Classes
struct	histogram
	Histogram density estimator. More...

Functions
template<typename ForwardIt >
constexpr meta::value_type_t< ForwardIt >	centroid (ForwardIt first, ForwardIt last)
	Computes the centroid value of the range [first, last) More...

template<typename ForwardIt >
constexpr meta::value_type_t< ForwardIt >	centroid (ForwardIt first1, ForwardIt last1, ForwardIt first2)
	Computes the centroid value of the range [first1, last1) More...

template<typename ForwardIt >
constexpr meta::value_type_t< ForwardIt >	crest (ForwardIt first, ForwardIt last)
	Computes the crest value of the range [first, last) More...

template<typename ForwardIt >
constexpr meta::value_type_t< ForwardIt >	entropy (ForwardIt first, ForwardIt last)
	Computes the normalized entropy of the probability mass function given in the range [first, last). More...

template<typename ForwardIt >
constexpr meta::value_type_t< ForwardIt >	flatness (ForwardIt first, ForwardIt last)
	Computes the flatness value of the range [first, last) More...

template<distances d, typename InputIt >
constexpr meta::value_type_t< InputIt >	flux (InputIt first1, InputIt last1, InputIt first2)
	Computes the flux between the elements in the range [first1, last1) and the elements starting at first2. More...

template<typename ForwardIt , typename Integer >
constexpr meta::value_type_t< ForwardIt >	generalized_mean (ForwardIt first, ForwardIt last, Integer beta)
	Computes the generalized mean of the range [first, last) More...

template<typename ForwardIt >
constexpr meta::value_type_t< ForwardIt >	geometric_mean (ForwardIt first, ForwardIt last)
	Computes the geometric mean of the range [first, last) More...

template<typename ForwardIt >
constexpr meta::value_type_t< ForwardIt >	harmonic_mean (ForwardIt first, ForwardIt last)
	Computes the harmonic mean of the range [first, last) More...

template<typename ForwardIt >
constexpr meta::value_type_t< ForwardIt >	kurtosis (ForwardIt first, ForwardIt last)
	Computes the Kurtosis of the range [first, last) More...

template<typename ForwardIt >
constexpr meta::value_type_t< ForwardIt >	max (ForwardIt first, ForwardIt last)
	Computes the maximum value of the range [first, last) More...

template<typename ForwardIt >
constexpr meta::value_type_t< ForwardIt >	maxabs (ForwardIt first, ForwardIt last)
	Computes the maximum absolute value of the range [first, last) More...

template<typename ForwardIt >
constexpr meta::value_type_t< ForwardIt >	mean (ForwardIt first, ForwardIt last)
	Computes the average or mean value of the range [first, last) More...

template<typename ForwardIt >
constexpr meta::value_type_t< ForwardIt >	median (ForwardIt first, ForwardIt last)
	Computes the median of the range [first, last) More...

template<typename ForwardIt >
constexpr meta::value_type_t< ForwardIt >	min (ForwardIt first, ForwardIt last)
	Computes the minimum value of the range [first, last) More...

template<typename ForwardIt >
constexpr meta::value_type_t< ForwardIt >	minabs (ForwardIt first, ForwardIt last)
	Computes the minimum absolute value of the range [first, last) More...

template<std::size_t N, typename ForwardIt >
constexpr meta::value_type_t< ForwardIt >	moment (ForwardIt first, ForwardIt last)
	Computes the n-th moment of the range [first, last) More...

template<std::size_t N, typename ForwardIt >
constexpr meta::value_type_t< ForwardIt >	moment (ForwardIt first, ForwardIt last, const meta::value_type_t< ForwardIt > mean)
	Computes the nth moment of the range [first, last) considering the precomputed average. More...

template<typename InputIt >
constexpr meta::value_type_t< InputIt >	norm (InputIt first, InputIt last)
	Compute the L2-norm of the signals in the range [first1, last1). More...

template<typename ForwardIt >
constexpr auto	peak (ForwardIt first, ForwardIt last) -> std::pair< typename meta::diff_type_t< ForwardIt >, typename meta::value_type_t< ForwardIt >>
	Computes the peak value of the range [first, last) More...

template<typename ForwardIt >
constexpr auto	peakabs (ForwardIt first, ForwardIt last) -> std::pair< typename meta::diff_type_t< ForwardIt >, typename meta::value_type_t< ForwardIt >>
	Computes the absolute peak value of the range [first, last) More...

