Abstract

Present day computer systems allow computation of an approximate Wiener operator for the time-domain filtering and smoothing of signals of finite (and short) length. However, the memory capacity of a particular computer storage introduces a constraint on the length of the operator and signal. To produce the least mean-square-error, it was helpful to know the extent to which the length of the operator whould be compromised by including additional information (sample points) of the signal. If N is the number of samples of the signal to be equalized and T is the number of points in the optimum digital operator, then the system imposes the constraint that  
KN+f(T)<M
where M is the free capacity of the computer memory and K is the number of multiples of signal length required for the correlations.

To find out whether an optimum relation between T and N exists, a program to determine the digital operator and to compute the mean-square-error between the filtered result and the desired signal was written for an IBM 7090 computer. The computed errors for some typical seismic signals are presented as a function of operator length, signal length, signal-to-noise ratio, and the number of records used to determine averages. The results suggest that equalization occurs both as a process of signal shaping and of noise-reduction, but not necessarily simultaneously.

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