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# Fourier Analysis of MSI (Motorola Solutions, Inc. Common)

MSI (Motorola Solutions, Inc. Common) appears to have interesting cyclic behaviour every 123 weeks (4.7793*sine), 210 weeks (4.275*sine), and 175 weeks (4.165*cosine).

MSI (Motorola Solutions, Inc. Common) has an average price of 35.67 (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.

## Fourier Analysis

Using data from 1/3/1977 to 3/20/2017 for MSI (Motorola Solutions, Inc. Common), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
035.67421   0
1-13.16428 -23.83872 (1*2π)/20982,098 weeks
211.52191 -2.00049 (2*2π)/20981,049 weeks
3-.50464 -7.93462 (3*2π)/2098699 weeks
46.66754 -7.24504 (4*2π)/2098525 weeks
5-1.4123 -10.66613 (5*2π)/2098420 weeks
6-7.58237 -.0641 (6*2π)/2098350 weeks
78.16497 1.20183 (7*2π)/2098300 weeks
8-1.76082 -7.55289 (8*2π)/2098262 weeks
9.68308 -.30303 (9*2π)/2098233 weeks
10-.40298 -4.275 (10*2π)/2098210 weeks
11-.78767 .50796 (11*2π)/2098191 weeks
124.16503 -3.1305 (12*2π)/2098175 weeks
13-2.28721 -2.03571 (13*2π)/2098161 weeks
141.89253 -1.40661 (14*2π)/2098150 weeks
15-1.59481 -2.91477 (15*2π)/2098140 weeks
161.46123 .62707 (16*2π)/2098131 weeks
17-.11592 -4.77928 (17*2π)/2098123 weeks
18-.78566 1.11567 (18*2π)/2098117 weeks
191.81995 -3.73794 (19*2π)/2098110 weeks
20-2.69428 .3837 (20*2π)/2098105 weeks
211.96937 -.60147 (21*2π)/2098100 weeks
22.32904 -2.28214 (22*2π)/209895 weeks
23-.99273 -1.192 (23*2π)/209891 weeks
24.40413 -.94253 (24*2π)/209887 weeks
25-.72185 -.65586 (25*2π)/209884 weeks
26.80074 -.77427 (26*2π)/209881 weeks
27-.06257 -1.05236 (27*2π)/209878 weeks
28.46758 -.43123 (28*2π)/209875 weeks
29-.05594 -1.94402 (29*2π)/209872 weeks
30-.46422 -.00783 (30*2π)/209870 weeks
311.03712 -1.08036 (31*2π)/209868 weeks
32-.64528 -.75638 (32*2π)/209866 weeks
33.49294 -.68434 (33*2π)/209864 weeks
34-.30569 -1.21091 (34*2π)/209862 weeks
35.2154 -.45148 (35*2π)/209860 weeks
36-.21838 -1.1748 (36*2π)/209858 weeks
37-.25819 .21166 (37*2π)/209857 weeks
38.61428 -.96978 (38*2π)/209855 weeks
39.49876 -1.0012 (39*2π)/209854 weeks
40-.41291 -.91924 (40*2π)/209852 weeks
41-.24461 -.93087 (41*2π)/209851 weeks
42.44935 -.20714 (42*2π)/209850 weeks
43.18848 -1.76723 (43*2π)/209849 weeks
44-1.13128 -.41542 (44*2π)/209848 weeks
45-.08768 -.83509 (45*2π)/209847 weeks
46-.45997 .60231 (46*2π)/209846 weeks
47.80474 -1.36723 (47*2π)/209845 weeks
48-.88085 -.22633 (48*2π)/209844 weeks
49.56232 -.22217 (49*2π)/209843 weeks
50-.26933 -1.07938 (50*2π)/209842 weeks
