AVR

Average input X over evaluation cycles.

[SPU SUM X TYP T RS OUT Y]

In:	X	a number, vector or matrix containing the data to be averaged
	TYP	a number or string; defines the averaging method
	T	averaging parameter (number); depends on method
	RS	reset flag (number)
Out:	Y	averaged input X; same type as X

Description

The averaging algorithm is defined by the inputs TYP and T. The atom averages the elements X[i,j]_t over evaluation cycles t (i=row index, j=column index, t=cycle counter) and stores the averaged value in the element Y[i,j]_t.

invinite average

TYP=0 or linear

T=0

Y [ i , j ] t = { X [ i , j ] t if  t = 0 1 t + 1 ( t . Y [ i , j ] t − 1 + X [ i , j ] t ) if  t > 0 {\displaystyle Y[i,j]_{t}={\begin{cases}X[i,j]_{t}&{\mbox{if }}t=0\\{\frac {1}{t+1}}(t.Y[i,j]_{t-1}+X[i,j]_{t})&{\mbox{if }}t>0\end{cases}}} $Y[i,j]_{t}={\begin{cases}X[i,j]_{t}&{\mbox{if }}t=0\\{\frac {1}{t+1}}(t.Y[i,j]_{t-1}+X[i,j]_{t})&{\mbox{if }}t>0\end{cases}}$

running average

TYP=0 or linear

T>0; T is the number of averaging cycles

Y [ i , j ] t = { X [ i , j ] t if  t = 0 1 t + 1 ( t . Y [ i , j ] t − 1 + X [ i , j ] t ) if  t > 0 {\displaystyle Y[i,j]_{t}={\begin{cases}X[i,j]_{t}&{\mbox{if }}t=0\\{\frac {1}{t+1}}(t.Y[i,j]_{t-1}+X[i,j]_{t})&{\mbox{if }}t>0\end{cases}}} $Y[i,j]_{t}={\begin{cases}X[i,j]_{t}&{\mbox{if }}t=0\\{\frac {1}{t+1}}(t.Y[i,j]_{t-1}+X[i,j]_{t})&{\mbox{if }}t>0\end{cases}}$

See also

<SP-atoms>