edsp::feature::spectral Namespace Reference

Functions
template<typename ForwardIt >
constexpr auto	spectral_crest (ForwardIt first, ForwardIt last)
	Computes the spectral crest of the of the magnitude spectrum represented by the elements in the range [first, last) More...
template<typename ForwardIt >
constexpr auto	spectral_decrease (ForwardIt first, ForwardIt last)
	Computes the spectral decrease of the of the magnitude spectrum represented by the elements in the range [first, last) More...
template<typename ForwardIt >
constexpr auto	spectral_entropy (ForwardIt first, ForwardIt last)
	Computes the spectral entropy of the of the power spectral density represented by the elements in the range [first, last) More...
template<typename ForwardIt >
constexpr auto	spectral_flatness (ForwardIt first, ForwardIt last)
	Computes the spectral flatness of the of the magnitude spectrum represented by the elements in the range [first, last) More...
template<typename ForwardIt >
constexpr auto	spectral_flux (ForwardIt first1, ForwardIt last1, ForwardIt first2)
	Computes the spectral flux of the of the magnitude spectrum represented by the elements in the range [first, last) More...
template<typename ForwardIt >
constexpr auto	spectral_irregularity (ForwardIt first, ForwardIt last)
	Computes the spectral irregularity of the of the magnitude spectrum represented by the elements in the range [first, last) More...
template<typename ForwardIt >
constexpr auto	spectral_kurtosis (ForwardIt first, ForwardIt last)
	Computes the spectral kurtosis of the of the magnitude spectrum represented by the elements in the range [first, last) More...
template<typename ForwardIt , typename Numeric >
constexpr auto	spectral_rolloff (ForwardIt first, ForwardIt last, Numeric percentage=0.95)
	Computes the spectral roll-off of the of the magnitude spectrum represented by the elements in the range [first, last) More...
template<typename ForwardIt >
constexpr auto	spectral_skewness (ForwardIt first, ForwardIt last)
	Computes the spectral skewness of the of the magnitude spectrum represented by the elements in the range [first, last) More...
template<typename ForwardIt >
constexpr auto	spectral_slope (ForwardIt first1, ForwardIt last1, ForwardIt first2)
	Computes the spectral slope of the of the magnitude spectrum represented by the elements in the range [first, last) More...
template<typename ForwardIt >
constexpr auto	spectral_spread (ForwardIt first1, ForwardIt last1, ForwardIt first2)
	Computes the spectral spread of the of the magnitude spectrum represented by the elements in the range [first, last) More...
template<typename ForwardIt >
constexpr auto	spectral_variation (ForwardIt first1, ForwardIt last1, ForwardIt first2)
	Computes the spectral variation of the of the magnitude spectrum represented by the elements in the range [first, last) More...

Function Documentation

spectral_crest()

template<typename ForwardIt >

constexpr auto edsp::feature::spectral::spectral_crest	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the spectral crest of the of the magnitude spectrum represented by the elements in the range [first, last)

The spectral crest is a measure of the noisiness of the spectrum.

Parameters

first	Forward iterator defining the begin of the magnitude spectrum.
last	Forward iterator defining the end of the magnitude spectrum.

Returns

Estimated spectral crest.

See also

spectral_flatness, crest

spectral_decrease()

template<typename ForwardIt >

constexpr auto edsp::feature::spectral::spectral_decrease	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the spectral decrease of the of the magnitude spectrum represented by the elements in the range [first, last)

The spectral decrease represents the amount of decreasing of the spectral amplitude. It is defined as:

\[ d = \frac{1}{ \sum_{n=2}^{N-1} x(n)} \sum_{n=2}^{N-1} \frac{x(n) - x(n-1)}{n - 1} \]

Parameters

first	Forward iterator defining the begin of the magnitude spectrum.
last	Forward iterator defining the end of the magnitude spectrum.

Returns

Estimated spectral decrease.

spectral_entropy()

template<typename ForwardIt >

constexpr auto edsp::feature::spectral::spectral_entropy	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the spectral entropy of the of the power spectral density represented by the elements in the range [first, last)

Spectral Entropy describes the complexity of a system. The PSD of a audio signal can be computed as the normalized version of the Power Spectral Density:

\[ p_i=\frac{P(\omega_i)}{\sum_iP(\omega_i)} \]

The Power Spectral entropy can be now calculated using a standard formula for an entropy calculation.

Warning

This function normalize/modifies the input range.

Parameters

first	Forward iterator defining the begin of the magnitude spectrum.
last	Forward iterator defining the end of the magnitude spectrum.
first2	Forward iterator defining the begin of the center frequencies range.

Returns

Estimated spectral entropy.

See also

entropy

spectral_flatness()

template<typename ForwardIt >

constexpr auto edsp::feature::spectral::spectral_flatness	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the spectral flatness of the of the magnitude spectrum represented by the elements in the range [first, last)

The spectral flatness is a measure of the noisiness of the spectrum.

Parameters

first	Forward iterator defining the begin of the magnitude spectrum.
last	Forward iterator defining the end of the magnitude spectrum.

Returns

Estimated spectral flatness.

See also

spectral_crest, flatness

spectral_flux()

template<typename ForwardIt >

constexpr auto edsp::feature::spectral::spectral_flux	(	ForwardIt	first1,
		ForwardIt	last1,
		ForwardIt	first2
	)

Computes the spectral flux of the of the magnitude spectrum represented by the elements in the range [first, last)

Parameters

first1	Forward iterator defining the begin of the first magnitude spectrum.
last1	Forward iterator defining the end of the first magnitude spectrum.
first2	Input iterator defining the beginning of the second magnitude spectrum.

