Programmer Guide/SPU Reference/EXSTAT - Revision history

Toni at 10:56, 9 May 2011

2011-05-09T10:56:35Z

← Older revision		Revision as of 12:56, 9 May 2011
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	\|<var>M2</var>\|\|2nd moment (variance or spread)\|\|number\|\|variable		\|<var>M2</var>\|\|2nd moment (variance or spread)\|\|number\|\|variable
	\|-		\|-
	\|<var>M2</var>\|\|3rd moment (skewness)\|\|number\|\|variable		\|<var>M3</var>\|\|3rd moment (skewness)\|\|number\|\|variable
	\|-		\|-
	\|<var>M4</var>\|\|4th moment (kurtosis)\|\|number\|\|variable		\|<var>M4</var>\|\|4th moment (kurtosis)\|\|number\|\|variable
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	\|<math>\frac{S}{\sqrt{V^3}}</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>		\|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>
			\|<math>K\!</math>
			\|<math>\frac{K}{V^2}</math>
			\|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:
	<[[../#Signal Processing Atoms\|SP-atoms]]>		<[[../#Signal Processing Atoms\|SP-atoms]]>
	<!-- AN, 2.5.2011 -->		<!-- AN, 2.5.2011 -->

Toni: /* [SPU EXSTAT X PX NORM OUT M1 M2 M3 M4 N] */

2011-05-09T10:54:57Z

[SPU EXSTAT X PX NORM OUT M1 M2 M3 M4 N]

← Older revision		Revision as of 12:54, 9 May 2011
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	*If <var>PX</var> is not a vector, the probabilies ''px''<sub>i</sub> are set to 1.		*If <var>PX</var> is not a vector, the probabilies ''px''<sub>i</sub> are set to 1.
	;Description:		;Description:
	~~<math>\begin{matrix}~~
	~~\mu = \frac{\sum_{i=0}^{N-1} x_i px_i}{\sum_{i=0}^{N-1} px_i} & V = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^2px_i}{\sum_{i=0}^{N-1} px_i} \\~~
	~~S = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^3px_i}{\sum_{i=0}^{N-1} px_i} & K = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^4px_i}{\sum_{i=0}^{N-1} px_i}~~
	~~\end{matrix}</math>~~
	{\|class="einrahmen"		{\|class="einrahmen"
	!output !!<var>NORM</var>=<code>0</code> !!<var>NORM</var>=<code>1</code> !!~~stat. moment~~		!output !!<var>NORM</var>=<code>0</code> !!<var>NORM</var>=<code>1</code> !!description
	\|-		\|-
	\|<var>M1</var>		\|<var>M1</var>
	\|<math>\mu\!</math>		\|<math>\mu\!</math>
	\|<math>\mu\!</math>		\|<math>\mu\!</math>
	\|<math>\mu = \frac{\sum_{i=0}^{N-1} x_i px_i}{\sum_{i=0}^{N-1} px_i}</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>		\|<var>M2</var>
	\|<math>V\!</math>		\|<math>V\!</math>
	\|<math>\frac{V}{\mu}</math>		\|<math>\frac{V}{\mu}</math>
	\|<math>\sigma^2 = V = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^2px_i}{\sum_{i=0}^{N-1} px_i}</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>		\|<var>M3</var>
	\|<math>S\!</math>		\|<math>S\!</math>
	\|<math>\frac{S}{\sqrt{V^3}}</math>		\|<math>\frac{S}{\sqrt{V^3}}</math>
	\|<math>S = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^3px_i}{\sum_{i=0}^{N-1} px_i}</math>		\|skewness: <math>S = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^3px_i}{\sum_{i=0}^{N-1} px_i}</math>
	\|}		\|}
	;See also:		;See also:
	<[[../#Signal Processing Atoms\|SP-atoms]]>		<[[../#Signal Processing Atoms\|SP-atoms]]>
	<!-- AN, 2.5.2011 -->		<!-- AN, 2.5.2011 -->

