Programmer Guide/SPU Reference/ZEROCROSS: Difference between revisions

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In this atom the zero crossings ''Z'' of the signal <var>X</var> are counted and than converted to the value selected by <var>TYPE</var>. If <var>XMIN</var>=0 all zero crossings, i.e. changes of signs, are counted. If <var>XMIN</var>&gt;0 the absolute signal magnitude has to exceed this value between two zero crossings.
In this atom the zero crossings ''Z'' of the signal <var>X</var> are counted and than converted to the value selected by <var>TYPE</var>. If <var>XMIN</var>=0 all zero crossings, i.e. changes of signs, are counted. If <var>XMIN</var>&gt;0 the absolute signal magnitude has to exceed this value between two zero crossings.
 
To compute more exact density, frequency and periode values, also the index (position) of the first (I<sub>1</sub>) and last (I<sub>N</sub>) zero crossing is computed.




{|class="einrahmen"
{|class="einrahmen"
!output !!<var>NORM</var>=<code>0</code> !!<var>NORM</var>=<code>1</code> !!description
!<var>TYPE</var> !!<var>Y</var> !!description
|-
|<var>M1</var>
|<math>\mu\!</math>
|<math>\mu\!</math>
|mean: <math>\mu = \frac{\sum_{i=0}^{N-1} x_i px_i}{\sum_{i=0}^{N-1} px_i}</math>
|-
|<var>M2</var>
|<math>V\!</math>
|<math>\frac{V}{\mu}</math>
|variance: <math>\sigma^2 = V = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^2px_i}{\sum_{i=0}^{N-1} px_i}</math>
|-
|<var>M3</var>
|<math>S\!</math>
|<math>\frac{S}{\sqrt{V^3}}</math>
|skewness: <math>S = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^3px_i}{\sum_{i=0}^{N-1} px_i}</math>
|-
|-
|<var>M4</var>
|<code>0</code> or <code>DENSITY</code>
|<math>K\!</math>
|<math>SR<\cdot\frac{Z-1}{I_N-I_1+1}</math>
|<math>\frac{K}{V^2}</math>
|density; number of zero crossings per second
|kurtosis: <math>K = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^4px_i}{\sum_{i=0}^{N-1} px_i}</math>
|}
|}
;See also:
;See also:

Revision as of 12:17, 9 May 2011

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. To compute more exact density, frequency and periode values, also the index (position) of the first (I1) and last (IN) zero crossing is computed.


TYPE Y description
0 or DENSITY {\displaystyle SR<\cdot {\frac {Z-1}{I_{N}-I_{1}+1}}} density; number of zero crossings per second
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.

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