STATISTICS GOVERNING THE DESIGN AND PERFORMANCE OF NOISE-PREDICTION FILTERS
Abstract
In designing a digital multichannel filter from a limited sample of noise, a highly important parameter, alpha, is defined as the true mean-square error of the estimated filter (i.e., the average long-term performance of the filter obtained from the noise sample) divided by the true mean-square error of the optimum filter. The value of alpha, which is equal to or greater than one, is not known before or after an experiment since the true covariance of the data is required to calculate its value; however, the probability density of alpha turns out to be invariant with respect to the true covariance and depends only on the amount of data and the number of channels in the filter. Thus, one can determine before collecting any data how long a sample is needed in order to design a filter which is within 1 db (for example) of optimum with 90-percent confidence. A second similar parameter, beta, defined as the estimated mean- square error of the estimated filter (i.e., the regression error) divided by the true mean-square error of the optimum filter is highly useful in deciding the reliability of the apparent effectiveness of the designed filter. The probability densities of alpha and beta are derived for the Gaussian assumption and graphs useful in experiment design are presented in this report.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 08, 1967
- Accession Number
- AD0826558
Entities
People
- Aaron H. Brooker
- George D. Hair
- John P. Burg
- T. J. Cruise
Organizations
- Texas Instruments