LPF – Low-pass filter

Block SymbolLicensing group: STANDARD

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

Fs=1a2s2+2ξas+1,<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow> <msub><mrow><mi>F</mi></mrow><mrow><mi>s</mi></mrow></msub> <mo class="MathClass-rel">=</mo> <mfrac><mrow><mn>1</mn></mrow> <mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msup> <mo class="MathClass-bin">+</mo> <mn>2</mn><mi>ξ</mi><mi>a</mi><mi>s</mi> <mo class="MathClass-bin">+</mo> <mn>1</mn></mrow></mfrac><mo class="MathClass-punc">,</mo> </mrow></math>

where

a=√√2√2ξ4−2ξ2+1−2ξ2+12πfb<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow> <mi>a</mi> <mo class="MathClass-rel">=</mo> <mfrac><mrow><msqrt><mrow><msqrt><mrow><mn>2</mn></mrow></msqrt> <msqrt> <mrow><mn>2</mn><msup><mrow><mi>ξ</mi></mrow><mrow><mn>4</mn> </mrow> </msup> <mo class="MathClass-bin">−</mo> <mn>2</mn><msup><mrow><mi>ξ</mi></mrow><mrow><mn>2</mn> </mrow> </msup> <mo class="MathClass-bin">+</mo> <mn>1</mn></mrow></msqrt> <mo class="MathClass-bin">−</mo> <mn>2</mn><msup><mrow><mi>ξ</mi></mrow><mrow><mn>2</mn> </mrow> </msup> <mo class="MathClass-bin">+</mo> <mn>1</mn></mrow></msqrt></mrow> <mrow><mn>2</mn><mi>π</mi><msub><mrow><mi>f</mi></mrow><mrow><mi>b</mi></mrow></msub></mrow></mfrac> </mrow></math>

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)
R1	Block reset (same state as after init)	Bool
HLD	Hold block execution	Bool

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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