template<typename ForwardIt >
constexpr meta::value_type_t< ForwardIt >	rms (ForwardIt first, ForwardIt last)
	Computes the root-mean-square (RMS) value of the range [first, last) More...

template<typename ForwardIt , typename Floating >
constexpr auto	rolloff (ForwardIt first, ForwardIt last, Floating percentage)
	Computes the roll-off index of the elements in the range [first, last) More...

template<typename ForwardIt >
constexpr meta::value_type_t< ForwardIt >	rssq (ForwardIt first, ForwardIt last)
	Computes the root-sum-of-squares (RSSS) value of the range [first, last) More...

template<typename ForwardIt >
constexpr meta::value_type_t< ForwardIt >	skewness (ForwardIt first, ForwardIt last)
	Computes the skewness of the range [first, last) More...

template<typename InputIt , typename Allocator = std::allocator<meta::value_type_t<InputIt>>>
constexpr meta::value_type_t< InputIt >	snr (InputIt first1, InputIt last1, InputIt first2)
	Compute the SNR of the signals in the range [first1, last1) and the signal starting in first2. More...

template<typename ForwardIt >
constexpr meta::value_type_t< ForwardIt >	variance (ForwardIt first, ForwardIt last)
	Computes the variance of the range [first, last) More...

template<typename ForwardIt >
meta::value_type_t< ForwardIt >	standard_deviation (ForwardIt first, ForwardIt last)
	Computes the standard deviation of the range [first, last) More...

Function Documentation

◆ centroid() [1/2]

template<typename ForwardIt >

constexpr meta::value_type_t<ForwardIt> edsp::statistics::centroid	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the centroid value of the range [first, last)

It is calculated as the division of the weighted mean of the the signal and the average of the magnitudes.

\[ y = \frac{\sum_{n=0}^{N-1}nx(n)}{\sum_{n=0}^{N-1}x(n)} \]

Parameters

first	Forward iterator defining the begin of the range to examine.
last	Forward iterator defining the end of the range to examine.

Returns: The centroid value of the input range.

See also: mean

◆ centroid() [2/2]

template<typename ForwardIt >

constexpr meta::value_type_t<ForwardIt> edsp::statistics::centroid	(	ForwardIt	first1,
		ForwardIt	last1,
		ForwardIt	first2
	)

Computes the centroid value of the range [first1, last1)

It is calculated as the division of the weighted mean of the the signal and the average of the magnitudes.

\[ y = \frac{\sum_{n=0}^{N-1}f(n)x(n)}{\sum_{n=0}^{N-1}x(n)} \]

Parameters

first1	Forward iterator defining the begin of the range to examine.
last1	Forward iterator defining the end of the range to examine.
first2	Forward iterator defining the beginning of the range representing the weights, \(f(i)\).

Returns: The centroid value of the input range.

See also: mean

◆ crest()

template<typename ForwardIt >

constexpr meta::value_type_t<ForwardIt> edsp::statistics::crest	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the crest value of the range [first, last)

It is calculated as the division of mean of the the signal and the maximum value of the magnitudes.

\[ y = \frac{ \frac{1}{N} \sum_{n=0}^{N-1}x(n)}{max \left( x \right)} \]

Parameters

first	Forward iterator defining the begin of the range to examine.
last	Forward iterator defining the end of the range to examine.

Returns: The crest value of the input range.

See also: mean

◆ entropy()

template<typename ForwardIt >

constexpr meta::value_type_t<ForwardIt> edsp::statistics::entropy	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the normalized entropy of the probability mass function given in the range [first, last).

Given a normalized probability mass function \( p(n) \), the entropy can explicitly be written as:

\[ H = - \sum_{n=0}^{N-1} p(n) \log_2 \left( p(n) \right) \]

Normalizing:

\[ H_n = - \frac{H}{log2(N)} \]

Parameters

first	Forward iterator defining the begin of the probability mass function.
last	Forward iterator defining the end of the probability mass function.

Returns: The entropy of the probability mass function.

◆ flatness()

template<typename ForwardIt >

constexpr meta::value_type_t<ForwardIt> edsp::statistics::flatness	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the flatness value of the range [first, last)

It is calculated as the division of geometric mean and the average of the magnitudes.

\[ y = \frac{\mu_g}{\mu} \]

Parameters

first	Forward iterator defining the begin of the range to examine.
last	Forward iterator defining the end of the range to examine.

Returns: The flatness value of the input range.

