spectralSlope

Spectral slope for audio signals and auditory spectrograms

Syntax

slope = spectralSlope(x,f)

slope = spectralSlope(x,f,Name,Value)

Description

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

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

Examples

Spectral Slope of Time-Domain Audio

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

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

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

Spectral Slope of Frequency-Domain Audio Data

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

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

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

slope = spectralSlope(s,cf);

plot(t,slope)
xlabel('Time (s)')
ylabel('Slope')

Specify Nondefault Parameters

Read in an audio file.

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

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

slope = spectralSlope(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(slope,1));
plot(t,slope)
xlabel('Time (s)')
ylabel('Slope')

Calculate Spectral Slope of Streaming Audio

Create a dsp.AudioFileReader object to read in audio data frame-by-frame. Create a dsp.SignalSink to log the spectral slope 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 slope for the frame of audio.

3. Log the spectral slope for later plotting.

To calculate the spectral slope 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();
    slope = spectralSlope(audioIn,fileReader.SampleRate, ...
                          'Window',win, ...
                          'OverlapLength',0);
    logger(slope)
end

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

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 spectralSlope.

• You want to calculate the spectral slope 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 slope 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);
        
        slope = spectralSlope(audioBuffered,fs, ...
                              'Window',win, ...
                              'OverlapLength',0);
        logger(slope)
    end
    
end
release(fileReader)

Plot the logged data.

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

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.

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

Data Types: single | double

Name-Value 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

'magnitude' (default) | 'power'

Spectrum type, specified as the comma-separated pair consisting of 'SpectrumType' and 'power' or 'magnitude':

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

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

Data Types: char | string

Output Arguments

slope — Spectral slope

scalar | vector | matrix

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

Algorithms

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

$$\text{slope}=\frac{{\displaystyle \sum _{k=b_1}^{b_2}\left(f_k-{\mu }_f\right)\left(s_k-{\mu }_S\right)}}{{\displaystyle \sum _{k=b_1}^{b_2}{\left(f_k-{\mu }_f\right)}^2}}$$

where

• f_k is the frequency in Hz corresponding to bin k.

• μ_f is the mean frequency.

• s_k is the spectral value at bin k.

• μ_s is the mean spectral value.

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

References

[1] Lerch, Alexander. An Introduction to Audio Content Analysis Applications in Signal Processing and Music Informatics. Piscataway, NJ: IEEE Press, 2012.

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™.