51-.19108 .02939 (51*2π)/209841 weeks
52.42844 -.90856 (52*2π)/209840 weeks
53-.73241 -.28537 (53*2π)/209840 weeks
54.73044 -.2871 (54*2π)/209839 weeks
55-.70866 -.4372 (55*2π)/209838 weeks
56.82359 -.41781 (56*2π)/209837 weeks
57-.34144 -.688 (57*2π)/209837 weeks
58-.0698 -.43462 (58*2π)/209836 weeks
59.09988 -.24916 (59*2π)/209836 weeks
60-.08583 -.85291 (60*2π)/209835 weeks
61.25724 -.03406 (61*2π)/209834 weeks
62-.19167 -1.31695 (62*2π)/209834 weeks
63-.16598 -.15686 (63*2π)/209833 weeks
64-.47905 -.89284 (64*2π)/209833 weeks
65-.04107 .49588 (65*2π)/209832 weeks
66.21873 -1.39748 (66*2π)/209832 weeks
67-1.14399 .22667 (67*2π)/209831 weeks
68.5205 -.10837 (68*2π)/209831 weeks
69-.39561 -.32604 (69*2π)/209830 weeks
70.19149 -.14084 (70*2π)/209830 weeks
71-.27512 -.60191 (71*2π)/209830 weeks
72-.14383 .28385 (72*2π)/209829 weeks
73.42353 -.51198 (73*2π)/209829 weeks
74-.46194 -.44708 (74*2π)/209828 weeks
75.43809 .10425 (75*2π)/209828 weeks
76-.25234 -.64697 (76*2π)/209828 weeks
77.09016 .18508 (77*2π)/209827 weeks
78.14633 -.85571 (78*2π)/209827 weeks
79-.46245 .17191 (79*2π)/209827 weeks
80.53837 -.38905 (80*2π)/209826 weeks
81-.33119 -.04869 (81*2π)/209826 weeks
82.55721 -.5813 (82*2π)/209826 weeks
83-.41195 -.41128 (83*2π)/209825 weeks
84.26779 -.04604 (84*2π)/209825 weeks
85.11888 -.44458 (85*2π)/209825 weeks
86-.28784 -.49533 (86*2π)/209824 weeks
87.31756 .01299 (87*2π)/209824 weeks
88-.16924 -.71705 (88*2π)/209824 weeks
89.07823 -.03337 (89*2π)/209824 weeks
90.13525 -.84328 (90*2π)/209823 weeks
91-.33257 -.19665 (91*2π)/209823 weeks
92.21172 -.28091 (92*2π)/209823 weeks
93-.40727 -.77937 (93*2π)/209823 weeks
94-.03854 .13687 (94*2π)/209822 weeks
95-.08732 -.56445 (95*2π)/209822 weeks
96-.30764 .0031 (96*2π)/209822 weeks
97.05363 -.2927 (97*2π)/209822 weeks
98-.2065 -.43579 (98*2π)/209821 weeks
99.19492 .0308 (99*2π)/209821 weeks
100-.10641 -.83188 (100*2π)/209821 weeks
101-.49606 .02535 (101*2π)/209821 weeks
102.1023 -.16672 (102*2π)/209821 weeks
103-.20331 -.18688 (103*2π)/209820 weeks
104.21868 -.33588 (104*2π)/209820 weeks
105-.46393 -.5142 (105*2π)/209820 weeks
106-.13762 .25339 (106*2π)/209820 weeks
107.01735 -.26949 (107*2π)/209820 weeks
108-.18952 -.24018 (108*2π)/209819 weeks
109-.21771 -.07877 (109*2π)/209819 weeks
110.00206 -.15305 (110*2π)/209819 weeks
111-.08311 -.00109 (111*2π)/209819 weeks
112-.05758 -.35588 (112*2π)/209819 weeks
113-.10369 .13519 (113*2π)/209819 weeks
114.10211 -.31244 (114*2π)/209818 weeks
115-.3562 -.01987 (115*2π)/209818 weeks
