THE PROBLEM 



Ao part of the general study of low frequency ambient sea 

 noise, investigate the characteristics of statistical filters 

 for smoothing of time series data. 



RESULTS 



1. Smoothing with equally weighted running means is computa- 

 tionally simple and results in a relatively sharp cutoff 

 filter. However, the frequency response decreases contin- 

 uously within the pass band and high frequency ripples are 

 introduced into the data because of large oscillations in 

 the frequency response above the cutoff. 



2. The Gaussian filter does not introduce high frequency 

 ripples into the data since its frequency response approaches 

 zero asymptotically without a finite cutoff. However, its 

 arbitrarily defined 1 per cent cutoff is not very sharp. 



3. The defects inherent in the two filters discussed above 

 can be minimized by determining weights for a filter which 

 approximates the square-shaped ideal filter in the least 

 square sense, with corrections for unity gain at zero fre- 

 quency and a sine termination to reduce oscillations above 

 cutoff. Weights have been determined for ll8 such filters 

 which depart from the ideal filter in the pass-band region 

 and below the cutoff by an absolute error less than or 



equaJ to 1 per cent. These weights are given in the Appendix. 



ADMINISTRATIVE INFORMATION 



Work was performed under AS 02101, NE O516OO-8V7.6O (now 

 S-R004 03 01, Task 8119) (NEL L2-^) from July i960 through 

 April 1961 . Thi? - report was approved for publication 

 10 July 196I. The author wishes to thank G. M. Wenz and 

 E. C. Westerfield for advice and helpful suggestions, and 

 R. F. Arenz for assistance relative to computer programming. 



