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# Fourier Analysis of SPEX (Spherix Incorporated)

SPEX (Spherix Incorporated) appears to have interesting cyclic behaviour every 74 weeks (1326.416*sine), 96 weeks (1203.712*cosine), and 80 weeks (1202.424*sine).

SPEX (Spherix Incorporated) has an average price of 9,110.06 (topmost row, frequency = 0).

Click on the checkboxes shown on the right to see how the various frequencies contribute to the graph. Look for large magnitude coefficients (sine or cosine), as these are associated with frequencies which contribute most to the associated stock plot. If you find a large magnitude coefficient which dramatically changes the graph, look at the associated "Period" in weeks, as you may have found a significant recurring cycle for the stock of interest.

Right click on the graph above to see the menu of operations (download, full screen, etc.)

## Fourier Analysis

Using data from 1/3/2000 to 5/21/2018 for SPEX (Spherix Incorporated), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
09,110.064   0
16,070.874 10,697.27 (1*2π)/960960 weeks
2270.6949 7,106.094 (2*2π)/960480 weeks
3-1,626.094 2,755.476 (3*2π)/960320 weeks
4-206.845 1,612.879 (4*2π)/960240 weeks
51,064.528 1,288.881 (5*2π)/960192 weeks
6-694.3425 2,546.579 (6*2π)/960160 weeks
7-554.6841 281.2172 (7*2π)/960137 weeks
8-126.7866 84.99689 (8*2π)/960120 weeks
91,189.8 -194.3728 (9*2π)/960107 weeks
101,203.712 932.1698 (10*2π)/96096 weeks
11888.5844 967.7998 (11*2π)/96087 weeks
12869.8904 1,202.424 (12*2π)/96080 weeks
13447.3984 1,326.416 (13*2π)/96074 weeks
14113.4885 1,045.801 (14*2π)/96069 weeks
15475.2888 918.4785 (15*2π)/96064 weeks
16-185.4418 1,122.099 (16*2π)/96060 weeks
17294.4481 282.5753 (17*2π)/96056 weeks
18527.752 978.7178 (18*2π)/96053 weeks
19127.1936 1,096.434 (19*2π)/96051 weeks
20-155.1042 684.9158 (20*2π)/96048 weeks
21226.609 750.4239 (21*2π)/96046 weeks
22-202.6316 807.3896 (22*2π)/96044 weeks
23-288.0413 383.3791 (23*2π)/96042 weeks
24175.2066 -3.60403 (24*2π)/96040 weeks
25589.8721 362.535 (25*2π)/96038 weeks
26633.9587 711.5284 (26*2π)/96037 weeks
27371.0216 1,072.687 (27*2π)/96036 weeks
28-80.49151 1,064.064 (28*2π)/96034 weeks
29-174.9487 681.0551 (29*2π)/96033 weeks
30-65.0932 686.2699 (30*2π)/96032 weeks
31-84.55235 680.7526 (31*2π)/96031 weeks
32-145.2932 675.8035 (32*2π)/96030 weeks
33-258.3206 706.2608 (33*2π)/96029 weeks
34-350.4338 499.7851 (34*2π)/96028 weeks
35-357.6108 409.7971 (35*2π)/96027 weeks
36-283.5074 264.4729 (36*2π)/96027 weeks
37-182.497 96.4894 (37*2π)/96026 weeks
3886.64824 299.6781 (38*2π)/96025 weeks
3914.96373 264.8203 (39*2π)/96025 weeks
40112.6174 658.6989 (40*2π)/96024 weeks
41-408.5233 542.8168 (41*2π)/96023 weeks
42-386.9284 231.3762 (42*2π)/96023 weeks
