Regular LMS verses Normalized LMS Evaluation


Purpose:

  1. To test and validate the Normalized LMS Algorithm
  2. To determine which algorithm was better suited for our uses

Procedure:

Regular and Normalized LMS Algorithms Against a Simple 370 Hz Tone:

  1. A "noise source" data file was created using Cool Edit to generate a simple 370 Hz tone data file
  2. A "quiet zone" was created by feeding the "noise source" into a 64 sample delay line.
  3. The regular and normalized LMS algorithms were then used to process the data.
  4. A time verses amplitude plot was created for the original tone, the regular LMS and the normalized LMS algorithms

Results:

370 Hz Tone with regular and normalized LMS filters
This plot represents the tone signal that would normally be at the quiet zone and the same place with regular and normalized LMS ANC turned on.
Both of the algorithms converge to cancel noise, but the regular algorithm has a much larger overshoot (50 units vs. 10) when the noise arrives. The normalized algorithm takes a marginally longer time ( 20 msec vs. 10 msec) to converge, but its error is much smaller.

The tone results show that both algorithms are acceptable with regular being slightly faster to converge but with larger error.

Procedure:

Regular and Normalized LMS Algorithms Against White Noise:

  1. A "noise source" data file was created using Cool Edit to generate a white noise data file
  2. A "quiet zone" was created by feeding the "noise source" into a 64 sample delay line.
  3. The regular and normalized LMS algorithms were then used to process the data.
  4. A time verses amplitude plot was created for the original tone, the regular LMS and the normalized LMS algorithms

Results:

Regular and Normalized LMS verses white noise
This picture represents the white noise you would hear at the protected zone and the same signal with regular LMS and normalized LMS ANC turned on.

While the regular LMS (green points) does converge slowly, the normalized LMS (red dots) converge quickly (about 25 msec) and elimate essentually all the noise.
In this case, the normalized LMS is clearly better than the regular LMS.

Our goals are:
  1. Flexibility to respond to the real site characteristics
  2. Eliminate specific tones
  3. Eliminate broadband noise
The two algorithms have almost identical performance on single tones. The normalized LMS does markedly better on white noise. The site data is much closer to white noise than a single tone. I believe that the normalized LMS should be used.

Questions?


dak 10/19/97