The performance of any web site can be analyzed in the Fourier sense during a given time-window provided comprehensive statistics exist for that time-window.

Before we attempt an analysis, we need to decide what exactly constitutes a signal for a web site. The most prominent characteristic of any web site is the number of pageloads (L) or hits it receives, therefore we can define the signal of a web site to be related to the number of hits the web site receives.

Owners of web sites are primarily interested in increasing their web site's hits because this increases the web site's popularity, therefore if the hits go up the performance is becoming better and if the hits go down the performance is worsening.

We are therefore interested in the total variance of hits, or, in other words, in tracking the ups and downs of hits for the web site in question. If p is the period of the time-window in question, we have available data about the total number of hits/p as L[n] from a web page's statistics counter, therefore we can define the web site variance, as:

(1)

In turn, (1) now defines a web site signal in terms of the Heaviside step function H, as:

(2)

Once we have a signal S(t), we can analyze it in the Fourier sense using Maple. Follows the analysis for this web site starting with year 2011^[1].

Weekly Performance

Week #	Hits[2]	S(t)/F25(t)[3]	Spectrum[4]	Trend[5]
1 (2-8/1)	390,539,434,449,515,479,345			-
2 (9-15/1)	438,452,552,484,524,575,505			+
3 (16-22/1)	532,498,576,543,611,608,604			+
4 (23-29/1)	480,540,539,577,472,457,343			-
5 (30/1-5/2)	442,538,648,477,448,473,397			-
6 (6/2-12/2)	340,479,481,608,684,527,421			+
7 (13/2-19/2)	468,593,650,564,592,496,441			-
8 (20/2-26/2)	447,686,636,707,521,498,472			+
9 (27/2-5/3)	518,571,563,627,585,519,464			-
10 (6/3-12/3)	578,607,608,656,640,539,429			-
11 (13/3-19/3)	568,659,677,574,472,493,384			-
12 (20/3-26/3)	563,540,688,590,512,516,416			-
13 (27/3-2/4)	532,576,661,723,665,536,577			+
14 (3/4-9/4)	476,664,661,616,621,595,372			-
15 (10/4-16/4)	510,635,616,661,656,484,425			-
16 (17/4-23/4)	585,542,559,514,524,413,357			-
17 (24/4-30/4)	461,556,690,641,678,434,402			-
18 (1/5-7/5)	474,504,498,642,524,431,343			-
19 (8/5-14/5)	444,653,569,571,494,489,364			-
20 (15/5-21/5)	542,598,550,624,536,476,357			-
21 (22/5-28/5)	444,538,486,518,604,399,310			-
22 (29/5-4/6)	504,470,569,499,437,419,314			-
23 (5/6-11/6)	399,456,438,427,476,466,404			+
24 (12/6-18/6)	458,375,400,427,417,292,240			-
25 (19/6-25/6)	547,457,402,341,382,343,397			-
26 (26/6-2/7)	397,341,342,369,451,291,275			-
27 (3/7-9/7)	348,365,337,384,393,331,271			-
28 (10/7-16/7)	290,427,368,432,408,357,325			+
29 (17/7-23/7)	297,350,426,383,452,350,276			-
30 (24/7-30/7)	286,364,411,387,371,352,264			-
31 (31/7-6/8)	219,477,368,287,346,367,250			+
32 (7/7-13/8)	194,331,324,424,337,362,350			+
33 (14/8-20/8)	217,273,313,395,321,336,280			+
34 (21/8-27/8)	296,337,492,343,425,350,238			-
35 (28/8-3/9)	302,344,416,409,391,344,295			-
36 (4/9-10/9)	359,449,435,476,488,435,347			-
37 (11/9-17/9)	386,489,391,525,468,446,441			+
38 (18/9-24/9)	428,623,497,497,610,496,307			-
39 (25/9-1/10)	448,614,689,719,664,568,378			-
40 (2/10-8/10)	516,523,607,654,612,688,352			-
41 (9/10-15/10)	525,749,780,686,660,700,350			-
42 (16/10-22/10)	620,725,873,863,770,804,422			-
43 (23/10-29/10)	602,775,868,885,729,598,459			-
44 (30/10-5/11)	534,649,657,787,755,624,412			-
45 (6/11-12/11)	491,616,670,682,775,573,485			-
46 (13/11-19/11)	549,666,713,805,687,648,383			-
47 (20/11-26/11)	611,678,735,660,649,473,438			-
48 (27/11-3/12)	834,904,907,615,641,581,481			-
49 (4/12-10/12)	513,622,575,652,776,674,350			-
50 (11/12-17/12)	511,650,628,566,665,538,676			+
51 (18/12-24/12)	471,510,610,460,711,836,642			0
52 (25/12-31/12)	344,418,422,494,466,435,405			+

Monthly Performance

Month	Hits[2]	S(t)/F25(t)[3]	Spectrum[4]	Trend[5]
January	3199,3624,3920,3370			+
February	3321,3625,3804,3967			+
March	3847,4057,3827,3825			-
April	4270,4005,3987,3494			-
May	3862,3416,3584,3683			-
June	3299,3212,3066,2609			-
July	2429,2607,2534,2435			+
August	2345,2214,2487,2558			+
September	3016,3158,3478,4148			+
October	3961,4545,5059,4848			+
November	4375,4350,4513,4467			+
December	4642,4160,4194,4113			-

Yearly Performance

Year	Hits[2]	S(t)/F25(t)[3]	Spectrum[4]	Trend[5]
2011	15260,14006,16457,14293,13414,10568, 9489,10504,14295,19956,19482,17323			+

Overall Performance

Years	Hits[2]	S(t)/F25(t)[3]	Spectrum[4]	Trend[5]
2004 -2011	66984,146956,194358,225904, 177857,178876,178441,175047			+

Notes/References

1. Starting with year 2011, using data from StatCounter. The data is not perfectly accurate, because many custom hosts files now include 127.0.0.1 blocks to StatCounter, so the data collected is only correct on average.
2. Daily, weekly, monthly, yearly or overall web site hits for time-window in question as recorded on StatScounter. Hits by the author to his own web site have been excluded.
3. Weekly, monthly, yearly or overall signal S(t) (2) for this web site (red) and Fourier Series approximation with 25 terms (green).
4. Weekly, monthly, yearly or overall Harmonic Spectrum of S(t), showing amplitude of first 10 harmonics. From left to right: 0-th harmonic (DC-term) (red), 1-st harmonic (dominant) (green), 2-nd harmonic (yellow), 3-rd harmonic (blue), 4-th harmonic (magenta), 5-th harmonic (cyan), etc. Note that the n*p-th harmonic for n \in N is always 0.
5. v_p>0, Period trend: +. v_p<0, Period trend: -. v_p=0, Period trend: undefined. The "intensity" of the harmonics shows roughly how "abrupt" the Period trend is.

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