43-112.327 127.3577 (43*2π)/96022 weeks
44-267.6053 216.1202 (44*2π)/96022 weeks
45-35.03165 49.52361 (45*2π)/96021 weeks
46-4.10213 160.7152 (46*2π)/96021 weeks
47-3.07384 293.2604 (47*2π)/96020 weeks
48-83.34637 136.7531 (48*2π)/96020 weeks
4967.26125 212.4607 (49*2π)/96020 weeks
5068.08324 340.3811 (50*2π)/96019 weeks
51-115.396 346.2894 (51*2π)/96019 weeks
52-89.07487 282.6866 (52*2π)/96018 weeks
53-133.4186 320.7592 (53*2π)/96018 weeks
54-265.3505 149.9055 (54*2π)/96018 weeks
5525.37458 91.22546 (55*2π)/96017 weeks
56-85.13831 254.595 (56*2π)/96017 weeks
57-111.6396 151.6741 (57*2π)/96017 weeks
5820.92019 71.10461 (58*2π)/96017 weeks
5994.48866 271.6611 (59*2π)/96016 weeks
60-16.057 319.0754 (60*2π)/96016 weeks
61-53.10529 337.3754 (61*2π)/96016 weeks
62-166.8903 403.5469 (62*2π)/96015 weeks
63-316.3789 221.1151 (63*2π)/96015 weeks
64-225.1284 128.4508 (64*2π)/96015 weeks
65-145.0708 88.11303 (65*2π)/96015 weeks
66-200.8345 131.7741 (66*2π)/96015 weeks
67-87.46822 -3.22941 (67*2π)/96014 weeks
68-25.00672 107.0468 (68*2π)/96014 weeks
69-39.30062 201.2204 (69*2π)/96014 weeks
70-123.4957 159.835 (70*2π)/96014 weeks
71-135.853 196.6334 (71*2π)/96014 weeks
72-197.412 111.1043 (72*2π)/96013 weeks
73-137.153 66.07958 (73*2π)/96013 weeks
74-119.1526 134.2895 (74*2π)/96013 weeks
75-225.3 82.03122 (75*2π)/96013 weeks
76-168.1298 -3.03094 (76*2π)/96013 weeks
77-140.2087 45.13448 (77*2π)/96012 weeks
78-267.4055 -57.92023 (78*2π)/96012 weeks
79-73.14041 -251.3501 (79*2π)/96012 weeks
80141.2559 -134.0935 (80*2π)/96012 weeks
81128.9594 78.27085 (81*2π)/96012 weeks
8210.55311 36.7097 (82*2π)/96012 weeks
8379.03207 82.43446 (83*2π)/96012 weeks
84-8.59792 107.1008 (84*2π)/96011 weeks
851.16995 50.409 (85*2π)/96011 weeks
8649.03823 94.52811 (86*2π)/96011 weeks
87-29.01285 174.3314 (87*2π)/96011 weeks
88-124.755 63.5159 (88*2π)/96011 weeks
89-27.75856 -27.08137 (89*2π)/96011 weeks
9056.66842 52.10317 (90*2π)/96011 weeks
91-11.35487 91.58658 (91*2π)/96011 weeks
928.23216 90.13014 (92*2π)/96010 weeks
93-59.82209 86.55412 (93*2π)/96010 weeks
94-40.79493 11.54199 (94*2π)/96010 weeks
9570.07944 34.55871 (95*2π)/96010 weeks
9615.30551 153.0493 (96*2π)/96010 weeks
97-83.2442 110.5702 (97*2π)/96010 weeks
98-58.28027 5.58255 (98*2π)/96010 weeks
9938.95234 47.91639 (99*2π)/96010 weeks
1002.42774 129.2787 (100*2π)/96010 weeks
101-91.65113 100.5509 (101*2π)/96010 weeks
102-66.1488 35.88931 (102*2π)/9609 weeks
103-42.56026 34.98983 (103*2π)/9609 weeks
104-63.78609 36.07678 (104*2π)/9609 weeks
105-21.0556 6.89188 (105*2π)/9609 weeks
106-58.46986 26.63656 (106*2π)/9609 weeks
107-30.96685 -23.38797 (107*2π)/9609 weeks
1088.73774 -40.42152 (108*2π)/9609 weeks
10924.11731 -3.99945 (109*2π)/9609 weeks
11082.31782 -41.30808 (110*2π)/9609 weeks
111121.4907 65.02563 (111*2π)/9609 weeks
