vaaima-smieV &S '^■:X'k -t 



A brief discussion of figure IB will reveal the nature of 

 the departure of the equally weighted running mean filter 

 from the ideal low -pass filter. The graph in figure IB 

 shows' the frequency-response curve with cutoff frequency/ 

 equal to O.OI96 cycle per data interval. At frequency 

 0.012 cycle per data interval, the frequency response is 

 0.5 or only 50 per cent. This implies that the filter has 

 removed 50 per cent of the contribution associated with this 

 frequency component in the input data, as compared with the 

 ideal filter (with the same cutoff) which would pass the 

 frequency component at 0.012 cycle per unit data unaltered. 



Equation (12) shows the significance of N as related to the 

 total number of weights (2jV+i) in the filtering function. 

 The curve in figure 2 gives a graphical description of the 

 cutoff frequency f c as a function of N. The cutoff fre- 

 quency is seen to decrease as number of weights in the 

 weighting function increases and, in particular, as N 

 increases . 



Figure 2. Variation of cutoff frequency f c with N for the 

 equally weighted running mean filtering function. The curve 

 indicates how the cutoff frequency f c decreases as N increases ■ 

 Note that for N greater than 60 decrease in f c is not very 

 sensitive to increasing N. 



11 



