A realtime digital signal processing (DSP) library for Arduino.

Filters implements digital filters, which mimic the following common analog filters:

• FiltersOnePole implement a digital “RC” type filter, both highpass and lowpass.

• FiltersTwoPole implements a digital lowpass “RLC” type of filter. Since an RLC filter is a just a dampened harmonic oscillator, the FiltersTwoPole class can be used to implement oscillators as well, by setting the quality factor and resonant frequency to the desired values.

In addition, the Filters library implements a class for keeping track of a variable’s statistics in realtime.

• RunningStatistics - keeps track variable’s statistics, over a specified window of time (a “running window”), up to the current time. The class calculates variance and mean, as well as the derived values such as standard deviation (sigma) and coefficient of variation.

Installation

Unzip the code, and place it in the Arduino/libraries directory. (If Arduino is already started, it must be restarted to register the library.) All of the filter classes can be added to the program by declaring

#include <Filters.h>

The code can be dowloaded from The GitHub repository

Usage

To use a filter, first declare an instance of the class. Various parameters, such as the filter frequency, can be set by additional calls to the filter class.

The filters are updated by continually calling the “input( newValue )” function on the filter, and passing in a new value. For more information, see the documentation (below) as well as the code examples in the library.

The following code implements a simple one pole (RC type) lowpass filter, which can be used for smoothing an analog input. This is extremely useful if the input data is noisy, since the filter will average together many reads into a single value.

// filters out changes faster that 5 Hz.
float filterFrequency = 5.0  

// create a one pole (RC) lowpass filter
FilterOnePole lowpassFilter( LOWPASS, filterFrequency );   

while( true ) {
  lowpassFilter.input( analogRead( INPUT_PIN ) );
  // do something else
}

Implementation Notes

The filters are implemented as IIR (infinite impulse response) filters, which allows them to operate in real time. In a typical IIR implementation, the time step between samples is constant, and known at the beginning.

In this case, the time step between update can vary, and is computed dynamically by taking the difference between the time of the current input() and the last input() to the filter. In general, the filter values will be more accurate if input() is called more frequently.

All of the filters remain stable, even if input() is not called frequently enough. In the case of the single pole (RC type) filters, the value of the filter will simply decay to it's resting value. The two pole filters use a time-stepped simulation of a damped harmonic oscillator. Normally, this type of simulation simulation can become unstable if the input() is called infrequently.

The code prevents this by setting a maximum allowable timestep (approximately a sixth of the resonant period of the oscillator). If the input() in called less frequently that this, the time step is throttled to this value, and the oscillator remains stable.

The filter classes use implemented using 32-bit floating point numbers (“float”).