







ff = 31, 







St 

































0.02 0.01* O.Ob 0.08 0.1 

 FREQUENCY, CYCLES PER DAT* INTERVAL 



Figure 3- Frequency response of the Gaussian weighting function. 



tion of how the cutoff frequency f c , as defined, varies as 

 a function of a or N, where 6a = 2N + 1. Note that since 

 the normal curve ordinates have negligible values beyond 

 3a from the origin, the filtering interval for the Gaussian 

 filter is taken as 6a- With this choice the filtering 

 interval is equal to (a/+l) data intervals, equivalent to 

 6a. 



For equivalent filtering intervals, a study of figure 5 

 will indicate the following significant differences between 

 the frequency function for the equally weighted running 

 mean filter of 2/I/+1 consecutive weights and the frequency 

 response for the corresponding Gaussian weighting function. 



(a) The frequency response for the equally weighted 

 running mean weighting function shows positive and negative 

 values above the frequency of the first zero response point. 

 Such maxima and minima are undesirable because i,hey intro- 

 duce into the smoothed output misleading high frequency 

 ripples. The frequency response for the normal curve 



13 