See also: mean, geometric_mean

◆ flux()

template<distances d, typename InputIt >

constexpr meta::value_type_t<InputIt> edsp::statistics::flux	(	InputIt	first1,
		InputIt	last1,
		InputIt	first2
	)

Computes the flux between the elements in the range [first1, last1) and the elements starting at first2.

The flux is a measure of the difference between two signals, it is frequently used to estimates the differences in the power spectral between consecutive frames.

Template Parameters

d	Type of distance to be compute between each point.

Parameters

first1	Input iterator defining the beginning of the first input range.
last1	Input iterator defining the ending of the first input range.
first2	Input iterator defining the beginning of the second input range.

Returns: The estimated flux.

See also: distances, distance

◆ generalized_mean()

template<typename ForwardIt , typename Integer >

constexpr meta::value_type_t<ForwardIt> edsp::statistics::generalized_mean	(	ForwardIt	first,
		ForwardIt	last,
		Integer	beta
	)

Computes the generalized mean of the range [first, last)

The generalized mean or power mean with exponent \( \beta \) is defined as:

\[ \mu_{\beta} = \left( \frac{1}{N}\sum_{n=0}^{N-1}x(n)^{\beta} \right) ^{\frac{1}{\beta}} \]

Parameters

first	Forward iterator defining the begin of the range to examine.
last	Forward iterator defining the end of the range to examine.
beta	Exponent ( \( \beta \)).

Returns: The generalized mean of the input range.

◆ geometric_mean()

template<typename ForwardIt >

constexpr meta::value_type_t<ForwardIt> edsp::statistics::geometric_mean	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the geometric mean of the range [first, last)

The geometric mean is defined as:

\[ {\displaystyle \left(\prod _{i=1}^{n}x_{i}\right)^{\frac {1}{n}}={\sqrt[{n}]{x_{1}x_{2}\cdots x_{n}}}} \]

Parameters

first	Forward iterator defining the begin of the range to examine.
last	Forward iterator defining the end of the range to examine.

Returns: The geometric mean of the input range.

◆ harmonic_mean()

template<typename ForwardIt >

constexpr meta::value_type_t<ForwardIt> edsp::statistics::harmonic_mean	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the harmonic mean of the range [first, last)

The harmonic mean is defined as:

\[ {\displaystyle H={\frac {n}{{\frac {1}{x_{1}}}+{\frac {1}{x_{2}}}+\cdots +{\frac {1}{x_{n}}}}} ={\frac {n}{\sum \limits _{i=1}^{n}{\frac {1}{x_{i}}}}}=\left({\frac {\sum \limits _{i=1}^{n}x_{i}^{-1}}{n}}\right)^{-1}.} \]

Parameters

first	Forward iterator defining the begin of the range to examine.
last	Forward iterator defining the end of the range to examine.

Returns: The geometric mean of the input range.

◆ kurtosis()

template<typename ForwardIt >

constexpr meta::value_type_t<ForwardIt> edsp::statistics::kurtosis	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the Kurtosis of the range [first, last)

The kurtosis is the fourth standardized moment, defined as:

\[ {\displaystyle K [X] =E \left[\left({\frac {X-\mu }{\sigma }}\right)^{4}\right]={\frac {\mu _{4}}{\sigma ^{4}}} ={\frac {E [(X-\mu )^{4}]}{(E[(X-\mu )^{2}])^{2}}},} \]

where \( \mu_4 \) is the fourth central moment and \( \sigma \) is the standard deviation.

Parameters

first	Forward iterator defining the begin of the range to examine.
last	Forward iterator defining the end of the range to examine.

Returns: The Kurtosis of the input range.

See also: moment, standard_deviation

◆ max()

template<typename ForwardIt >

constexpr meta::value_type_t<ForwardIt> edsp::statistics::max	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the maximum value of the range [first, last)

Parameters

first	Forward iterator defining the begin of the range to examine.
last	Forward iterator defining the end of the range to examine.

Returns: The maximum value of the input range.

◆ maxabs()

template<typename ForwardIt >

constexpr meta::value_type_t<ForwardIt> edsp::statistics::maxabs	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the maximum absolute value of the range [first, last)

Parameters

first	Forward iterator defining the begin of the range to examine.
last	Forward iterator defining the end of the range to examine.

Returns: The maximum value of the input range.

◆ mean()

template<typename ForwardIt >

constexpr meta::value_type_t<ForwardIt> edsp::statistics::mean	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the average or mean value of the range [first, last)

The average is defined as:

\[ \mu = \frac{1}{N}\sum_{n=0}^{N-1}x(n) \]

Parameters

first	Forward iterator defining the begin of the range to examine.
last	Forward iterator defining the end of the range to examine.

