Programmer Guide/SPU Reference/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.

The cycle counter t is initialized with 0 and incremented by 1 after each evaluation cycle. The cycle counter is reset, if the input RS is set to a value greater than 0. The input RS is checked each time the SPU is started.

infinite 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 (integer) number of averaging cycles

Y [ i , j ] t = { 1 t + 1 ∑ z = 0 t X [ i , j ] z if  0 ⩽ t < T 1 T ∑ z = 0 T − 1 X [ i , j ] t − z if  t ⩾ T {\displaystyle Y[i,j]_{t}={\begin{cases}{\frac {1}{t+1}}\sum _{z=0}^{t}X[i,j]_{z}&{\mbox{if }}0\leqslant t<T\\{\frac {1}{T}}\sum _{z=0}^{T-1}X[i,j]_{t-z}&{\mbox{if }}t\geqslant T\end{cases}}} $Y[i,j]_{t}={\begin{cases}{\frac {1}{t+1}}\sum _{z=0}^{t}X[i,j]_{z}&{\mbox{if }}0\leqslant t<T\\{\frac {1}{T}}\sum _{z=0}^{T-1}X[i,j]_{t-z}&{\mbox{if }}t\geqslant T\end{cases}}$

exponential average

TYP=1 or exponential

0<T<1; T is the averaging factor

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

minimum

TYP=2 or minimum

0<T<1; T is the averaging factor

Y [ i , j ] t = { X [ i , j ] t if  t = 0 m i n ( 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\\min(Y[i,j]_{t-1},X[i,j]_{t})&{\mbox{if }}t>0\end{cases}}} $Y[i,j]_{t}={\begin{cases}X[i,j]_{t}&{\mbox{if }}t=0\\min(Y[i,j]_{t-1},X[i,j]_{t})&{\mbox{if }}t>0\end{cases}}$

See also

<SP-atoms>