AVR

Average input X over evaluation cycles.

[SPU AVR X TYP T RS OUT Y]

input	description	data type	value type	default value
X	data to be averaged	number, vector, matrix	variable
TYP	averaging method	number (int.), string	constant
T	averaging parameter, depends on method	number or n.c.	TYP=1→variable TYP≠2→constant
RS	reset flag	number or n.c.	variable
output	description	data type	value type	comment
Y	averaged input data	same type as X	variable

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

T is not used

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

maximum

TYP=3 or maximum

T is not used

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

Since STx version 4.5.0 the following two new average modes are available, which were used to implement the spectral averaging mode power of the applications Viewer2 (sectioner) and Viewer3.

power

TYP=4 or power

T is not used

• each input element X_i,j is squared
• same averaging as for TYP=0 is performed
• square root of each output element Y_i,j is taken

db-power

TYP=5 or dbpower

T is not used

• each input element X_i,j is converted from dB to squared magnitude (power)
• same averaging as for TYP=0 is performed
• each output element Y_i,j is converted to dB

See also

<SP-atoms>