### LPF – Low-pass filter

Block SymbolLicensing group: STANDARD

Function Description
The LPF block implements a second order filter in the form

${F}_{s}=\frac{1}{{a}^{2}{s}^{2}+2\xi as+1},$

where

$a=\frac{\sqrt{\sqrt{2}\sqrt{2{\xi }^{4}-2{\xi }^{2}+1}-2{\xi }^{2}+1}}{2\pi {f}_{b}}$

and fb and $\xi =\mathtt{\text{xi}}$ are the block parameters. The fb parameter defines the filter bandwidth and xi is the relative damping coefficient. The recommended value is $\mathtt{\text{xi}}=0.71$ for the Butterworth filter and $\mathtt{\text{xi}}=0.87$ for the Bessel filter.

If $\mathtt{\text{ISSF}}=\mathtt{\text{on}}$, then the state of the filter is set to the steady value at the block initialization according to the input signal u.

Input

 u Input signal to be filtered double

Output

 y Filtered output signal double

Parameters

 fb Filter bandwidth [Hz]; the frequencies in the range $⟨0,\mathtt{\text{fb}}⟩$ pass through the filter, the attenuation at the frequency fb is 3 dB and approximately 40 dB at $10\cdot \mathtt{\text{fb}}$; it must hold ${f}_{b}<\frac{1}{10{T}_{S}}$ for proper function of the filter, where ${T}_{S}$ is the block execution period  $\odot$1.0 double xi Relative damping coefficient (recommended value 0.5 to 1)  $\odot$0.707 double ISSF Steady state at start-up bool off .. Zero initial state on ... Initial steady state

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