11254.99193 147.4925 (112*2π)/9609 weeks
113-34.91103 52.66285 (113*2π)/9608 weeks
11482.24615 74.49876 (114*2π)/9608 weeks
115-8.80142 144.9266 (115*2π)/9608 weeks
116-61.47683 85.38429 (116*2π)/9608 weeks
117-9.27613 25.53378 (117*2π)/9608 weeks
118-4.20502 89.40097 (118*2π)/9608 weeks
119-42.35036 66.68512 (119*2π)/9608 weeks
120-34.03948 5.37062 (120*2π)/9608 weeks
12125.83408 55.05407 (121*2π)/9608 weeks
122-1.59009 14.6473 (122*2π)/9608 weeks
12361.67171 110.4108 (123*2π)/9608 weeks
124-39.61536 90.73482 (124*2π)/9608 weeks
125-40.72007 89.15829 (125*2π)/9608 weeks
126-39.27749 16.62924 (126*2π)/9608 weeks
12727.89671 80.24328 (127*2π)/9608 weeks
128-43.88154 81.62735 (128*2π)/9608 weeks
129-22.66799 84.41898 (129*2π)/9607 weeks
130-38.96594 119.7314 (130*2π)/9607 weeks
131-180.5863 117.876 (131*2π)/9607 weeks
132-146.788 -73.05845 (132*2π)/9607 weeks
133-62.77261 -56.48852 (133*2π)/9607 weeks
1345.78451 -61.13452 (134*2π)/9607 weeks
13522.38058 -.78672 (135*2π)/9607 weeks
1364.60362 62.65094 (136*2π)/9607 weeks
137-80.48798 34.51094 (137*2π)/9607 weeks
138-65.52466 -14.5506 (138*2π)/9607 weeks
139-45.37359 -50.7882 (139*2π)/9607 weeks
140-3.13607 -31.54287 (140*2π)/9607 weeks
14110.34143 -46.16774 (141*2π)/9607 weeks
14247.60491 52.22484 (142*2π)/9607 weeks
143-88.04295 38.79449 (143*2π)/9607 weeks
144-80.06474 -37.91179 (144*2π)/9607 weeks
145-30.24515 -112.4587 (145*2π)/9607 weeks
14629.26393 -45.94536 (146*2π)/9607 weeks
14717.30232 -63.78617 (147*2π)/9607 weeks
14817.66796 -41.72652 (148*2π)/9606 weeks
14958.43026 -76.57514 (149*2π)/9606 weeks
15065.29966 -31.46957 (150*2π)/9606 weeks
151109.9861 -16.24926 (151*2π)/9606 weeks
15268.72844 67.24221 (152*2π)/9606 weeks
153-5.53686 56.7512 (153*2π)/9606 weeks
154-38.85514 -10.72432 (154*2π)/9606 weeks
15515.16698 -45.22687 (155*2π)/9606 weeks
15611.77308 -58.09552 (156*2π)/9606 weeks
157119.5846 -48.65259 (157*2π)/9606 weeks
15861.51167 48.33237 (158*2π)/9606 weeks
15919.52177 40.28754 (159*2π)/9606 weeks
160-21.65988 -46.43982 (160*2π)/9606 weeks
16187.45559 -40.13697 (161*2π)/9606 weeks
16259.52787 8.69122 (162*2π)/9606 weeks
16339.97817 8.38951 (163*2π)/9606 weeks
16445.87477 -29.58035 (164*2π)/9606 weeks
16571.79257 19.15967 (165*2π)/9606 weeks
16613.52689 -16.43105 (166*2π)/9606 weeks
16765.44281 -49.02735 (167*2π)/9606 weeks
168103.2055 -41.28665 (168*2π)/9606 weeks
169133.7919 -3.74154 (169*2π)/9606 weeks
170143.365 39.84465 (170*2π)/9606 weeks
171105.6082 93.08715 (171*2π)/9606 weeks
17253.90526 88.60883 (172*2π)/9606 weeks
17338.74128 52.96575 (173*2π)/9606 weeks
17449.15063 38.67543 (174*2π)/9606 weeks
17563.26501 41.82769 (175*2π)/9605 weeks
17688.36369 45.30911 (176*2π)/9605 weeks
17765.45378 115.0223 (177*2π)/9605 weeks
17814.68812 73.72089 (178*2π)/9605 weeks