Toni: /* [SPU EXSTAT X PX NORM OUT M1 M2 M3 M4 N] */

2011-05-09T10:53:52Z

[SPU EXSTAT X PX NORM OUT M1 M2 M3 M4 N]

← Older revision		Revision as of 12:53, 9 May 2011
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	\end{matrix}</math>		\end{matrix}</math>
	{\|class="einrahmen"		{\|class="einrahmen"
	!output !!<var>NORM</var>=<code>0</code> !!<var>NORM</var>=<code>1</code>		!output !!<var>NORM</var>=<code>0</code> !!<var>NORM</var>=<code>1</code> !!stat. moment
	\|-		\|-
	\|<var>M1</var>		\|<var>M1</var>
	\|<math>\mu\!</math>		\|<math>\mu\!</math>
	\|<math>\mu\!</math>		\|<math>\mu\!</math>
			\|<math>\mu = \frac{\sum_{i=0}^{N-1} x_i px_i}{\sum_{i=0}^{N-1} px_i}</math>
	\|-		\|-
	\|<var>M2</var>		\|<var>M2</var>
	\|<math>V\!</math>		\|<math>V\!</math>
	\|<math>\frac{V}{\mu}</math>		\|<math>\frac{V}{\mu}</math>
			\|<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>		\|<var>M3</var>
	\|<math>S\!</math>		\|<math>S\!</math>
	\|<math>\frac{S}{\sqrt{V^3}}</math>		\|<math>\frac{S}{\sqrt{V^3}}</math>
			\|<math>S = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^3px_i}{\sum_{i=0}^{N-1} px_i}</math>
	\|}		\|}
	;See also:		;See also:
	<[[../#Signal Processing Atoms\|SP-atoms]]>		<[[../#Signal Processing Atoms\|SP-atoms]]>
	<!-- AN, 2.5.2011 -->		<!-- AN, 2.5.2011 -->

Toni at 10:50, 9 May 2011

2011-05-09T10:50:16Z

← Older revision		Revision as of 12:50, 9 May 2011
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	;Description:		;Description:
	<math>\begin{matrix}		<math>\begin{matrix}
	\mu = \frac{\sum_{i=0}^{N-1} x_i px_i}{\sum_{i=0}^{N-1} px_i} & ~~\sigma^2~~ = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^2px_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} & V = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^2px_i}{\sum_{i=0}^{N-1} px_i} \\
	K = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^3px_i}{\sum_{i=0}^{N-1} px_i} & S = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^4px_i}{\sum_{i=0}^{N-1} px_i}		S = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^3px_i}{\sum_{i=0}^{N-1} px_i} & K = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^4px_i}{\sum_{i=0}^{N-1} px_i}
	\end{matrix}</math>		\end{matrix}</math>
	{\|class="einrahmen"		{\|class="einrahmen"
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	\|-		\|-
	\|<var>M2</var>		\|<var>M2</var>
	\|<math>~~\sigma^2~~\!</math>		\|<math>V\!</math>
	\|<math>\frac{~~\sigma^2~~}{\mu}</math>		\|<math>\frac{V}{\mu}</math>
	\|-
	\|-		\|-
			\|<var>M3</var>
			\|<math>S\!</math>
			\|<math>\frac{S}{\sqrt{V^3}}</math>
	\|}		\|}
	;See also:		;See also:
	<[[../#Signal Processing Atoms\|SP-atoms]]>		<[[../#Signal Processing Atoms\|SP-atoms]]>
	<!-- AN, 2.5.2011 -->		<!-- AN, 2.5.2011 -->

Toni at 10:44, 9 May 2011

2011-05-09T10:44:29Z

← Older revision		Revision as of 12:44, 9 May 2011
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	\|-		\|-
	\|<var>M1</var>		\|<var>M1</var>
	\|<math>\mu</math>		\|<math>\mu\!</math>
	\|<math>\mu</math>		\|<math>\mu\!</math>
	\|-		\|-
	\|<var>M2</var>		\|<var>M2</var>
	\|<math>\sigma^2</math>		\|<math>\sigma^2\!</math>
	\|<math>\frac{\sigma^2}{\mu}</math>		\|<math>\frac{\sigma^2}{\mu}</math>
	\|-		\|-

