Programmer Guide/SPU Reference/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	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu\!}	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu\!}	mean: Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu = \frac{\sum_{i=0}^{N-1} x_i px_i}{\sum_{i=0}^{N-1} px_i}}
M2	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V\!}	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{V}{\mu}}	variance: Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma^2 = V = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^2px_i}{\sum_{i=0}^{N-1} px_i}}
M3	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S\!}	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{S}{\sqrt{V^3}}}	skewness: Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^3px_i}{\sum_{i=0}^{N-1} px_i}}
M4	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K\!}	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{K}{V^2}}	kurtosis: Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^4px_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.