Stability Measures for Spectral Analysis Using Discrete Sampling with the Kaiser-Bessel or Dolph-Chebyshev Window

摘要

Spectral estimation in sonar systems is usually performed by the classicweighted, overlap method. With this technique, the data to be analyzed are divided into overlapping sections. Each section is then weighted multiplicatively before it is fast Fourier transformed to the frequency domain. Next, all these magnitude-squared spectral estimates are averaged to produce the final estimate. As with all estimation techniques, the ratio of the mean to the standard deviation of the estimator should be as large as possible, which will ensure that a good spectral estimate 'on the average' is obtained. In this report, an expression is derived for this important ratio called stability, which depends on only three quantities: the total number of data points T, the size of each section N, and the autocorrelation phi-w(m) of the discrete weighting function w(n). The optimum overlap that maximizes stability for different values of T and N and for two commonly used windows (namely, Kaiser-Bessel and Dolph-Chebyshev) is computed. It is found that an overlap of 50 percent yields almost the same amount of stability as the optimal overlap for a wide variety of values of T, N, and w(n).