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 parameter defines the filter bandwidth and xi is the relative damping coefficient . 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.

Input

u	Input signal to be filtered	Double (F64)

Output

y	Filtered output signal	Double (F64)

Parameters

fb	Filter bandwidth [Hz]; the frequencies in the range $⟨ 0, fb ⟩$ pass through the filter, the attenuation at the frequency fb is 3 dB and approximately 40 dB at $10 \cdot fb$ ; it must hold $f_{b} < \frac{1}{10 T_{S}}$ for proper function of the filter, where $T_{S}$ is the block execution period $⊙$ 1.0	Double (F64)
xi	Relative damping coefficient (recommended value 0.5 to 1) $⊙$ 0.707	Double (F64)
ISSF	Steady state at start-up	Bool
	off .. Zero initial state on ... Initial steady state

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