OPTIMUM INVERSE FILTERS WHICH SHORTEN THE SPACING OF VELOCITY LOGS

Geophysics ◽  
1962 ◽  
Vol 27 (3) ◽  
pp. 317-326 ◽  
Author(s):  
M. R. Foster ◽  
W. G. Hicks ◽  
J. T. Nipper
Keyword(s):  
Moving Average ◽  
Calibration Error ◽  
Inverse Filter ◽  
Short Spacing ◽  
Filter Theory ◽  
Smoothing Filter ◽  
Finite Memory ◽  
Optimum Filter ◽  
Noise Amplification ◽  
Distorted Form

A long‐spacing velocity log contains almost the same information as an ideal short‐spacing log, but in a distorted form with added noise. The distortion can be thought of as a moving average or smoothing filter. Its inverse, called a “sharpening” filter by astronomers, amplifies noise. If the inverse is to be useful, it must be designed with a balance between errors due to noise amplification and those due to incomplete sharpening. The Wiener optimum filter theory gives a prescription for achieving this balance. The result is called an optimum inverse filter. We have calculated finite‐memory optimum inverse filters using the IBM 704. We have applied them to actual data, digitized in the field, to produce synthetic short‐spacing velocity logs. These we have compared with their field counterparts. The synthetic logs have less calibration error and are free from noise spikes. The general agreement is good.

Fully Automated High-Performance Signal-to-Noise Ratio Enhancement Based on an Iterative Three-Point Zero-Order Savitzky—Golay Filter

2008 ◽  
Vol 62 (10) ◽  
pp. 1160-1166 ◽  
Author(s):  
H. Georg Schulze ◽  
Rod B. Foist ◽  
Andre Ivanov ◽  
Robin F. B. Turner
Keyword(s):  
Average Method ◽  
High Performance ◽  
Signal To Noise Ratio ◽  
Moving Average ◽  
Median Filter ◽  
Zero Order ◽  
Smoothing Filter ◽  
Crucial Difference ◽  
Automated Processing ◽  
Better Than

The automated processing of data from high-throughput and real-time collection procedures is becoming a pressing problem. Currently the focus is shifting to automated smoothing techniques where, unlike background subtraction techniques, very few methods exist. We have developed a filter based on the widely used and conceptually simple moving average method or zero-order Savitzky–Golay filter and its iterative relative, the Kolmogorov–Zurbenko filter. A crucial difference, however, between these filters and our implementation is that our fully automated smoothing filter requires no parameter specification or parameter optimization. Results are comparable to, or better than, Savitzky–Golay filters with optimized parameters and superior to the automated iterative median filter. Our approach, because it is based on the highly familiar moving average concept, is intuitive, fast, and straightforward to implement and should therefore be of immediate and considerable practical use in a wide variety of spectroscopy applications.

Automatic Identification of Autoregressive Integrated Moving Average Time Series

1982 ◽  
Vol 14 (3) ◽  
pp. 156-166 ◽  
Author(s):  
Chin-Sheng Alan Kang ◽  
David D. Bedworth ◽  
Dwayne A. Rollier
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Automatic Identification ◽  
Autoregressive Integrated Moving Average

Smoothing Facilitates the Detection of Coupled Responses in Psychophysiological Time Series

2000 ◽  
Vol 14 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Joni Kettunen ◽  
Niklas Ravaja ◽  
Liisa Keltikangas-Järvinen
Keyword(s):  
Time Series ◽  
Type I Error ◽  
Electrodermal Activity ◽  
Moving Average ◽  
Type I ◽  
Facial Electromyography ◽  
Response Characteristics ◽  
Smoothing Methods ◽  
Response Systems ◽  
Different Response

Abstract We examined the use of smoothing to enhance the detection of response coupling from the activity of different response systems. Three different types of moving average smoothers were applied to both simulated interbeat interval (IBI) and electrodermal activity (EDA) time series and to empirical IBI, EDA, and facial electromyography time series. The results indicated that progressive smoothing increased the efficiency of the detection of response coupling but did not increase the probability of Type I error. The power of the smoothing methods depended on the response characteristics. The benefits and use of the smoothing methods to extract information from psychophysiological time series are discussed.

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