Returns

The estimated flux.

See also

flux

spectral_irregularity()

template<typename ForwardIt >

constexpr auto edsp::feature::spectral::spectral_irregularity	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the spectral irregularity of the of the magnitude spectrum represented by the elements in the range [first, last)

The spectral irregularity quantifies the variations of the logarithmically-scaled rate-map across frequencies. This implementation is based on [Jensen 1999] where the spectral irregularity is estimated as the sum of the square of the difference in amplitude between adjoining partials.

See also

[Jensen, 1999] K. Jensen, Timbre Models of Musical Sounds, Ph.D. dissertation, University of Copenhagen, Rapport Nr. 99/7.

Parameters

first	Forward iterator defining the begin of the magnitude spectrum.
last	Forward iterator defining the end of the magnitude spectrum.

Returns

Estimated spectral irregularity.

See also

irregularity

spectral_kurtosis()

template<typename ForwardIt >

constexpr auto edsp::feature::spectral::spectral_kurtosis	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the spectral kurtosis of the of the magnitude spectrum represented by the elements in the range [first, last)

Parameters

first	Forward iterator defining the begin of the magnitude spectrum.
last	Forward iterator defining the end of the magnitude spectrum.

Returns

Estimated spectral kurtosis.

See also

kurtosis

spectral_rolloff()

template<typename ForwardIt , typename Numeric >

constexpr auto edsp::feature::spectral::spectral_rolloff	(	ForwardIt	first,
		ForwardIt	last,
		Numeric	percentage = 0.95
	)

Computes the spectral roll-off of the of the magnitude spectrum represented by the elements in the range [first, last)

The spectral roll-off point is the frequency so that \( \alpha \) of the signal energy is contained below this frequency.

Parameters

first	Forward iterator defining the begin of the magnitude spectrum.
last	Forward iterator defining the end of the magnitude spectrum.
percentage	Number between [0, 1] representing the percentage of the total energy of the roll-off frequency.

Returns

Estimated roll-off index.

See also

rolloff

spectral_skewness()

template<typename ForwardIt >

constexpr auto edsp::feature::spectral::spectral_skewness	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the spectral skewness of the of the magnitude spectrum represented by the elements in the range [first, last)

Parameters

first	Forward iterator defining the begin of the magnitude spectrum.
last	Forward iterator defining the end of the magnitude spectrum.

Returns

Estimated spectral skewness.

See also

skewness

spectral_slope()

template<typename ForwardIt >

constexpr auto edsp::feature::spectral::spectral_slope	(	ForwardIt	first1,
		ForwardIt	last1,
		ForwardIt	first2
	)

Computes the spectral slope of the of the magnitude spectrum represented by the elements in the range [first, last)

The spectral slope represents the amount of decreasing of the spectral amplitude. It is computed by linear regression of the spectral amplitude:

\[ G = a f + b \]

where a is the parameter of interest. In this case is computed as follows:

\[ a = \frac{1}{\sum_k a(k)} \frac{N \sum_k a(k) f(k) - \sum_k a(k) * \sum_k f(k)} {N \sum_k f^2(k) - \left( \sum_k f(k) \right)^2} \]

where f is a vector representing the different frequency bins.

Parameters

first1	Forward iterator defining the begin of the magnitude spectrum.
last1	Forward iterator defining the end of the magnitude spectrum.
first2	Forward iterator defining the begin of the center frequencies range.

Returns

Estimated spectral slope.

spectral_spread()

template<typename ForwardIt >

constexpr auto edsp::feature::spectral::spectral_spread	(	ForwardIt	first1,
		ForwardIt	last1,
		ForwardIt	first2
	)

Computes the spectral spread of the of the magnitude spectrum represented by the elements in the range [first, last)

The spectral spread describes the average deviation of the rate-map around its centroid, which is commonly associated with the bandwidth of the signal

\[ ss = \frac{\sum_{n = 0}^{N-1}((f(n) - sc)^2 X(n)}{\sum_{n = 0}^{N-1}X(n)} \]

where sc is the spectral centroid.

Parameters

first1	Forward iterator defining the begin of the magnitude spectrum.
last2	Forward iterator defining the end of the magnitude spectrum.
first2	Forward iterator defining the begin of the center frequencies range. The estimated spectral spread

See also

http://www.nyu.edu/classes/bello/MIR_files/timbre.pdf

spectral_variation()

template<typename ForwardIt >

constexpr auto edsp::feature::spectral::spectral_variation	(	ForwardIt	first1,
		ForwardIt	last1,
		ForwardIt	first2
	)

Computes the spectral variation of the of the magnitude spectrum represented by the elements in the range [first, last)

The spectral variation is a representation of the similarity between two magnitude spectrums. It is a parameter similar to the spectral flux.

\[ v = 1 - \frac{\sum_k X_1(k) X_2(K) }{ \sqrt{ \sum_k X_1(k)} \sqrt{\sum_k X_2(k)}} \]

If the variation is close to 0, the spectrum are really similar. Otherwise, if it is close to 1, the are highly dissimilar.

Parameters

first1	Forward iterator defining the begin of the first magnitude spectrum.
last1	Forward iterator defining the end of the first magnitude spectrum.
first2	Input iterator defining the beginning of the second magnitude spectrum.

Returns

The estimated spectral variation.

See also

flux