ZEROCROSS

Compute zero crossing rate.

[SPU ZEROCROSS X SR XMIN TYPE OUT Y]

input	description	data type	value type	default value
X	signal vector	vector	variable
SR	sampling rate in Hz	number	constant	1
XMIN	signal amplitude threshold	number	constant	0
TYPE	type of output value (DENSITY, FREQUENCY, PERIODE, COUNT)	number (int.), string	0 (= DENSITY)
output	description	data type	value type	comment
Y	zero crossing rate converted to the selected value	number	variable

Description

In this atom the zero crossings Z of the signal X are counted and than converted to the value selected by TYPE. If XMIN=0 all zero crossings, i.e. changes of signs, are counted. If XMIN>0 the absolute signal magnitude has to exceed this value between two zero crossings.

output	NORM=0	NORM=1	description
M1	μ {\displaystyle \mu \!} $\mu \!$	μ {\displaystyle \mu \!} $\mu \!$	mean: μ = ∑ i = 0 N − 1 x i p x i ∑ i = 0 N − 1 p x i {\displaystyle \mu ={\frac {\sum _{i=0}^{N-1}x_{i}px_{i}}{\sum _{i=0}^{N-1}px_{i}}}} $\mu ={\frac {\sum _{i=0}^{N-1}x_{i}px_{i}}{\sum _{i=0}^{N-1}px_{i}}}$
M2	V {\displaystyle V\!} $V\!$	V μ {\displaystyle {\frac {V}{\mu }}} ${\frac {V}{\mu }}$	variance: σ 2 = V = ∑ i = 0 N − 1 ( x i − μ ) 2 p x i ∑ i = 0 N − 1 p x i {\displaystyle \sigma ^{2}=V={\frac {\sum _{i=0}^{N-1}(x_{i}-\mu )^{2}px_{i}}{\sum _{i=0}^{N-1}px_{i}}}} $\sigma ^{2}=V={\frac {\sum _{i=0}^{N-1}(x_{i}-\mu )^{2}px_{i}}{\sum _{i=0}^{N-1}px_{i}}}$
M3	S {\displaystyle S\!} $S\!$	S V 3 {\displaystyle {\frac {S}{\sqrt {V^{3}}}}} ${\frac {S}{\sqrt {V^{3}}}}$	skewness: S = ∑ i = 0 N − 1 ( x i − μ ) 3 p x i ∑ i = 0 N − 1 p x i {\displaystyle S={\frac {\sum _{i=0}^{N-1}(x_{i}-\mu )^{3}px_{i}}{\sum _{i=0}^{N-1}px_{i}}}} $S={\frac {\sum _{i=0}^{N-1}(x_{i}-\mu )^{3}px_{i}}{\sum _{i=0}^{N-1}px_{i}}}$
M4	K {\displaystyle K\!} $K\!$	K V 2 {\displaystyle {\frac {K}{V^{2}}}} ${\frac {K}{V^{2}}}$	kurtosis: K = ∑ i = 0 N − 1 ( x i − μ ) 4 p x i ∑ i = 0 N − 1 p x i {\displaystyle K={\frac {\sum _{i=0}^{N-1}(x_{i}-\mu )^{4}px_{i}}{\sum _{i=0}^{N-1}px_{i}}}} $K={\frac {\sum _{i=0}^{N-1}(x_{i}-\mu )^{4}px_{i}}{\sum _{i=0}^{N-1}px_{i}}}$

See also

<SP-atoms>

ZEROCROSS - zerocrossing rate

Usage:

ZEROCROSS x sr xmin type

Inputs:

x	signal
sr	sampling rate in Hz
xmin	threshold	0 (default)
type	Frequency | Period)

Outputs:

y	number of zero crossings

Function:

In this atom the zero crossings per second are counted, i.e. the points where between the last counted point and the current point, there exists a value xprev >= xmin and the current value xcurr<= 0 or xprev <= xmin and the current value is xcurr >= 0.

So if xmin = 0 all zero crossings, i.e. changes of signs, are counted. If xmin > 0 the signal has to exceed a certain absolute value if another point is to be counted.