Toni at 10:44, 9 May 2011

2011-05-09T10:44:07Z

← Older revision		Revision as of 12:44, 9 May 2011
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	K = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^3px_i}{\sum_{i=0}^{N-1} px_i} & S = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^4px_i}{\sum_{i=0}^{N-1} px_i}		K = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^3px_i}{\sum_{i=0}^{N-1} px_i} & S = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^4px_i}{\sum_{i=0}^{N-1} px_i}
	\end{matrix}</math>		\end{matrix}</math>



	{\|class="einrahmen"		{\|class="einrahmen"
	!output !!<var>NORM</var>=<code>0</code> !!<var>NORM</var>=<code>1</code>		!output !!<var>NORM</var>=<code>0</code> !!<var>NORM</var>=<code>1</code>
	\|-		\|-
	\|<var>M1</var>		\|<var>M1</var>
	\|<math>\~~frac{\sum_{i=0}^{N-1} x_i px_i}{\sum_{i=0}^{N-1} px_i}~~</math>		\|<math>\mu</math>
	\|<math>\~~frac{\sum_{i=0}^{N-1} x_i px_i}{\sum_{i=0}^{N-1} px_i}~~</math>		\|<math>\mu</math>
	\|-		\|-
	\|<var>M1</var>		\|<var>M2</var>
	\|<math>\~~frac{\sum_{i=0}^{N-1}(x_i-M1)^2px_i}{\sum_{i=0}~~^~~{N-1} px_i}~~</math>		\|<math>\sigma^2</math>
	\|<math>\frac~~{1}{M1}\frac{\sum_{i=0}^{N-1}(x_i-M1)^2px_i}~~{\~~sum_{i=0}~~^~~{N-1} px_i}</math>~~		\|<math>\frac{\sigma^2}{\mu}</math>
	\|-
	\|-
	\|}


	This SP-atom applies a non-linear magnitude weighting (= limiter function) to the signal. The limiter function is only applied if the absolute value of the signal magnitude is higher than the specified limiter start magnitude <var>LIM</var>. For the limiter function, the following algorithm is used:
	~~:<math>y_i = \begin{cases}~~
	~~x_i & \mbox{ if }\|x_i\| \leqslant LIM \\~~
	~~sign(x_i).f \left ( \frac{\|x_i\|~~}{~~MAX}~~ \~~right ) & \mbox{ otherwise~~}
	~~\end{cases}~~
	~~</math>~~
	~~The absolute magitude of the limited signal is always lower than <var>MAX</var>. The limiter function is selected by the input <var>TYPE</var>.~~
	~~:{\|class="einrahmen"~~
	~~!<var>TYPE</var> !!limiter function ''f''(''z''<sub>i</sub>)~~
	\|-
	~~\|<code>0</code> or <code>RECTANGLE</code>~~
	~~\|<math>k\!~~</math>
	\|-		\|-
	~~\|<code>1</code> or <code>ATAN</code>~~
	~~\|<math>k+(1-k) \cdot \frac{2}{\pi} \cdot atan\left ( \frac{z-k}{1-k} \cdot \frac{\pi}{2} \right )</math>~~
	\|-		\|-
	~~\|<code>2</code> or <code>EXPONENTIAL</code>~~
	~~\|<math>1-(1-k) \cdot e^{-\frac{z-k}{1-k}}</math>~~
	\|}		\|}
	~~:with: <math>z_i = \frac{\|x_i\|}{MAX}, k = \frac{LIM}{MAX}</math>~~


	~~The output <var>Q</var> is set to the relative number of limited (changed) samples.~~
	~~:<math>Q = \frac{changedSamples}{processedSamples}</math>~~

	;See also:		;See also:
	<[[../#Signal Processing Atoms\|SP-atoms]]>		<[[../#Signal Processing Atoms\|SP-atoms]]>
	<!-- AN, 2.5.2011 -->		<!-- AN, 2.5.2011 -->