17917.9556 65.73396 (179*2π)/9605 weeks
18036.64288 52.83165 (180*2π)/9605 weeks
18117.33802 47.33967 (181*2π)/9605 weeks
18281.27264 45.47551 (182*2π)/9605 weeks
18395.87497 138.117 (183*2π)/9605 weeks
184-51.29429 230.369 (184*2π)/9605 weeks
185-157.1271 55.63336 (185*2π)/9605 weeks
186-68.97057 -3.716 (186*2π)/9605 weeks
187-46.66113 2.94931 (187*2π)/9605 weeks
188-31.56878 -19.80854 (188*2π)/9605 weeks
189-16.61951 2.24127 (189*2π)/9605 weeks
190-23.86398 -7.60319 (190*2π)/9605 weeks
191-30.50038 -47.21611 (191*2π)/9605 weeks
19258.29817 -31.32818 (192*2π)/9605 weeks
19312.03879 22.63458 (193*2π)/9605 weeks
194-16.22016 -4.42202 (194*2π)/9605 weeks
19532.32184 -53.05768 (195*2π)/9605 weeks
19665.43833 24.41793 (196*2π)/9605 weeks
1976.44569 53.57899 (197*2π)/9605 weeks
198-30.78859 14.57026 (198*2π)/9605 weeks
199-38.04036 8.53923 (199*2π)/9605 weeks
200-53.99178 -65.21589 (200*2π)/9605 weeks
20110.19204 -82.07531 (201*2π)/9605 weeks
20239.31071 -61.59932 (202*2π)/9605 weeks
20320.19006 -82.59821 (203*2π)/9605 weeks
204131.6008 -80.50412 (204*2π)/9605 weeks
205101.0884 35.41204 (205*2π)/9605 weeks
20615.50678 23.0137 (206*2π)/9605 weeks
20734.92996 -42.52448 (207*2π)/9605 weeks
20839.70025 -49.50995 (208*2π)/9605 weeks
209120.9819 -40.67101 (209*2π)/9605 weeks
21086.74178 .93538 (210*2π)/9605 weeks
211103.1654 59.11155 (211*2π)/9605 weeks
212-9.16815 10.24391 (212*2π)/9605 weeks
21370.96048 -30.82962 (213*2π)/9605 weeks
21471.28547 11.81894 (214*2π)/9604 weeks
21536.70767 7.86946 (215*2π)/9604 weeks
21652.08516 -40.92448 (216*2π)/9604 weeks
21795.24326 -8.55366 (217*2π)/9604 weeks
21871.54056 -1.80128 (218*2π)/9604 weeks
21974.40304 -3.16137 (219*2π)/9604 weeks
22087.76774 -40.76638 (220*2π)/9604 weeks
221158.8961 .09826 (221*2π)/9604 weeks
222144.1672 71.0948 (222*2π)/9604 weeks
223101.5224 102.6193 (223*2π)/9604 weeks
22436.6927 115.2636 (224*2π)/9604 weeks
22518.78465 52.05467 (225*2π)/9604 weeks
22621.3597 88.90764 (226*2π)/9604 weeks
227-54.41467 29.21855 (227*2π)/9604 weeks
228-27.74858 -37.77613 (228*2π)/9604 weeks
22948.0649 -92.12939 (229*2π)/9604 weeks
23088.66527 -26.5502 (230*2π)/9604 weeks
231103.0053 -39.12613 (231*2π)/9604 weeks
23294.88493 -3.66192 (232*2π)/9604 weeks
233158.9193 -22.69559 (233*2π)/9604 weeks
234135.2022 61.88109 (234*2π)/9604 weeks
235149.9812 80.70245 (235*2π)/9604 weeks
23654.89482 108.3534 (236*2π)/9604 weeks
23797.65581 80.70541 (237*2π)/9604 weeks
23834.55417 108.4712 (238*2π)/9604 weeks
23917.68848 110.9089 (239*2π)/9604 weeks
240-57.83502 39.02318 (240*2π)/9604 weeks
2414.2759 -58.10265 (241*2π)/9604 weeks
242127.7325 -27.8136 (242*2π)/9604 weeks
243105.1005 72.03709 (243*2π)/9604 weeks
24450.94958 68.01976 (244*2π)/9604 weeks
24550.21476 45.44679 (245*2π)/9604 weeks
24667.38455 37.26047 (246*2π)/9604 weeks
