I am implementing a simple LPF in Java.

But I have problems in choosing the value of ALPHA.

public class LowPassFilter {

     * Time smoothing constant for low-pass filter 0 ≤ α ≤ 1 ; a smaller value
     * basically means more smoothing See:
     * http://en.wikipedia.org/wiki/Low-pass_filter#Discrete-time_realization
    private static final float ALPHA = 0.2f;

    private LowPassFilter() {

     * Filter the given input against the previous values and return a low-pass
     * filtered result.
     * @param input
     *            float array to smooth.
     * @param prev
     *            float array representing the previous values.
     * @return float array smoothed with a low-pass filter.
    public static float[] filter(float[] input, float[] prev) {

        if (input == null || prev == null)
            throw new NullPointerException("input and prev float arrays must be non-NULL");
        if (input.length != prev.length)
            throw new IllegalArgumentException("input and prev must be the same length");

        for (int i = 0; i < input.length; i++) {
            prev[i] = prev[i] + ALPHA * (input[i] - prev[i]);

        return prev;

ALPHA is defined to be dT/(dT+RC), where dT is the event delivering rate and RC is the time-constant of LPF.

To find the value of ALPHA, I need to know the values of dT and RC.

My LPF should have a cut-off frequency of 4Hz and the sampling rate is 350Hz. Anybody can help determine the proper ALPHA value?

Thanks in advance!


1 Answer 1


All formulas I'm using come from the wikipedia page you cite in your code.

First, calculate RC. We have,

fc = 1/(2*pi*RC)


RC = 1/(2*pi*fc)

Now, ALPHA is simply:

ALPHA = dt / ( dt + RC )

where dt is 1/samplerate.

For your values (samplerate=350, fc=4) I got

ALPHA = 0.0670

Caveat: I tried this on a few other values and the shape of the filter was what I expected, but the exact 3dB cutoff frequency was never quite where it should have been. Not sure if this indicates something wrong, or that's just the nature of the beast.


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