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 ξ a s + 1},

where

a = \frac{\sqrt{\sqrt{2} \sqrt{2 ξ^{4} - 2 ξ^{2} + 1} - 2 ξ^{2} + 1}}{2 π f_{b}}

and fb and $ξ = xi$ are the block parameters. The fb [Hz] parameter defines the filter bandwidth and xi is the relative damping coefficient . Attenuation at frequency fb is 3 dB, at $10 \cdot fb$ approximately 40 dB. For the correct function of the filter, $f_{b} < \frac{1}{10 T_{S}}$ must hold, where $T_{S}$ is the block triggering period. The recommended value is $xi = 0.71$ for the Butterworth filter and $xi = 0.87$ for the Bessel filter .

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

This block propagates the signal quality. More information can be found in the 1.4 section.

Input

u	Input signal to be filtered	Double (F64)
R1	Block reset	Bool
HLD	Hold	Bool

Parameter

fb	Filter bandwidth [Hz] $⊙$ 1.0	Double (F64)
xi	Relative damping coefficient $⊙$ 0.707	Double (F64)
ISSF	Steady state at start-up	Bool
	off .. Zero initial state on ... Initial steady state

Output

y	Filtered output signal	Double (F64)

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