spectralFlatness

Spectral flatness for signals and spectrograms

Syntax

flatness = spectralFlatness(x,f)

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

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

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.

example

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

example

[flatness,arithmeticMean,geometricMean] = spectralFlatness(___) returns the spectral arithmetic mean and spectral geometric mean. You can specify an input combination from any of the previous syntaxes.

spectralFlatness(___) with no output arguments plots the spectral flatness.

If the input is in the time domain, the spectral flatness is plotted against time.
If the input is in the frequency domain, the spectral flatness is plotted against frame number.

example

Examples

collapse all

Spectral Flatness of Time-Domain Signal

Open Live Script

Create a chirp signal with white Gaussian noise and calculate the flatness using default parameters.

fs = 1000;
t = (0:1/fs:10)';
f1 = 300;
f2 = 400;
x = chirp(t,f1,10,f2) + randn(length(t),1);

flatness = spectralFlatness(x,fs);

Plot the spectral flatness against time.

spectralFlatness(x,fs)

Figure contains an axes object. The axes object with xlabel Time (s), ylabel Flatness contains an object of type line.

ans = 311×1

    0.5951
    0.4338
    0.4518
    0.4575
    0.5389
    0.4725
    0.4386
    0.4528
    0.5575
    0.5752
      ⋮

Spectral Flatness of Frequency-Domain Signal

Open Live Script

Create a chirp signal with white Gaussian noise and then calculate the spectrogram using the stft function.

fs = 1000;
t = (0:1/fs:10)';
f1 = 300;
f2 = 400;
x = chirp(t,f1,10,f2) + randn(length(t),1);

[s,f] = stft(x,fs,FrequencyRange="onesided");
s = abs(s).^2;

Calculate the flatness of the spectrogram over time.

flatness = spectralFlatness(s,f);

Plot the spectral flatness against the frame number.

spectralFlatness(s,f)

Figure contains an axes object. The axes object with xlabel Frame, ylabel Flatness contains an object of type line.

ans = 309×1

    0.3776
    0.4179
    0.4589
    0.4403
    0.4123
    0.4337
    0.4280
    0.5758
    0.4992
    0.4452
      ⋮

Specify Nondefault Parameters

Open Live Script

Create a chirp signal with white Gaussian noise.

fs = 1000;
t = (0:1/fs:10)';
f1 = 300;
f2 = 400;
x = chirp(t,f1,10,f2) + randn(length(t),1);

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.

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

Plot the flatness against time.

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

Figure contains an axes object. The axes object with xlabel Time (s), ylabel Flatness contains an object of type line.

ans = 399×1

    0.4357
    0.6851
    0.5681
    0.5968
    0.4498
    0.4208
    0.4830
    0.2688
    0.4361
    0.5611
      ⋮

Input Arguments

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`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 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` — 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 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

collapse all

`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]:

$flatness = \frac{{(\prod_{k = b_{1}}^{b_{2}} s_{k})}^{\frac{1}{b_{2} - b_{1}}}}{\frac{1}{b_{2} - b_{1}} \sum_{k = b_{1}}^{b_{2}} s_{k}}$

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™.

Version History

Introduced in R2019a

spectralFlatness

Syntax

Description

Examples

Spectral Flatness of Time-Domain Signal

Spectral Flatness of Frequency-Domain Signal

Specify Nondefault Parameters

Input Arguments

`x` — Input signal
column vector | matrix | 3-D array

`f` — Sample rate or frequency vector (Hz)
scalar | vector

Name-Value Arguments

`Window` — Window applied in time domain
`rectwin(round(f*0.03))` (default) | vector

`OverlapLength` — Number of samples overlapped between adjacent windows
`round(f*0.02)` (default) | non-negative scalar

`FFTLength` — Number of bins in DFT
`numel(Window)` (default) | positive scalar integer

`Range` — Frequency range (Hz)
`[0,f/2]` (default) | two-element row vector

`SpectrumType` — Spectrum type
`"power"` (default) | `"magnitude"`

Output Arguments

`flatness` — Spectral flatness
scalar | vector | matrix

`arithmeticMean` — Spectral arithmetic mean
scalar | vector | matrix

`geometricMean` — Spectral geometric mean
scalar | vector | matrix

Algorithms

References

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

See Also

Topics

spectralFlatness

Syntax

Description

Examples

Spectral Flatness of Time-Domain Signal

Spectral Flatness of Frequency-Domain Signal

Specify Nondefault Parameters

Input Arguments

x — Input signal column vector | matrix | 3-D array

f — Sample rate or frequency vector (Hz) scalar | vector

Name-Value Arguments

Window — Window applied in time domain rectwin(round(f*0.03)) (default) | vector

OverlapLength — Number of samples overlapped between adjacent windows round(f*0.02) (default) | non-negative scalar

FFTLength — Number of bins in DFT numel(Window) (default) | positive scalar integer

Range — Frequency range (Hz) [0,f/2] (default) | two-element row vector

SpectrumType — Spectrum type "power" (default) | "magnitude"

Output Arguments

flatness — Spectral flatness scalar | vector | matrix

arithmeticMean — Spectral arithmetic mean scalar | vector | matrix

geometricMean — Spectral geometric mean scalar | vector | matrix

Algorithms

References

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

See Also

Topics

`x` — Input signal
column vector | matrix | 3-D array

`f` — Sample rate or frequency vector (Hz)
scalar | vector

`Window` — Window applied in time domain
`rectwin(round(f*0.03))` (default) | vector

`OverlapLength` — Number of samples overlapped between adjacent windows
`round(f*0.02)` (default) | non-negative scalar

`FFTLength` — Number of bins in DFT
`numel(Window)` (default) | positive scalar integer

`Range` — Frequency range (Hz)
`[0,f/2]` (default) | two-element row vector

`SpectrumType` — Spectrum type
`"power"` (default) | `"magnitude"`

`flatness` — Spectral flatness
scalar | vector | matrix

`arithmeticMean` — Spectral arithmetic mean
scalar | vector | matrix

`geometricMean` — Spectral geometric mean
scalar | vector | matrix

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™.