*o<t) 



f 



fc 



fa : 

 tf = 



ft a 



J/(t) = 



T = 



DEFINITIONS 



= the filter input. 



- the filter output. 



* frequency in cycles per unit time. 



= cutoff frequency in cycles per unit time. 



= sampling frequency (rate). 



= an integer defined by the total number of weights 

 (av+l) in the weighting function. 



■ an integer whose range is 1, 2, . . . N. 



■ continuous weighting function 

 3 variable time parameter. 



weights of the discrete weighting function. 



yt 



T 



T 

 2OT-.1 



frequency-response function which relates a 

 sinusoidal input to the output that it produces. 



variable in the smoothed time series. 



filtering interval. 



duta. interval. 



normalized frequency ratio defined by f/f 3 where 

 / is in cycles per unit time and f g is the sampling 

 rate. 



normalized cutoff frequency for the ideal filter 

 defined by the ratio f c /f s where f c is the cutoff 

 frequency in cycles per unit time. 



the normalized cutoff frequency ratio for the 

 approximate filter. 



maximum absolute error in the filter gain from 

 zero frequency to the normalized cutoff r c , and 

 the frequency range between the first zero crossing 

 and the frequency limit, r = 0.5- Note the range 

 of r is from r = to r = 0.5 for the filters 

 discussed. 



29 



J 



