LIMITER

Apply limiter function to a signal.

[SPU LIMITER X TYPE MAX LIM OUT Y Q]

input	description	data type	value type	default value
X	input signal	number, vector	variable
TYPE	limiter function (RECTANGLE, ATAN, EXPONENTIAL)	number (int.), string	constant	0 (= RECTANGLE)
MAX	maximum value; 0 < MAX	number	constant	1
LIM	limiter start value; 0 < LIM ≤ MAX	number	constant	1
output	description	data type	value type	comment
Y	limited signal	same type as A	variable
Q	overload ratio	number	variable

Description

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 LIM. For the limiter function, the following algorithm is used:

y i = { x i  if  | x i | ⩽ L I M s i g n ( x i ) . f ( | x i | M A X )  otherwise {\displaystyle 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}}} $y_{i}={\begin{cases}x_{i}&{\mbox{ if }}|x_{i}|\leqslant LIM\\sign(x_{i}).f\left({\frac {|x_{i}|}{MAX}}\right)&{\mbox{ otherwise}}\end{cases}}$

The limiter function is selected by the input TYPE.

TYPE	limiter function f(zi)
0 or RECTANGLE	k {\displaystyle k\!} $k\!$
1 or ATAN	k + ( 1 − k ) ⋅ 2 π ⋅ a t a n ( z − k 1 − k ⋅ π 2 ) {\displaystyle k+(1-k)\cdot {\frac {2}{\pi }}\cdot atan\left({\frac {z-k}{1-k}}\cdot {\frac {\pi }{2}}\right)} $k+(1-k)\cdot {\frac {2}{\pi }}\cdot atan\left({\frac {z-k}{1-k}}\cdot {\frac {\pi }{2}}\right)$
2 or EXPONENTIAL	1 − ( 1 − k ) ⋅ e − z − k 1 − k {\displaystyle 1-(1-k)\cdot e^{-{\frac {z-k}{1-k}}}} $1-(1-k)\cdot e^{-{\frac {z-k}{1-k}}}$

with: z = | x i | M A X , k = L I M M A X {\displaystyle z={\frac {|x_{i}|}{MAX}},k={\frac {LIM}{MAX}}} $z={\frac {|x_{i}|}{MAX}},k={\frac {LIM}{MAX}}$

The output Q (overload ratio) is set to the relative number of limited (changed) samples.

Q = c h a n g e d S a m p l e s p r o c e s s e d S a m p l e s {\displaystyle Q={\frac {changedSamples}{processedSamples}}} $Q={\frac {changedSamples}{processedSamples}}$

See also

<SP-atoms>