# spectralSlope

Spectral slope for audio signals and auditory spectrograms

## Description

example

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.

example

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

example

spectralSlope(___) with no output arguments plots the spectral slope. You can specify an input combination from any of the previous syntaxes.

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

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

## Examples

collapse all

Read in an audio file, calculate the slope using default parameters.

slope = spectralSlope(audioIn,fs);

Plot the spectral slope against time.

spectralSlope(audioIn,fs)

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.

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

slope = spectralSlope(s,cf);

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

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.

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

Plot the spectral slope against time.

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

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

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.

'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)

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

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

samplesPerHop = samplesPerFrame - samplesOverlap;

win = hamming(samplesPerFrame);

write(buff,audioIn);

slope = spectralSlope(audioBuffered,fs, ...
'Window',win, ...
'OverlapLength',0);
logger(slope)
end

end

Plot the logged data.

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

## Input Arguments

collapse all

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

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 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)

Note

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

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

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

Data Types: single | double

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

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

Spectrum type, specified as "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

collapse all

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]:

$\text{slope}=\frac{\sum _{k={b}_{1}}^{{b}_{2}}\left({f}_{k}-{\mu }_{f}\right)\left({s}_{k}-{\mu }_{S}\right)}{\sum _{k={b}_{1}}^{{b}_{2}}{\left({f}_{k}-{\mu }_{f}\right)}^{2}}$

where

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

• μf is the mean frequency.

• sk is the spectral value at bin k.

• μs 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.

## Version History

Introduced in R2019a