) | vector

Window applied in the time domain, specified as a real vector. The number of elements in the vector must be in the range [1, size(x,1)]. The number of elements in the vector must also be greater than OverlapLength.

Data Types: single | double

OverlapLength — Number of samples overlapped between adjacent windows

round(f*0.02) (default) | non-negative scalar

Number of samples overlapped between adjacent windows, specified as an integer in the range [0, size(Window,1)).

Data Types: single | double

FFTLength — Number of bins in DFT

numel(Window) (default) | positive scalar integer

Number of bins used to calculate the DFT of windowed input samples, specified as a positive scalar integer. If unspecified, FFTLength defaults to the number of elements in the Window.

Data Types: single | double

Range — Frequency range (Hz)

[0,f/2] (default) | two-element row vector

Frequency range in Hz, specified as a two-element row vector of increasing real values in the range [0, f/2].

Data Types: single | double

SpectrumType — Spectrum type

"power" (default) | "magnitude"

Spectrum type, specified as "power" or "magnitude":

• "power" –– The spectral flux is calculated for the one-sided power spectrum.

• "magnitude" –– The spectral flux is calculated for the one-sided magnitude spectrum.

Data Types: char | string

Output Arguments

flux — Spectral flux (Hz)

scalar | vector | matrix

Spectral flux in Hz, returned as a scalar, vector, or matrix. Each row of flux corresponds to the spectral flux of a window of x. Each column of flux corresponds to an independent channel.

finalCondition — Final spectral state

matrix

Final spectral state, returned as an L-by-N matrix, where:

• L is the number of bins in the one-sided spectral representation, equal to numel(f).

• N is the number of channels of audio data, equal to size(x,3).

Dependencies

This output argument is only valid if the input, x, is a frequency-domain representation of audio. The spectralFlux function interprets the domain of the input x based on the size of f.

Algorithms

The spectral flux is calculated as described in [1]:

$$\text{flux(}t\text{)}={\left({\displaystyle \sum _{k=b_1}^{b_2}{\left|s_k(t)-s_k(t-1)\right|}^P}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$P$}\right.}$$

where

• s_k is the spectral value at bin k.

• b₁ and b₂ are the band edges, in bins, over which to calculate the spectral flux.

• P is the norm type. You can specify the norm type using NormType.

References

[1] Scheirer, E., and M. Slaney. "Construction and Evaluation of a Robust Multifeature Speech/Music Discriminator." IEEE International Conference on Acoustics, Speech, and Signal Processing. Volume 2, 1997, pp. 1221–1224.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Version History

Introduced in R2019a