Shape filter

Shape filter is a term from electrical engineering. It describes a category of transmission systems that reduce normally distributed , stationary , ergodic and mean- value -free noise signals to white noise . They belong to the class of stochastic systems .

Properties and use

Shape filters are asymptotically stable, linear and time-invariant.

They are used to trace stationary, ergodic and normally distributed noise back to white noise, as this is easier to deal with mathematically.

species

A rough subdivision is:

• Broadband filters make broadband noise with a power density spectrum

${\displaystyle S_{X}(s)={\frac {1}{-a^{2}s^{2}+b^{2}}}}$

White noise. The transfer function is

${\displaystyle G(s)={\frac {1}{as+b}}}$

in which ${\displaystyle a,b>0}$

• Narrow band filters make narrow band noise with a power density spectrum

${\displaystyle S_{X}(s)={\frac {1}{s^{4}+(wb-a^{2})s^{2}+b^{2}}}}$

White noise. The transfer function is

${\displaystyle G(s)={\frac {1}{s^{2}+as+b}}}$

in which ${\displaystyle a,b>0}$

literature

• G. Wunsch, H. Schreiber: Stochastic Systems . Springer, Berlin, Heidelberg, New York, 2006