24755.5167 81.33663 (247*2π)/9604 weeks
24838.24071 43.8768 (248*2π)/9604 weeks
24924.72165 66.21909 (249*2π)/9604 weeks
25036.59019 12.72341 (250*2π)/9604 weeks
25143.93708 41.32161 (251*2π)/9604 weeks
25246.22474 28.04348 (252*2π)/9604 weeks
25348.8837 12.53673 (253*2π)/9604 weeks
25487.61539 32.89701 (254*2π)/9604 weeks
25567.53245 41.67667 (255*2π)/9604 weeks
25690.63408 63.53794 (256*2π)/9604 weeks
25762.17677 79.23793 (257*2π)/9604 weeks
25850.25663 93.03204 (258*2π)/9604 weeks
259-4.11238 87.93862 (259*2π)/9604 weeks
260-1.38602 7.84867 (260*2π)/9604 weeks
26156.51995 21.50238 (261*2π)/9604 weeks
26253.36306 23.43107 (262*2π)/9604 weeks
26382.12852 32.26708 (263*2π)/9604 weeks
26486.59143 85.85394 (264*2π)/9604 weeks
26529.92836 64.83335 (265*2π)/9604 weeks
26663.60429 72.07142 (266*2π)/9604 weeks
26740.68601 66.89616 (267*2π)/9604 weeks
26843.6834 87.00879 (268*2π)/9604 weeks
26923.99513 72.59555 (269*2π)/9604 weeks
2704.87748 70.95284 (270*2π)/9604 weeks
27123.08322 33.49382 (271*2π)/9604 weeks
27235.21267 41.99625 (272*2π)/9604 weeks
27351.47314 48.77528 (273*2π)/9604 weeks
27435.72203 53.81917 (274*2π)/9604 weeks
27567.34341 35.7796 (275*2π)/9603 weeks
27695.26054 88.62637 (276*2π)/9603 weeks
27746.56884 122.7478 (277*2π)/9603 weeks
27838.24763 115.7539 (278*2π)/9603 weeks
27911.56474 144.5449 (279*2π)/9603 weeks
280-46.11134 137.5037 (280*2π)/9603 weeks
281-89.4163 70.32722 (281*2π)/9603 weeks
282-37.94561 25.97552 (282*2π)/9603 weeks
283-31.79062 17.02752 (283*2π)/9603 weeks
28410.62882 19.82845 (284*2π)/9603 weeks
28510.17104 29.40272 (285*2π)/9603 weeks
28615.93032 53.26354 (286*2π)/9603 weeks
287.09049 36.47251 (287*2π)/9603 weeks
28835.01963 50.31982 (288*2π)/9603 weeks
289-5.66185 91.6328 (289*2π)/9603 weeks
290-35.69709 63.82989 (290*2π)/9603 weeks
291-50.04613 21.42267 (291*2π)/9603 weeks
2924.90552 11.70861 (292*2π)/9603 weeks
293-10.9568 36.15269 (293*2π)/9603 weeks
294-24.68143 15.31261 (294*2π)/9603 weeks
29515.14976 -3.28051 (295*2π)/9603 weeks
29618.33521 24.6944 (296*2π)/9603 weeks
29716.84387 29.55705 (297*2π)/9603 weeks
29824.05913 45.41107 (298*2π)/9603 weeks
299-17.87163 52.89653 (299*2π)/9603 weeks
300-5.04035 33.91827 (300*2π)/9603 weeks
301-36.24105 34.93771 (301*2π)/9603 weeks
302-44.84968 5.2361 (302*2π)/9603 weeks
303-25.35357 -66.5163 (303*2π)/9603 weeks
30455.96134 -56.25399 (304*2π)/9603 weeks
305118.7441 -18.85327 (305*2π)/9603 weeks
30695.33291 100.6873 (306*2π)/9603 weeks
30716.74093 92.94357 (307*2π)/9603 weeks
308-21.7779 73.90388 (308*2π)/9603 weeks
309-17.02187 28.17839 (309*2π)/9603 weeks
31013.81746 20.81605 (310*2π)/9603 weeks
3113.54301 84.53069 (311*2π)/9603 weeks
312-76.25166 19.43911 (312*2π)/9603 weeks
313-20.84991 -31.2821 (313*2π)/9603 weeks
31418.819 -30.39536 (314*2π)/9603 weeks
