Low-pass Filter · Low-pass Filter!"= $(") '(") = 1)*"+1 A Low-pass Filter has the following...
Transcript of Low-pass Filter · Low-pass Filter!"= $(") '(") = 1)*"+1 A Low-pass Filter has the following...
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Contents• Introduction to Filters–Overview of different Filters–What is a Low-pass Filter?–Why do we need a Lowpass Filter?
• Using a built-in Lowpass Filter in LabVIEW• Create your own Lowpass Filter from
scratch
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Filters• A Filters are typically used in frequency response analysis • A filter is used to remove given frequencies or an interval
of frequencies from a signal. • Such an application would typically be to remove noise
from a signal. • The most common is the low pass filter.• We have 4 types of filter:– Low-pass Filter– High-pass Filter– Band-pass Filter– Band-stop Filter
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Filters
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Low-pass Filter
High frequencies (above !") are removed (or attenuated)
# $ = 1'$ + 1 =
11!" $ + 1
Low-pass Filter in LabVIEW
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Low-pass Filter• In Measurement systems and Control Systems
we typically need to deal with noise• Noise is something we typically don’t want• Noise is high-frequency signals• Low-pass Filters are used to remove noise
from the measured signals
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High-pass Filter
Low frequencies (below !") are removed (or attenuated)
# $ = &$&$ + 1 =
1!) $1!) $ + 1
High-pass Filter in LabVIEW
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Band-pass Filter
and High frequencies (above !") are removed (or attenuated)
Low frequencies (below !#) are removed (or attenuated)
Band-pass Filter in LabVIEW
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Band-stop Filter
Frequencies between !" and !# are removed
Band-stop Filter in LabVIEW
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Using a built-in Low-pass Filter in LabVIEW
Hans-Petter Halvorsen
https://www.halvorsen.blog
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Using a Low-pass Filter to reduce NoiseFunctions palette: Express -> Signal Analysis -> Simulate Signal
Functions palette: Express -> Signal Analysis -> Filter
Here we use one of the built-in (Low-pass) Filters
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Properties
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Using a Low-pass Filter to reduce Noise
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Using a Low-pass Filter to reduce Noise
We see the noise from the signal
has been reduced
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Create your own Low-pass Filter from scratch
Hans-Petter Halvorsen
https://www.halvorsen.blog
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Low-pass Filter
! " = $(")'(") =
1)*" + 1
A Low-pass Filter has the following Transfer Function:
In LabVIEW we can implement a Low-pass Filter in many ways.If we want to implement the Low-pass Filter in a text-based programming or using e.g., the Formula Node in LabVIEW we typically need to find a discrete version of the filter.
! "'(") $(")
Input Output
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Low-pass Filter
! " = $(")'(") =
1)*" + 1
A Low-pass Filter has the following Transfer Function
We can find the Differential Equation for this filter using Inverse Laplace
We get:
$ " )*" + 1 = ' "
)*$ " " + $ " = ' "
Finally we get the following differential equation:
)*$̇ + $ = ' We apply Euler on the Differential Equation in order to find the Discrete Differential equation
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Discretization of Low-pass FilterWe have the following differential equation:
!"$̇ + $ = '
We use Euler Backward method: (̇ ≈ * + ,* +,-./
Then we get:
!"$ 0 − $ 0 − 1
!3+ $ 0 = ' 0
This gives: $ 0 = .4.45./
$ 0 − 1 + ./.45./
' 0
We define:!3
!" + !3≡ 7
This finally gives:
$ 0 = 1 − 7 $ 0 − 1 + 7' 0
This equation can easily be implemented in LabVIEW or another programming language
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Discrete Low-pass Filter Example
We use the Euler Backward method:
Inverse Laplace the differential Equation:
This gives:
Lowpass Filter Transfer function:We define:
This gives:
This algorithm can be easly implemented in a Programming language
Filter output Noisy input signal
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Low-pass Filter/Measurement Filter - Example
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Testing the FilterIn this example we add noise to a Sine function. We then use the Measurement Filter to see if we can remove the noise afterwards.
As you can see this gives good results. The filter removes the noise from the signal.
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Hans-Petter Halvorsen
University of South-Eastern Norwaywww.usn.no
E-mail: [email protected]: https://www.halvorsen.blog