spectralFlatness

Spectral flatness for audio signals and auditory spectrograms

Syntax

flatness = spectralFlatness(x,f)

flatness = spectralFlatness(x,f,Name,Value)

[flatness,arithmeticMean,geometricMean] = spectralFlatness(___)

Description

flatness = spectralFlatness(x,f) returns the spectral flatness of the signal, x, over time. How the function interprets x depends on the shape of f.

flatness = spectralFlatness(x,f,Name,Value) specifies options using one or more Name,Value pair arguments.

[flatness,arithmeticMean,geometricMean] = spectralFlatness(___) returns the spectral arithmetic mean and spectral geometric mean.

Examples

Spectral Flatness of Time-Domain Audio

Read in an audio file, calculate the flatness using default parameters, and then plot the results.

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

t = linspace(0,size(audioIn,1)/fs,size(flatness,1));
plot(t,flatness)
xlabel('Time (s)')
ylabel('Flatness')

Spectral Flatness of Frequency-Domain Audio Data

Read in an audio file and then calculate the mel spectrogram using the melSpectrogram function.

[audioIn,fs] = audioread('Counting-16-44p1-mono-15secs.wav');
[s,cf,t] = melSpectrogram(audioIn,fs);

Calculate the flatness of the mel spectrogram over time. Plot the results.

flatness = spectralFlatness(s,cf);

plot(t,flatness)
xlabel('Time (s)')
ylabel('Flatness')

Specify Nondefault Parameters

Read in an audio file.

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

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

flatness = spectralFlatness(audioIn,fs, ...
                            'Window',hamming(round(0.05*fs)), ...
                            'OverlapLength',round(0.025*fs), ...
                            'Range',[62.5,fs/2]);
                        
t = linspace(0,size(audioIn,1)/fs,size(flatness,1));
plot(t,flatness)
xlabel('Time (s)')
ylabel('Flatness')

Calculate Spectral Flatness of Streaming Audio

Create a dsp.AudioFileReader object to read in audio data frame-by-frame. Create a dsp.SignalSink to log the spectral flatness calculation.

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

In an audio stream loop:

1. Read in a frame of audio data.

2. Calculate the spectral flatness for the frame of audio.

3. Log the spectral flatness for later plotting.

To calculate the spectral flatness for only a given input frame, specify a window with the same number of samples as the input, and set the overlap length to zero. Plot the logged data.

win = hamming(fileReader.SamplesPerFrame);
while ~isDone(fileReader)
    audioIn = fileReader();
    flatness = spectralFlatness(audioIn,fileReader.SampleRate, ...
                               'Window',win, ...
                               'OverlapLength',0);
    logger(flatness)
end

plot(logger.Buffer)
ylabel('Flatness')

Use dsp.AsyncBuffer if

• The input to your audio stream loop has a variable samples-per-frame.

• The input to your audio stream loop has an inconsistent samples-per-frame with the analysis window of spectralFlatness.

• You want to calculate the spectral flatness for overlapped data.

Create a dsp.AsyncBuffer object, reset the logger, and release the file reader.

buff = dsp.AsyncBuffer;
reset(logger)
release(fileReader)

Specify that the spectral flatness is calculated for 50 ms frames with a 25 ms overlap.

fs = fileReader.SampleRate;

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

samplesPerHop = samplesPerFrame - samplesOverlap;

win = hamming(samplesPerFrame);

while ~isDone(fileReader)
    audioIn = fileReader();
    write(buff,audioIn);
    
    while buff.NumUnreadSamples >= samplesPerHop
        audioBuffered = read(buff,samplesPerFrame,samplesOverlap);
        
        flatness = spectralFlatness(audioBuffered,fs, ...
                                   'Window',win, ...
                                   'OverlapLength',0);
        logger(flatness)
    end
    
end
release(fileReader)

Plot the logged data.

plot(logger.Buffer)
ylabel('Flatness')

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 spectrums, and N is the number of channels.

• The number of rows of x, L, must be equal to the number of elements of f.

Data Types: single | double

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: 'Window',hamming(256)

Note

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

'Window' — Window applied in time domain

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

Window applied in the time domain, specified as the comma-separated pair consisting of 'Window' and 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 the comma-separated pair consisting of 'OverlapLength' and 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 the comma-separated pair consisting of 'FFTLength' and 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 the comma-separated pair consisting of 'Range' and 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 the comma-separated pair consisting of 'SpectrumType' and 'power' or 'magnitude':

• 'power' –– The spectral flatness is calculated for the one-sided power spectrum.

• 'magnitude' –– The spectral flatness is calculated for the one-sided magnitude spectrum.

Data Types: char | string

Output Arguments

flatness — Spectral flatness

scalar | vector | matrix

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

arithmeticMean — Spectral arithmetic mean

scalar | vector | matrix

Spectral arithmetic mean, returned as a scalar, vector, or matrix. Each row of arithmeticMean corresponds to the arithmetic mean of the spectrum of a window of x. Each column of arithmeticMean corresponds to an independent channel.

geometricMean — Spectral geometric mean

scalar | vector | matrix

Spectral geometric mean, returned as a scalar, vector, or matrix. Each row of geometricMean corresponds to the geometric mean of the spectrum of a window of x. Each column of geometricMean corresponds to an independent channel.

Algorithms

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

$$\text{flatness}=\frac{{\left({\displaystyle \prod _{k=b_1}^{b_2}{s}_k}\right)}^{\frac{1}{b_2-b_1}}}{\frac{1}{b_2-b_1}{\displaystyle \sum _{k=b_1}^{b_2}{s}_k}}$$

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 spread.

References

[1] Johnston, J.d. "Transform Coding of Audio Signals Using Perceptual Noise Criteria." IEEE Journal on Selected Areas in Communications. Vol. 6, Number 2, 1988, pp. 314–323.

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™.