Returns: The average of the input range.

◆ median()

template<typename ForwardIt >

constexpr meta::value_type_t<ForwardIt> edsp::statistics::median	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the median of the range [first, last)

The median of a finite list of numbers can be found by arranging all the numbers from smallest to greatest. If there is an odd number of numbers, the middle one is picked. If there is an even number of observations, then there is no single middle value; the median is then usually defined to be the mean of the two middle values

Parameters

first	Forward iterator defining the begin of the range to examine.
last	Forward iterator defining the end of the range to examine.

Returns: The median of the input range.

◆ min()

template<typename ForwardIt >

constexpr meta::value_type_t<ForwardIt> edsp::statistics::min	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the minimum value of the range [first, last)

Parameters

first	Forward iterator defining the begin of the range to examine.
last	Forward iterator defining the end of the range to examine.

Returns: The minimum value of the input range.

◆ minabs()

template<typename ForwardIt >

constexpr meta::value_type_t<ForwardIt> edsp::statistics::minabs	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the minimum absolute value of the range [first, last)

Parameters

first	Forward iterator defining the begin of the range to examine.
last	Forward iterator defining the end of the range to examine.

Returns: The minimum value of the input range.

◆ moment() [1/2]

template<std::size_t N, typename ForwardIt >

constexpr meta::value_type_t<ForwardIt> edsp::statistics::moment	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the n-th moment of the range [first, last)

Parameters

first	Forward iterator defining the begin of the range to examine.
last	Forward iterator defining the end of the range to examine.

Template Parameters

N	Order of the moment.

Returns: The n-th moment of the input range.

◆ moment() [2/2]

template<std::size_t N, typename ForwardIt >

constexpr meta::value_type_t<ForwardIt> edsp::statistics::moment	(	ForwardIt	first,
		ForwardIt	last,
		const meta::value_type_t< ForwardIt >	mean
	)

Computes the nth moment of the range [first, last) considering the precomputed average.

Parameters

first	Forward iterator defining the begin of the range to examine.
last	Forward iterator defining the end of the range to examine.
mean	Average of the range [first, last)

Template Parameters

N	Order of the moment.

Returns: The n-th moment of the input range.

See also: mean

◆ norm()

template<typename InputIt >

constexpr meta::value_type_t<InputIt> edsp::statistics::norm	(	InputIt	first,
		InputIt	last
	)

Compute the L2-norm of the signals in the range [first1, last1).

The \( l^2 \)-norm is defined as:

\[ |x|=\sqrt(\sum_{n=0}^{N - 1}|x(n)|^2), \]

where \( |x_k| \) denotes the complex modules.

Parameters

first	Input iterator defining the beginning of the first input range.
last	Input iterator defining the ending of the first input range.

Returns: L2-norm of the input signal.

◆ peak()

template<typename ForwardIt >

constexpr auto edsp::statistics::peak	(	ForwardIt	first,
		ForwardIt	last
	)		-> std::pair<typename meta::diff_type_t<ForwardIt>, typename meta::value_type_t<ForwardIt>>

Computes the peak value of the range [first, last)

Parameters

first	Forward iterator defining the begin of the range to examine.
last	Forward iterator defining the end of the range to examine.

Returns: Pair representing the index position and the value of the peak.

◆ peakabs()

template<typename ForwardIt >

constexpr auto edsp::statistics::peakabs	(	ForwardIt	first,
		ForwardIt	last
	)		-> std::pair<typename meta::diff_type_t<ForwardIt>, typename meta::value_type_t<ForwardIt>>

Computes the absolute peak value of the range [first, last)

Parameters

first	Forward iterator defining the begin of the range to examine.
last	Forward iterator defining the end of the range to examine.

Returns: Pair representing the index position and the value of the peak.

◆ rms()

template<typename ForwardIt >

constexpr meta::value_type_t<ForwardIt> edsp::statistics::rms	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the root-mean-square (RMS) value of the range [first, last)

The RMS value is defined as:

\[ x_{\mathrm {rms} }={\sqrt {{\frac {1}{n}}\left(x_{1}^{2}+x_{2}^{2}+\cdots +x_{n}^{2}\right)}} \]

Parameters

first	Forward iterator defining the begin of the range to examine.
last	Forward iterator defining the end of the range to examine.

Returns: The root mean square value of the input range.

