Low-pass Filter

https://www.halvorsen.blogLow-pass FilterHans-Petter Halvorsen

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 fromscratch

Filters A Filters are typically used in frequency response analysis A filter is used to remove given frequencies or an intervalof frequencies from a signal. Such an application would typically be to remove noisefrom a signal. The most common is the low pass filter. We have 4 types of filter:––––Low-pass FilterHigh-pass FilterBand-pass FilterBand-stop Filter

Filters

Low-pass Filter# 11 1' 1 1!"High frequencies (above !" ) are removed (or attenuated)Low-pass Filter in LabVIEW

Low-pass Filter In Measurement systems and Control Systemswe 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 noisefrom the measured signals

High-pass Filter# 1 !)& 1& 1!) 1Low frequencies (below !" ) are removed (or attenuated)High-pass Filter in LabVIEW

Band-pass FilterLow frequencies (below !# ) are removed (or attenuated)and High frequencies (above !" ) are removed (or attenuated)Band-pass Filter in LabVIEW

Band-stop FilterFrequencies between !" and !# are removedBand-stop Filter in LabVIEW

https://www.halvorsen.blogUsing a built-in Low-passFilter in LabVIEWHans-Petter Halvorsen

Using a Low-pass Filter to reduce NoiseFunctions palette: Express - Signal Analysis - Simulate SignalFunctions palette: Express - Signal Analysis - FilterHere we use one of the built-in (Low-pass) Filters

Properties

Using a Low-pass Filter to reduce Noise

Using a Low-pass Filter to reduce NoiseWe see the noisefrom the signalhas been reduced

https://www.halvorsen.blogCreate your own Low-passFilter from scratchHans-Petter Halvorsen

Low-pass FilterA Low-pass Filter has the following Transfer Function: (")1! " '(") )* " 1'(")Input! " (")OutputIn 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., theFormula Node in LabVIEW we typically need to find a discrete version of the filter.

Low-pass FilterA Low-pass Filter has the following Transfer Function! " (")1 '(") )* " 1We can find the Differential Equationfor this filter using Inverse LaplaceWe get: " )* " 1 ' ")* " " " ' "Finally we get the following differential equation:)* ̇ 'We apply Euler on the Differential Equation inorder to find the Discrete Differential equation

Discretization of Low-pass FilterWe have the following differential equation:We define:!3 7!" !3!" ̇ 'We use Euler Backward method: (̇ * ,* ,./This finally gives:Then we get: 0 1 7 0 1 7' 0 0 0 1!" 0 ' 0!3This gives: 0 .44 5./ 0 1 ./.4 5./' 0This equation can easily beimplemented in LabVIEW or anotherprogramming language

Discrete Low-pass Filter ExampleLowpass Filter Transfer function:We define:Inverse Laplace the differential Equation:We use the Euler Backward method:This gives:This gives:Filter outputNoisy input signalThis algorithm can be easly implementedin a Programming language

Low-pass Filter/Measurement Filter - Example

Testing the FilterIn this example we add noise to a Sinefunction. We then use the MeasurementFilter to see if we can remove the noiseafterwards.As you can see this gives goodresults.The filter removes the noisefrom the signal.

Hans-Petter HalvorsenUniversity of South-Eastern Norwaywww.usn.noE-mail: hans.p.halvorsen@usn.noWeb: https://www.halvorsen.blog

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