Toni at 10:42, 9 May 2011

2011-05-09T10:42:01Z

← Older revision		Revision as of 12:42, 9 May 2011
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	;Description:		;Description:
	<math>\begin{matrix}		<math>\begin{matrix}
	\mu = \frac{\sum_{i=0}^{N-1} x_i px_i}{\sum_{i=0}^{N-1} px_i} & \sigma^2 = \frac{\sum_{i=0}^{N-1}(x_i-M1)^2px_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} & \sigma^2 = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^2px_i}{\sum_{i=0}^{N-1} px_i} \\
	K = \frac{\sum_{i=0}^{N-1}(x_i-M1)^3px_i}{\sum_{i=0}^{N-1} px_i} & S = \frac{\sum_{i=0}^{N-1}(x_i-M1)^4px_i}{\sum_{i=0}^{N-1} px_i}		K = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^3px_i}{\sum_{i=0}^{N-1} px_i} & S = \frac{\sum_{i=0}^{N-1}(x_i-\mu)^4px_i}{\sum_{i=0}^{N-1} px_i}
	\end{matrix}</math>		\end{matrix}</math>

Toni at 10:41, 9 May 2011

2011-05-09T10:41:04Z

← Older revision		Revision as of 12:41, 9 May 2011
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	;Description:		;Description:
	<math>\begin{matrix}		<math>\begin{matrix}
	\mu = \frac{\sum_{i=0}^{N-1} x_i px_i}{\sum_{i=0}^{N-1} px_i} & \sigma = \frac{\sum_{i=0}^{N-1}(x_i-M1)^2px_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} & \sigma^2 = \frac{\sum_{i=0}^{N-1}(x_i-M1)^2px_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} & ~~\sigma~~ = \frac{\sum_{i=0}^{N-1}(x_i-M1)^~~2px_i~~}{\sum_{i=0}^{N-1} px_i}		K = \frac{\sum_{i=0}^{N-1}(x_i-M1)^3px_i}{\sum_{i=0}^{N-1} px_i} & S = \frac{\sum_{i=0}^{N-1}(x_i-M1)^4px_i}{\sum_{i=0}^{N-1} px_i}
	\end{matrix}</math>		\end{matrix}</math>

Toni at 10:39, 9 May 2011

2011-05-09T10:39:14Z

← Older revision		Revision as of 12:39, 9 May 2011
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	*If <var>PX</var> is not a vector, the probabilies ''px''<sub>i</sub> are set to 1.		*If <var>PX</var> is not a vector, the probabilies ''px''<sub>i</sub> are set to 1.
	;Description:		;Description:
	<math>begin{matrix}		<math>\begin{matrix}
	\mu = \frac{\sum_{i=0}^{N-1} x_i px_i}{\sum_{i=0}^{N-1} px_i} & \sigma = \frac{\sum_{i=0}^{N-1}(x_i-M1)^2px_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} & \sigma = \frac{\sum_{i=0}^{N-1}(x_i-M1)^2px_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} & \sigma = \frac{\sum_{i=0}^{N-1}(x_i-M1)^2px_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} & \sigma = \frac{\sum_{i=0}^{N-1}(x_i-M1)^2px_i}{\sum_{i=0}^{N-1} px_i}

Toni at 10:37, 9 May 2011

2011-05-09T10:37:58Z

← Older revision		Revision as of 12:37, 9 May 2011
Line 31:		Line 31:
	;Description:		;Description:
	<math>begin{matrix}		<math>begin{matrix}
	\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} & \sigma = \frac{\sum_{i=0}^{N-1}(x_i-M1)^2px_i}{\sum_{i=0}^{N-1} px_i} \\
	\sigma = \frac{\sum_{i=0}^{N-1}(x_i-M1)^2px_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} & \sigma = \frac{\sum_{i=0}^{N-1}(x_i-M1)^2px_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} &
	\sigma = \frac{\sum_{i=0}^{N-1}(x_i-M1)^2px_i}{\sum_{i=0}^{N-1} px_i}
	\end{matrix}</math>		\end{matrix}</math>