116.22529 .0049 (116*2π)/209818 weeks
117-.03163 -.13612 (117*2π)/209818 weeks
118.24713 .09284 (118*2π)/209818 weeks
119.01396 -.55998 (119*2π)/209818 weeks
120-.10534 -.04162 (120*2π)/209817 weeks
121.11926 -.08762 (121*2π)/209817 weeks
122.11189 -.1194 (122*2π)/209817 weeks
123.11807 -.39933 (123*2π)/209817 weeks
124-.31627 -.2916 (124*2π)/209817 weeks
125.10328 .1176 (125*2π)/209817 weeks
126.02704 -.2779 (126*2π)/209817 weeks
127.05646 .02723 (127*2π)/209817 weeks
128.12286 -.36346 (128*2π)/209816 weeks
129-.04349 -.15879 (129*2π)/209816 weeks
130-.10687 -.26129 (130*2π)/209816 weeks
131.08141 .05839 (131*2π)/209816 weeks
132.35866 -.31094 (132*2π)/209816 weeks
133-.23577 -.48479 (133*2π)/209816 weeks
134-.09045 .10131 (134*2π)/209816 weeks
135.12246 -.29551 (135*2π)/209816 weeks
136-.08074 -.25152 (136*2π)/209815 weeks
137.13132 -.21458 (137*2π)/209815 weeks
138-.28363 -.24782 (138*2π)/209815 weeks
139.17347 -.02697 (139*2π)/209815 weeks
140-.13459 -.32395 (140*2π)/209815 weeks
141.07964 .00994 (141*2π)/209815 weeks
142-.04252 -.4621 (142*2π)/209815 weeks
143-.13763 -.00539 (143*2π)/209815 weeks
144.21942 -.16463 (144*2π)/209815 weeks
145-.22895 -.37036 (145*2π)/209814 weeks
146-.0439 .08326 (146*2π)/209814 weeks
147.14458 -.34625 (147*2π)/209814 weeks
148-.3129 .04694 (148*2π)/209814 weeks
149.39589 -.18771 (149*2π)/209814 weeks
150-.22273 -.33012 (150*2π)/209814 weeks
151.15724 -.0231 (151*2π)/209814 weeks
152-.15698 -.28802 (152*2π)/209814 weeks
153.06338 -.02582 (153*2π)/209814 weeks
154.0841 -.26241 (154*2π)/209814 weeks
155-.02524 -.17426 (155*2π)/209814 weeks
156-.01721 -.16461 (156*2π)/209813 weeks
157-.0189 -.22503 (157*2π)/209813 weeks
158.05694 -.234 (158*2π)/209813 weeks
159-.13766 -.10261 (159*2π)/209813 weeks
160.18925 -.16274 (160*2π)/209813 weeks
161-.11472 -.30599 (161*2π)/209813 weeks
162-.01466 -.23465 (162*2π)/209813 weeks
163-.0397 -.15 (163*2π)/209813 weeks
164-.11835 -.34431 (164*2π)/209813 weeks
165-.05067 -.08663 (165*2π)/209813 weeks
166-.14937 -.23165 (166*2π)/209813 weeks
167-.0756 -.0057 (167*2π)/209813 weeks
168.07752 -.29524 (168*2π)/209812 weeks
169-.2217 .00467 (169*2π)/209812 weeks
170.14896 -.18521 (170*2π)/209812 weeks
171-.25349 -.23755 (171*2π)/209812 weeks
172.08214 .04385 (172*2π)/209812 weeks
173-.06471 -.31132 (173*2π)/209812 weeks
174-.0006 .03227 (174*2π)/209812 weeks
175-.00956 -.40168 (175*2π)/209812 weeks
176-.22688 .00402 (176*2π)/209812 weeks
177.22222 -.02982 (177*2π)/209812 weeks
178-.24732 -.4192 (178*2π)/209812 weeks
