An algorithm to partition DFT data into sections of constant variance

In the most common nonparametric method for detection of narrowband signals in underwater acoustic data, the time series are processed using overlapped and windowed discrete Fourier transforms (DFT's), and normalized with a noise mean estimator to obtain a display of frequency versus time for evaluation by the sonar operator. When the acoustic signals of interest are overresolved by the DFT, the usual normalization can degrade the detectability of these signals when the window size is not properly matched to the signal bandwidth. A novel algorithm is presented that uses the integrated DFT output to estimate the variance across all bins of the DFT. The algorithm can provide input for the autonomous identification of both broadband features of interest, like Lloyd's mirror, and overresolved narrowband features useful in target classification. It makes use of the maximum likelihood (ML) estimate of the partitioning of the DFT output vector into segments with constant variance. This approach is optimal when the number of partitions of the DFT data is known a priori. The combined maximum likelihood estimation of both the number of partitions and the partitions themselves results in as many partitions as there are data points. To avoid this, the idea of minimum description length is used to obtain a joint estimate of the number of partitions, the partition bins, and the variance within each partition. An efficient implementation of the algorithm is presented using dynamic programming. Some examples of the processing of underwater acoustic data are included.