Package edu.wpi.first.math.filter

Class LinearFilter

java.lang.Object
edu.wpi.first.math.filter.LinearFilter
public class LinearFilter
extends Object
This class implements a linear, digital filter. All types of FIR and IIR filters are supported. Static factory methods are provided to create commonly used types of filters.

Filters are of the form: y[n] = (b0 x[n] + b1 x[n-1] + ... + bP x[n-P]) - (a0 y[n-1] + a2 y[n-2] + ... + aQ y[n-Q])

Where: y[n] is the output at time "n" x[n] is the input at time "n" y[n-1] is the output from the LAST time step ("n-1") x[n-1] is the input from the LAST time step ("n-1") b0...bP are the "feedforward" (FIR) gains a0...aQ are the "feedback" (IIR) gains IMPORTANT! Note the "-" sign in front of the feedback term! This is a common convention in signal processing.

What can linear filters do? Basically, they can filter, or diminish, the effects of undesirable input frequencies. High frequencies, or rapid changes, can be indicative of sensor noise or be otherwise undesirable. A "low pass" filter smooths out the signal, reducing the impact of these high frequency components. Likewise, a "high pass" filter gets rid of slow-moving signal components, letting you detect large changes more easily.

Example FRC applications of filters: - Getting rid of noise from an analog sensor input (note: the roboRIO's FPGA can do this faster in hardware) - Smoothing out joystick input to prevent the wheels from slipping or the robot from tipping - Smoothing motor commands so that unnecessary strain isn't put on electrical or mechanical components - If you use clever gains, you can make a PID controller out of this class!

For more on filters, we highly recommend the following articles:
https://en.wikipedia.org/wiki/Linear_filter
https://en.wikipedia.org/wiki/Iir_filter
https://en.wikipedia.org/wiki/Fir_filter

Note 1: calculate() should be called by the user on a known, regular period. You can use a Notifier for this or do it "inline" with code in a periodic function.

Note 2: For ALL filters, gains are necessarily a function of frequency. If you make a filter that works well for you at, say, 100Hz, you will most definitely need to adjust the gains if you then want to run it at 200Hz! Combining this with Note 1 - the impetus is on YOU as a developer to make sure calculate() gets called at the desired, constant frequency!

  • Constructor Summary

    Constructors 
    Constructor Description
    LinearFilter​(double[] ffGains, double[] fbGains)
    Create a linear FIR or IIR filter.

  • Method Summary

    Modifier and Type Method Description
    static LinearFilter backwardFiniteDifference​(int derivative, int samples, double period)
    Creates a backward finite difference filter that computes the nth derivative of the input given the specified number of samples.
    double calculate​(double input)
    Calculates the next value of the filter.
    static LinearFilter finiteDifference​(int derivative, int[] stencil, double period)
    Creates a finite difference filter that computes the nth derivative of the input given the specified stencil points.
    static LinearFilter highPass​(double timeConstant, double period)
    Creates a first-order high-pass filter of the form: y[n] = gain x[n] + (-gain) x[n-1] + gain y[n-1] where gain = e-dt / T, T is the time constant in seconds.
    static LinearFilter movingAverage​(int taps)
    Creates a K-tap FIR moving average filter of the form: y[n] = 1/k (x[k] + x[k-1] + ...
    void reset()
    Reset the filter state.
    static LinearFilter singlePoleIIR​(double timeConstant, double period)
    Creates a one-pole IIR low-pass filter of the form: y[n] = (1-gain) x[n] + gain y[n-1] where gain = e-dt / T, T is the time constant in seconds.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • LinearFilter

      public LinearFilter​(double[] ffGains, double[] fbGains)
      Create a linear FIR or IIR filter.
      Parameters:
      ffGains - The "feedforward" or FIR gains.
      fbGains - The "feedback" or IIR gains.

  • Method Details

    • singlePoleIIR

      public static LinearFilter singlePoleIIR​(double timeConstant, double period)
      Creates a one-pole IIR low-pass filter of the form: y[n] = (1-gain) x[n] + gain y[n-1] where gain = e-dt / T, T is the time constant in seconds.

      Note: T = 1 / (2 pi f) where f is the cutoff frequency in Hz, the frequency above which the input starts to attenuate.

      This filter is stable for time constants greater than zero.

      Parameters:
      timeConstant - The discrete-time time constant in seconds.
      period - The period in seconds between samples taken by the user.
      Returns:
      Linear filter.

    • highPass

      public static LinearFilter highPass​(double timeConstant, double period)
      Creates a first-order high-pass filter of the form: y[n] = gain x[n] + (-gain) x[n-1] + gain y[n-1] where gain = e-dt / T, T is the time constant in seconds.

      Note: T = 1 / (2 pi f) where f is the cutoff frequency in Hz, the frequency below which the input starts to attenuate.

      This filter is stable for time constants greater than zero.

      Parameters:
      timeConstant - The discrete-time time constant in seconds.
      period - The period in seconds between samples taken by the user.
      Returns:
      Linear filter.

    • movingAverage

      public static LinearFilter movingAverage​(int taps)
      Creates a K-tap FIR moving average filter of the form: y[n] = 1/k (x[k] + x[k-1] + ... + x[0]).

      This filter is always stable.

      Parameters:
      taps - The number of samples to average over. Higher = smoother but slower.
      Returns:
      Linear filter.
      Throws:
      IllegalArgumentException - if number of taps is less than 1.

    • finiteDifference

      public static LinearFilter finiteDifference​(int derivative, int[] stencil, double period)
      Creates a finite difference filter that computes the nth derivative of the input given the specified stencil points.

      Stencil points are the indices of the samples to use in the finite difference. 0 is the current sample, -1 is the previous sample, -2 is the sample before that, etc. Don't use positive stencil points (samples from the future) if the LinearFilter will be used for stream-based online filtering (e.g., taking derivative of encoder samples in real-time).

      Parameters:
      derivative - The order of the derivative to compute.
      stencil - List of stencil points. Its length is the number of samples to use to compute the given derivative. This must be one more than the order of the derivative or higher.
      period - The period in seconds between samples taken by the user.
      Returns:
      Linear filter.
      Throws:
      IllegalArgumentException - if derivative < 1, samples <= 0, or derivative >= samples.

    • backwardFiniteDifference

      public static LinearFilter backwardFiniteDifference​(int derivative, int samples, double period)
      Creates a backward finite difference filter that computes the nth derivative of the input given the specified number of samples.

      For example, a first derivative filter that uses two samples and a sample period of 20 ms would be 

      
 LinearFilter.backwardFiniteDifference(1, 2, 0.02);
      Parameters:
      derivative - The order of the derivative to compute.
      samples - The number of samples to use to compute the given derivative. This must be one more than the order of derivative or higher.
      period - The period in seconds between samples taken by the user.
      Returns:
      Linear filter.

    • reset

      public void reset()
      Reset the filter state.

    • calculate

      public double calculate​(double input)
      Calculates the next value of the filter.
      Parameters:
      input - Current input value.
      Returns:
      The filtered value at this step