The traditional 13month running mean (centered on a given month with equal weights for months –5 to +5 and half weight for months –6 and +6) is both simple and widely used but does a poor job of filtering out high frequency variations (although it is better than the simple 12month average). Gaussian shaped filters are preferable because they have Gaussian shapes in the frequency domain and effectively remove high frequency variations (Hathaway et al., 1999). A tapered (to make the filter weights and their first derivatives vanish at the end points) Gaussian filter is given by
with where t is the time in months and 2a is the FWHM of the filter (note that this formula is slightly different than that given in Hathaway et al. (1999). There are significant variations in solar activity on time scales of one to three years (see Section 7). These variations can produce double peaked maxima which are filtered out by a 24month Gaussian filter. The frequency responses of these filters are shown in Figure 21.Using the 24month FWHM Gaussian filter on the data used to create Table 3 gives far more consistent results for both maxima and minima. The results for maxima are shown in Table 4. The ranges of dates for the last five maxima become: 1, 10, 13, 4, and 11 months – roughly half the ranges found using the 13month running mean.
Cycle 
24month
Gaussian
Maximum

24Month
Gaussian
Sunspot Area

24Month
Gaussian
10.7 cm Flux


Date  Value  Date  RValue  Date  RValue  
1  1761/05  72.9  
2  1770/01  100.5  
3  1778/09  137.4  
4  1788/03  130.6  
5  1804/06  45.7  
6  1816/08  43.8  
7  1829/10  67.1  
8  1837/04  146.9  
9  1848/06  115.7  
10  1860/03  92.1  
11  1870/11  138.5  
12  1883/11  64.7  1883/10  70.8  
13  1893/09  81.4  1893/09  84.7  
14  1906/05  59.6  1906/04  62.4  
15  1917/12  88.6  1918/01  79.6  
16  1927/12  71.6  1926/12  75.9  
17  1937/11  108.2  1938/02  118.1  
18  1948/03  141.7  1947/09  140.0  
19  1958/02  188.0  1958/03  192.0  1958/03  188.1 
20  1969/03  106.6  1968/09  95.5  1969/07  104.6 
21  1980/05  151.8  1981/06  140.2  1980/11  153.1 
22  1990/02  149.2  1990/06  141.7  1990/06  156.1 
23  2000/12  112.7  2001/11  106.2  2001/06  136.4 
http://www.livingreviews.org/lrsp20101 
This work is licensed under a Creative Commons License. Problems/comments to 