179.02995 .11179 (179*2π)/209812 weeks
180-.01867 -.36562 (180*2π)/209812 weeks
181-.20503 .13599 (181*2π)/209812 weeks
182.1303 -.1861 (182*2π)/209812 weeks
183-.03105 -.14035 (183*2π)/209811 weeks
184-.03571 -.22266 (184*2π)/209811 weeks
185-.07505 -.07068 (185*2π)/209811 weeks
186-.10724 -.03325 (186*2π)/209811 weeks
187.18825 -.14395 (187*2π)/209811 weeks
188-.18898 -.26542 (188*2π)/209811 weeks
189-.08635 -.06036 (189*2π)/209811 weeks
190-.04406 -.01681 (190*2π)/209811 weeks
191.06623 -.11895 (191*2π)/209811 weeks
192.08465 -.12914 (192*2π)/209811 weeks
193-.1479 -.21689 (193*2π)/209811 weeks
194.00397 -.05339 (194*2π)/209811 weeks
195-.00731 -.10335 (195*2π)/209811 weeks
196.10431 -.19139 (196*2π)/209811 weeks
197-.1337 -.17563 (197*2π)/209811 weeks
198-.0462 -.15432 (198*2π)/209811 weeks
199.06923 -.0297 (199*2π)/209811 weeks
200-.08423 -.25296 (200*2π)/209810 weeks
201-.02711 -.06259 (201*2π)/209810 weeks
202-.08053 -.23354 (202*2π)/209810 weeks
203-.11447 -.00626 (203*2π)/209810 weeks
204.08555 -.14165 (204*2π)/209810 weeks
205-.15519 -.11536 (205*2π)/209810 weeks
206.11809 -.11003 (206*2π)/209810 weeks
207-.18261 -.12074 (207*2π)/209810 weeks
208.08981 -.07554 (208*2π)/209810 weeks
209-.07643 -.14739 (209*2π)/209810 weeks
210-.06082 -.07302 (210*2π)/209810 weeks
211.0712 -.0515 (211*2π)/209810 weeks
212-.05799 -.13492 (212*2π)/209810 weeks
213.13864 -.15873 (213*2π)/209810 weeks
214-.18742 -.16526 (214*2π)/209810 weeks
215.06547 -.03498 (215*2π)/209810 weeks
216-.0426 -.23554 (216*2π)/209810 weeks
217-.00252 -.13077 (217*2π)/209810 weeks
218-.15592 -.02205 (218*2π)/209810 weeks
219.12198 -.1147 (219*2π)/209810 weeks
220-.06084 -.20722 (220*2π)/209810 weeks
221-.02143 -.04052 (221*2π)/20989 weeks
222.01623 -.11254 (222*2π)/20989 weeks
223-.01739 -.15162 (223*2π)/20989 weeks
224.01181 -.19934 (224*2π)/20989 weeks
225-.14706 -.17051 (225*2π)/20989 weeks
226.0258 .02642 (226*2π)/20989 weeks
227.03491 -.30169 (227*2π)/20989 weeks
228-.19429 -.07171 (228*2π)/20989 weeks
229.05524 -.03322 (229*2π)/20989 weeks
230-.06331 -.18073 (230*2π)/20989 weeks
231.0517 -.09749 (231*2π)/20989 weeks
232-.19059 -.25414 (232*2π)/20989 weeks
233-.06921 .12647 (233*2π)/20989 weeks
234.14019 -.23568 (234*2π)/20989 weeks
235-.15324 -.14801 (235*2π)/20989 weeks
236-.04591 -.10962 (236*2π)/20989 weeks
237-.09488 .02215 (237*2π)/20989 weeks
238.10262 -.09208 (238*2π)/20989 weeks
239.0009 -.24422 (239*2π)/20989 weeks
240-.20402 -.00827 (240*2π)/20989 weeks
241.18099 -.09039 (241*2π)/20989 weeks
