Samuel D. Stearns

An adaptive IIR structure for sinusoidal enhancement, frequency estimation, and detection

An adaptive IIR structure for processing a sinusoidal signal in broad-band noise is introduced. The structure contains three adaptive processors, each of which is computationally very simple. Useful features of the structure include enhancement, frequency estimation, and detection.

Lossless compression of waveform data for efficient storage and transmission

A two-stage technique for lossless waveform data compression is described. The first stage is a modified form of linear prediction with discrete coefficients, and the second stage is bilevel sequence coding. The linear predictor generates an error or residue sequence in a way such that exact reconstruction of the original data sequence can be accomplished with a simple algorithm. The residue sequence is essentially white Gaussian with seismic or other similar waveform data. Bilevel sequence coding, in which two sample sizes are chosen and the residue sequence is encoded into subsequences that alternate from one level to the other, further compresses the residue sequence. The algorithm is lossless, allowing exact, bit-for-bit recovery of the original data sequence. The performance of the algorithm at each stage is analyzed. Applications of the two-stage technique to typical seismic data indicates that an average number of compressed bits per sample close to the lower bound is achievable in practical situations. >

IIR algorithms for adaptive line enhancement

In this paper we introduce a simple IIR structure for the adaptive line enhancer. Two algorithms based on gradient-search techniques are presented for adapting the structure. Results from experiments which utilized real data as well as computer simulations are provided.

A bi-level coding technique for compressing broadband residue sequences

Many coding techniques result in residue sequences with Gaussian, Laplacian, and Gamma amplitude distributions. Such coding techniques occur in LPC (Linear Predictive Coding) of speech, image, and seismic waveforms [ l-4,6]. We assume that the residue sequence is a white (memoryless) signed integer sequence. For example, the residue sequence from a least-squares linear predictor for seismic waveform data [ 4,6] is shown to be white Gaussian. A technique called bi-level sequence coding is developed in this paper for such applications.

Seismic event detection using adaptive predictors

Adaptive digital predictors have been applied to the detection of seismic events. In this paper we review the structure of the adaptive predictor and discuss its implementation. Using seismic velocity data, we then demonstrate its ability to locate signal arrivals.

Techniques for geophysical data compression

Lossless compression is never as profitable, in terms of compression ratio, as lossy compression of the same data. However, lossless techniques that produce significant compression of geophysical waveform data are possible. A two-stage technique for lossless compression of geophysical waveform data is described. The first and most important stage is a form of linear prediction that allows exact recovery of the original waveform data from the predictor residue sequence. The second stage is an encoder of the first-stage residue sequence which approximately maximizes the entropy of the latter, while allowing exact recovery during decompression. We review the overall two-stage technique, which has been described previously, and concentrate in this paper on some recent performance examples and results using the technique. To obtain the latter, a seismic waveform data base is introduced and made available. We conclude that lossless compression of seismic data can save significant amounts of storage in seismic data bases and archives, and significant amounts of bandwidth in real- time communication of instrumentation data.

Tests of coherence unbiasing methods

The causes of bias in the mean-squared coherence (MSC) estimate are discussed, assuming that the estimate is made using the FFT method. Two known unbiasing methods, prewhitening and MSC averaging, are tested in situations where the true MSC is known, and are seen to reduce bias. MSC averaging is recommended as the best unbiasing method.

Rational parametric coherence estimation via convolved correlations

In this paper, the magnitude squared (MS) coherence is computed by estimating the parameters of a rational model. The parameters are constrained so that the estimated MS coherence is real-valued on the unit circle. The method entails first estimating the auto- and cross-correlation lags from raw data sequences. These lag estimates are then used to define two auxiliary sequences, the convolution of the cross-correlation function with itself and the convolution of the two autocorrelation functions. The MS coherence parameters will nearly satisfy a homogeneous set of equations involving these auxiliary sequences. This system of linear equations is solved via an eigenspace decomposition. The algorithm is compared with two traditional periodogram based estimation methods.

Estimation of time-varying coherence functions

Two methods for computing an estimate of the time-varying magnitude squared (MS) coherence between two data sequences are described. The first method estimates the time-varying parameters of two autoregressive moving average (ARMA) transfer functions, whose product approximates the time-varying MS coherence function. The ARMA parameters are computed by an exponentially weighted recursive least squares algorithm. The second method estimates the time-varying MS coherence function by substituting time-varying estimates of the auto- and cross-spectra into usual the definition of the MS coherence function. The time-varying spectra are obtained by bandpass filtering, squaring and averaging operations.

Adaptive Transfer Filter Considerations

A novel filter configuration known as the adaptive transfer filter is introduced. The performance of this filter is compared emperically with the conventional filter configuration which is generally referred to as the adaptive noise-cancellation filter. In the related experiments, both filters are implemented via Widrows LMS (least-mean-square) algorithm.