◆ rolloff()

template<typename ForwardIt , typename Floating >

constexpr auto edsp::statistics::rolloff	(	ForwardIt	first,
		ForwardIt	last,
		Floating	percentage
	)

Computes the roll-off index of the elements in the range [first, last)

The roll-off index is defined as the index under which some percentage (cutoff) of the total energy of the signal is contained.

Parameters

first	Forward iterator defining the begin of the range to examine.
last	Forward iterator defining the end of the range to examine.
percentage	Number between [0, 1] representing the percentage of the total energy of the roll-off index..

Returns: The estimated roll-off index.

◆ rssq()

template<typename ForwardIt >

constexpr meta::value_type_t<ForwardIt> edsp::statistics::rssq	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the root-sum-of-squares (RSSS) value of the range [first, last)

\[ x_{\mathrm {rms} }={\sqrt {\left(x_{1}^{2}+x_{2}^{2}+\cdots +x_{n}^{2}\right)}} \]

Parameters

first	Forward iterator defining the begin of the range to examine.
last	Forward iterator defining the end of the range to examine.

Returns: The root-sum-of-squares value of the input range.

◆ skewness()

template<typename ForwardIt >

constexpr meta::value_type_t<ForwardIt> edsp::statistics::skewness	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the skewness of the range [first, last)

The skewness is the third standardized moment, defined as:

\[ {\displaystyle K [X] =E \left[\left({\frac {X-\mu }{\sigma }}\right)^{3}\right]={\frac {\mu _{3}}{\sigma ^{3}}} ={\frac {E [(X-\mu )^{3}]}{(E[(X-\mu )^{2}])^{2}}},} \]

where \( \mu_3 \) is the fourth central moment and \( \sigma \) is the standard deviation.

Parameters

first	Forward iterator defining the begin of the range to examine.
last	Forward iterator defining the end of the range to examine.

Returns: The skewness of the input range.

See also: moment, standard_deviation

◆ snr()

template<typename InputIt , typename Allocator = std::allocator<meta::value_type_t<InputIt>>>

constexpr meta::value_type_t<InputIt> edsp::statistics::snr	(	InputIt	first1,
		InputIt	last1,
		InputIt	first2
	)

Compute the SNR of the signals in the range [first1, last1) and the signal starting in first2.

Signal-to-noise ratio (abbreviated SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to the noise power, often expressed in decibels. A ratio higher than 1:1 (greater than 0 dB) indicates more signal than noise.

If the variance of the signal and noise are known, and the signal and noise are both zero-mean, SNR can be:

\[ \mathrm{SNR} = \frac{\sigma^2_\mathrm{signal}}{\sigma^2_\mathrm{noise}}. \]

Parameters

first1	Input iterator defining the beginning of the first input range.
last1	Input iterator defining the ending of the first input range.
first2	Input iterator defining the beginning of the second input range.

Returns: SNR of the signals.

◆ standard_deviation()

template<typename ForwardIt >

meta::value_type_t<ForwardIt> edsp::statistics::standard_deviation	(	ForwardIt	first,
		ForwardIt	last
	)

inline

Computes the standard deviation of the range [first, last)

The standard deviation is defined as the square root of the variance:

\[ \sigma = \sqrt(v) \]

Parameters

first	Forward iterator defining the begin of the range to examine.
last	Forward iterator defining the end of the range to examine.

Returns: The variance of the input range.

See also: variance

◆ variance()

template<typename ForwardIt >

constexpr meta::value_type_t<ForwardIt> edsp::statistics::variance	(	ForwardIt	first,
		ForwardIt	last
	)

Computes the variance of the range [first, last)

The variance is defined as:

\[ v =\sum _{i=1}^{n}p_{i}\cdot (x_{i}-\mu )^{2} \]

Parameters

first	Forward iterator defining the begin of the range to examine.
last	Forward iterator defining the end of the range to examine.

Returns: The variance of the input range.

See also: standard_deviation

Classes

Functions

Function Documentation

◆ centroid() [1/2]

◆ centroid() [2/2]

◆ crest()

◆ entropy()

◆ flatness()

◆ flux()

◆ generalized_mean()

◆ geometric_mean()

◆ harmonic_mean()

◆ kurtosis()

◆ max()

◆ maxabs()

◆ mean()

◆ median()

◆ min()

◆ minabs()

◆ moment() [1/2]

◆ moment() [2/2]

◆ norm()

◆ peak()

◆ peakabs()

◆ rms()

◆ rolloff()

◆ rssq()

◆ skewness()

◆ snr()

◆ standard_deviation()

◆ variance()