242-.20869 -.22219 (242*2π)/20989 weeks
243.08698 -.01548 (243*2π)/20989 weeks
244-.15509 -.23239 (244*2π)/20989 weeks
245-.06181 .03669 (245*2π)/20989 weeks
246.02643 -.17719 (246*2π)/20989 weeks
247-.13315 -.02899 (247*2π)/20988 weeks
248.14021 -.04415 (248*2π)/20988 weeks
249-.14788 -.20387 (249*2π)/20988 weeks
250.02958 .00883 (250*2π)/20988 weeks
251-.04806 -.08707 (251*2π)/20988 weeks
252.10133 -.13125 (252*2π)/20988 weeks
253-.0746 -.12489 (253*2π)/20988 weeks
254.04615 -.13588 (254*2π)/20988 weeks
255-.09915 -.15252 (255*2π)/20988 weeks
256-.00581 -.14438 (256*2π)/20988 weeks
257-.06183 -.09885 (257*2π)/20988 weeks
258-.0904 -.1279 (258*2π)/20988 weeks
259-.00474 -.10611 (259*2π)/20988 weeks
260-.14058 -.00805 (260*2π)/20988 weeks
261.16067 -.09258 (261*2π)/20988 weeks
262-.12568 -.27178 (262*2π)/20988 weeks
263-.05232 -.02659 (263*2π)/20988 weeks
264-.10077 -.11347 (264*2π)/20988 weeks
265.07506 .03329 (265*2π)/20988 weeks
266-.05468 -.26086 (266*2π)/20988 weeks
267-.10561 .0019 (267*2π)/20988 weeks
268.02562 -.09509 (268*2π)/20988 weeks
269.06313 -.18212 (269*2π)/20988 weeks
270-.14219 -.09484 (270*2π)/20988 weeks
271.01895 -.13112 (271*2π)/20988 weeks
272-.11983 -.01749 (272*2π)/20988 weeks
273.12415 -.24132 (273*2π)/20988 weeks
274-.24194 -.14173 (274*2π)/20988 weeks
275.025 -.01104 (275*2π)/20988 weeks
276-.0553 -.19074 (276*2π)/20988 weeks
277-.08065 -.07107 (277*2π)/20988 weeks
278-.04583 -.11262 (278*2π)/20988 weeks
279-.09664 -.10532 (279*2π)/20988 weeks
280-.08315 -.06131 (280*2π)/20987 weeks
281-.10734 -.12515 (281*2π)/20987 weeks
282-.08074 .08763 (282*2π)/20987 weeks
283.07687 -.07657 (283*2π)/20987 weeks
284-.07085 -.193 (284*2π)/20987 weeks
285-.09248 .02671 (285*2π)/20987 weeks
286.01494 -.07884 (286*2π)/20987 weeks
287-.03529 -.08869 (287*2π)/20987 weeks
288-.08963 -.11738 (288*2π)/20987 weeks
289.03544 .06809 (289*2π)/20987 weeks
290-.00861 -.24916 (290*2π)/20987 weeks
291-.08829 -.06459 (291*2π)/20987 weeks
292-.06333 -.10419 (292*2π)/20987 weeks
293-.04478 .00964 (293*2π)/20987 weeks
294.01211 -.07241 (294*2π)/20987 weeks
295-.06523 -.13627 (295*2π)/20987 weeks
296-.01957 -.05682 (296*2π)/20987 weeks
297-.04399 -.09735 (297*2π)/20987 weeks
298-.08322 -.08935 (298*2π)/20987 weeks
299-.03332 -.04597 (299*2π)/20987 weeks
300-.00961 -.04082 (300*2π)/20987 weeks
301-.02845 -.04603 (301*2π)/20987 weeks
302-.0047 -.098 (302*2π)/20987 weeks
303-.00813 -.0672 (303*2π)/20987 weeks
304.05499 -.09364 (304*2π)/20987 weeks
305-.07474 -.18997 (305*2π)/20987 weeks
306