spectralCrest

Spectral crest for signals and spectrograms

Syntax

crest = spectralCrest(x,f)

crest = spectralCrest(x,f,Name=Value)

[crest,spectralPeak,spectralMean] = spectralCrest(___)

spectralCrest(___)

Description

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

example

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

example

[crest,spectralPeak,spectralMean] = spectralCrest(___) returns the spectral peak and spectral mean. You can specify an input combination from any of the previous syntaxes.

spectralCrest(___) with no output arguments plots the spectral crest.

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

example

Examples

collapse all

Spectral Crest of Time-Domain Signal

Open Live Script

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

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

crest = spectralCrest(x,fs);

Plot the spectral crest against time.

spectralCrest(x,fs)

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

ans = 311×1

    4.8498
    7.2279
    7.0162
    9.7382
    7.7927
    5.8750
   11.4581
    9.2194
    4.9127
    5.6860
      ⋮

Spectral Crest 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 crest of the spectrogram over time.

crest = spectralCrest(s,f);

Plot the spectral crest against the frame number.

spectralCrest(s,f)

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

ans = 309×1

    9.1787
   10.0647
   11.2031
   14.9817
   18.3313
   15.6068
   13.2379
   10.2947
   11.5981
   15.9572
      ⋮

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

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

Plot the crest against time.

spectralCrest(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 Crest contains an object of type line.

ans = 399×1

    4.0811
    3.5268
    6.1519
    4.7989
    4.2571
    8.9514
    5.2402
    7.7034
    7.4521
    7.4120
      ⋮

Input Arguments

collapse all

`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 crest is calculated for the one-sided power spectrum.
"magnitude" –– The spectral crest is calculated for the one-sided magnitude spectrum.

Data Types: char | string

Output Arguments

collapse all

`crest` — Spectral crest
scalar | vector | matrix

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

`spectralPeak` — Spectral peak
scalar | vector | matrix

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

`spectralMean` — Spectral mean
scalar | vector | matrix

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

Algorithms

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

$crest = \frac{\max (s_{k \in [b_{1}, b_{2}]})}{\frac{1}{b_{2} - b_{1}} \sum_{k = b_{1}}^{b_{2}} s_{k}}$

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 crest.

References

[1] Peeters, G. "A Large Set of Audio Features for Sound Description (Similarity and Classification) in the CUIDADO Project." Technical Report; IRCAM: Paris, France, 2004.

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

spectralCrest

Syntax

Description

Examples

Spectral Crest of Time-Domain Signal

Spectral Crest 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

`crest` — Spectral crest
scalar | vector | matrix

`spectralPeak` — Spectral peak
scalar | vector | matrix

`spectralMean` — Spectral 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

spectralCrest

Syntax

Description

Examples

Spectral Crest of Time-Domain Signal

Spectral Crest 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

crest — Spectral crest scalar | vector | matrix

spectralPeak — Spectral peak scalar | vector | matrix

spectralMean — Spectral 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"`

`crest` — Spectral crest
scalar | vector | matrix

`spectralPeak` — Spectral peak
scalar | vector | matrix

`spectralMean` — Spectral 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™.