31533.01935 -15.83272 (315*2π)/9603 weeks
31664.87105 1.85063 (316*2π)/9603 weeks
31742.55153 37.53454 (317*2π)/9603 weeks
31845.1252 18.14772 (318*2π)/9603 weeks
31958.24496 61.35047 (319*2π)/9603 weeks
32011.38311 68.62627 (320*2π)/9603 weeks
321-5.34516 42.49958 (321*2π)/9603 weeks
32229.98333 28.4418 (322*2π)/9603 weeks
3231.30797 72.11992 (323*2π)/9603 weeks
324-30.1921 26.3817 (324*2π)/9603 weeks
32514.65124 -13.12713 (325*2π)/9603 weeks
32643.62641 35.30154 (326*2π)/9603 weeks
32723.29033 53.83566 (327*2π)/9603 weeks
328-11.81337 31.54739 (328*2π)/9603 weeks
32929.51718 21.48476 (329*2π)/9603 weeks
33042.85184 27.70666 (330*2π)/9603 weeks
33133.09533 86.26007 (331*2π)/9603 weeks
3328.73684 69.54805 (332*2π)/9603 weeks
333-27.44458 73.65637 (333*2π)/9603 weeks
334-2.54619 46.01533 (334*2π)/9603 weeks
335-24.11728 57.04001 (335*2π)/9603 weeks
336-15.36995 51.9459 (336*2π)/9603 weeks
337-28.31067 42.96311 (337*2π)/9603 weeks
338-9.30422 51.91562 (338*2π)/9603 weeks
339-51.57865 64.01749 (339*2π)/9603 weeks
340-45.37621 38.73036 (340*2π)/9603 weeks
341-74.31665 21.01581 (341*2π)/9603 weeks
342-38.69679 17.90047 (342*2π)/9603 weeks
343-75.76384 -14.68203 (343*2π)/9603 weeks
344-24.9952 -7.30183 (344*2π)/9603 weeks
345-35.40974 -26.0202 (345*2π)/9603 weeks
346-36.81447 3.61191 (346*2π)/9603 weeks
347-32.99729 -55.78101 (347*2π)/9603 weeks
348-.56671 -40.72466 (348*2π)/9603 weeks
34940.92885 -26.42553 (349*2π)/9603 weeks
3507.19543 8.44863 (350*2π)/9603 weeks
35121.97898 15.95746 (351*2π)/9603 weeks
352-21.37412 17.18407 (352*2π)/9603 weeks
353-16.58292 4.63418 (353*2π)/9603 weeks
354-17.46113 -7.88279 (354*2π)/9603 weeks
355-30.07682 -5.46287 (355*2π)/9603 weeks
356-11.22648 -43.77077 (356*2π)/9603 weeks
35713.96045 -21.86342 (357*2π)/9603 weeks
3581.3977 -.59163 (358*2π)/9603 weeks
359-28.85928 -21.87792 (359*2π)/9603 weeks
360-5.83414 -66.13701 (360*2π)/9603 weeks
36140.35173 -60.66319 (361*2π)/9603 weeks
36270.01901 -43.20979 (362*2π)/9603 weeks
36380.69421 12.83757 (363*2π)/9603 weeks
36458.2233 35.53402 (364*2π)/9603 weeks
3655.83477 53.73143 (365*2π)/9603 weeks
3666.51407 8.32958 (366*2π)/9603 weeks
3676.41826 20.67543 (367*2π)/9603 weeks
368.1812 12.30863 (368*2π)/9603 weeks
3696.71616 -11.26694 (369*2π)/9603 weeks
37036.65931 23.74693 (370*2π)/9603 weeks
371-20.53238 44.74734 (371*2π)/9603 weeks
372-33.11002 -19.01538 (372*2π)/9603 weeks
3739.22587 -23.54448 (373*2π)/9603 weeks
37417.86133 -5.22612 (374*2π)/9603 weeks
3755.69009 -10.51254 (375*2π)/9603 weeks
37630.6291 -1.0034 (376*2π)/9603 weeks
3771.66947 7.65265 (377*2π)/9603 weeks
37816.51604 -25.26024 (378*2π)/9603 weeks
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76858.29817 31.32818 (768*2π)/9601 weeks
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