Chebyshev LPF introducing noise

Question

I have created a simple Chebyshev low pass filter based on coefficients generated by this site: http://www-users.cs.york.ac.uk/~fisher/mkfilter/, which I am using to filter out frequencies above 4kHz in an 16kHz sample rate audio signal before downsampling to 8kHz. Here's my code (which is C#, but this question is not C# specific, feel free to use other languages in different languages).

/// <summary>
/// Chebyshev, lowpass, -0.5dB ripple, order 4, 16kHz sample rte, 4kHz cutoff
/// </summary>
class ChebyshevLpf4Pole
{
    const int NZEROS = 4;
    const int NPOLES = 4;
    const float GAIN = 1.403178626e+01f;

    private float[] xv = new float[NZEROS+1];
    private float[] yv = new float[NPOLES + 1];

    public float Filter(float inValue)
    {
        xv[0] = xv[1]; xv[1] = xv[2]; xv[2] = xv[3]; xv[3] = xv[4];
        xv[4] = inValue / GAIN;
        yv[0] = yv[1]; yv[1] = yv[2]; yv[2] = yv[3]; yv[3] = yv[4];
        yv[4] = (xv[0] + xv[4]) + 4 * (xv[1] + xv[3]) + 6 * xv[2]
                     + (-0.1641503452f * yv[0]) + (0.4023376691f * yv[1])
                     + (-0.9100943707f * yv[2]) + (0.5316388226f * yv[3]);
        return yv[4];
    }
}

To test it I created a sine wave "chirp" from 20Hz to 8kHz using Audacity. The test signal looks like this:

After filtering it I get:

The waveform shows that the filter is indeed reducing the amplitude of frequencies above 4kHz, but I have a load of noise added to my signal. This seems to be the case whichever of the filter types I try to implement (e.g. Butterworth, Raised Cosine etc).

Am I doing something wrong, or do these filters simply introduce artefacts at other frequencies? If I downsample using the naive approach of averaging every pair of samples, I don't get this noise at all (but obviously the aliasing is much worse).

Answer 1

OK, it was me being really stupid. The creation of my LPF was happening inside a processing loop instead of outside, meaning that every 512 samples I was creating a new one meaning I was losing the saved state. With just one instance of my filter running over the whole file, the noise goes away, and as expected I get aliased frequencies as the filter cannot completely remove everything above the cutoff.

Answer 2

I checked your filter-code in Mathematica and it works fine here without introducing noise, so probably the noise comes from some other part of your code.

Answer 3

It's possible that you have numerical stability problems, particularly if any of the poles are close to the unit circle. Try making all your intermediate terms double precision and then cast back to single precision at the end. I'm not too familiar with C# but in C this would be:

yv[4] = (float)(((double)xv[0] + (double)xv[4]) + 4.0 * ((double)xv[1] + (double)xv[3]) + 6.0 * xv[2]
             + (-0.1641503452 * (double)yv[0]) + (0.4023376691 * (double)yv[1])
             + (-0.9100943707 * (double)yv[2]) + (0.5316388226 * (double)yv[3]));

Answer 4

You haven't properly initialized your xv and yv arrays before using them for the first time. In most languages this means their values are undefined which may lead to unexpected results like yours. Initializing them to a proper value (like 0) may solve your issue.