Cascade decimation--A technique for real time estimation of power spectra

Cascade decimation is a technique for computing power spectra estimates for single or multi-channel time series data. It was originally developed for processing broadband, low frequency geophysical data in real time using a small digital processor. Sine and Cosine transforms are applied to sequences of data produced by successively applying a low pass digital filter and decimation by two operator to the original data. The resulting spectra are the average of estimates which are independent in time and represent constant percentage bandwidths. Thus, the technique is particularly well suited to applications where it is desireable to reject intervals of bad data or those which are naturally expressed on a log-frequency scale. Because ascade decimation is a real time process, its memory requirements are a fraction of those for techniques which operate on a stored array of data, particularly when a broad band of frequencies is being analyzed.