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# Fourier Analysis of ZEN (Zendesk)

ZEN (Zendesk) appears to have interesting cyclic behaviour every 25 weeks (4.4213*sine), 38 weeks (3.7799*sine), and 27 weeks (3.2185*sine).

ZEN (Zendesk) has an average price of 55.36 (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 5/15/2014 to 7/26/2021 for ZEN (Zendesk), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
055.35597   0
117.24017 -37.50747 (1*2π)/377377 weeks
25.27244 -14.04532 (2*2π)/377189 weeks
37.35096 -16.79179 (3*2π)/377126 weeks
4-.22054 -14.04673 (4*2π)/37794 weeks
5-4.15713 -11.50268 (5*2π)/37775 weeks
6-3.2296 -5.70954 (6*2π)/37763 weeks
7-.8169 -5.76426 (7*2π)/37754 weeks
8-3.99984 -4.09654 (8*2π)/37747 weeks
9.12267 -2.23061 (9*2π)/37742 weeks
101.62426 -3.77993 (10*2π)/37738 weeks
11-1.77565 -3.02059 (11*2π)/37734 weeks
12.03942 -2.66834 (12*2π)/37731 weeks
131.34432 -3.12354 (13*2π)/37729 weeks
14.71633 -3.21847 (14*2π)/37727 weeks
15.25339 -4.42129 (15*2π)/37725 weeks
16-2.34333 -3.46761 (16*2π)/37724 weeks
17-1.28293 -1.58795 (17*2π)/37722 weeks
18.44018 -2.76487 (18*2π)/37721 weeks
19-.34126 -1.857 (19*2π)/37720 weeks
20-.26423 -2.30811 (20*2π)/37719 weeks
21-.72774 -2.60234 (21*2π)/37718 weeks
22-.83768 -1.49632 (22*2π)/37717 weeks
23.09557 -1.12881 (23*2π)/37716 weeks
24-.09932 -1.22542 (24*2π)/37716 weeks
25.12698 -1.92909 (25*2π)/37715 weeks
26-.77853 -1.85759 (26*2π)/37715 weeks
27.16133 -1.09889 (27*2π)/37714 weeks
28.00139 -1.23703 (28*2π)/37713 weeks
29.21587 -1.17123 (29*2π)/37713 weeks
30.13157 -2.05467 (30*2π)/37713 weeks
31-.67966 -1.90208 (31*2π)/37712 weeks
32-.59727 -1.22558 (32*2π)/37712 weeks
33-.70287 -1.03155 (33*2π)/37711 weeks
34-.37245 -1.10008 (34*2π)/37711 weeks
35-.38577 -1.72158 (35*2π)/37711 weeks
36-1.50067 -1.93799 (36*2π)/37710 weeks
37-1.70904 -.55513 (37*2π)/37710 weeks
38-.77788 -.48368 (38*2π)/37710 weeks
39-.72035 -.87685 (39*2π)/37710 weeks
40-.83881 -.35793 (40*2π)/3779 weeks
41-.75109 -.57829 (41*2π)/3779 weeks
42-.41934 -.19351 (42*2π)/3779 weeks
43-.10425 -.65846 (43*2π)/3779 weeks
44-.42363 -.44574 (44*2π)/3779 weeks
45.09558 -.48935 (45*2π)/3778 weeks
46-.01893 -.86818 (46*2π)/3778 weeks
47-.06638 -.90402 (47*2π)/3778 weeks
48-.03411 -.52612 (48*2π)/3778 weeks
49.14702 -.79671 (49*2π)/3778 weeks
50-.29455 -1.0448 (50*2π)/3778 weeks
51-.42935 -1.12949 (51*2π)/3777 weeks
52-.39667 -.85014 (52*2π)/3777 weeks
53-.5747 -.65676 (53*2π)/3777 weeks
54-.30313 -.54139 (54*2π)/3777 weeks
55-.16317 -.7606 (55*2π)/3777 weeks
56-.31112 -.92561 (56*2π)/3777 weeks
57-.65229 -.67431 (57*2π)/3777 weeks
58-.72488 -.29969 (58*2π)/3777 weeks
59-.21274 -.20983 (59*2π)/3776 weeks
60-.01568 -.32117 (60*2π)/3776 weeks
61-.08559 -.35538 (61*2π)/3776 weeks
62-.24345 -.55719 (62*2π)/3776 weeks
63-.21414 -.58152 (63*2π)/3776 weeks
64-.16101 -.59109 (64*2π)/3776 weeks
65-.46835 -.75043 (65*2π)/3776 weeks
66-.53909 -.37267 (66*2π)/3776 weeks
67-.25757 -.46844 (67*2π)/3776 weeks
68-.32872 -.69684 (68*2π)/3776 weeks
69-.67126 -.43745 (69*2π)/3775 weeks
70-.20636 -.26801 (70*2π)/3775 weeks
71-.05026 -.63856 (71*2π)/3775 weeks
72-.45938 -.72193 (72*2π)/3775 weeks
73-.18013 -.27106 (73*2π)/3775 weeks
74-.23105 -.62525 (74*2π)/3775 weeks
75-.42254 -.496 (75*2π)/3775 weeks
76-.18504 -.53797 (76*2π)/3775 weeks
77-.2834 -.21973 (77*2π)/3775 weeks
78-.00408 -.38954 (78*2π)/3775 weeks
79-.01118 -.69864 (79*2π)/3775 weeks
80-.52243 -.78117 (80*2π)/3775 weeks
81-.35968 -.54047 (81*2π)/3775 weeks
82-.60941 -.50051 (82*2π)/3775 weeks
83-.76875 -.42617 (83*2π)/3775 weeks
84-.48495 -.10272 (84*2π)/3774 weeks
85-.28343 -.27814 (85*2π)/3774 weeks
86-.46022 -.32777 (86*2π)/3774 weeks
87-.36728 -.35737 (87*2π)/3774 weeks
88-.5049 -.35657 (88*2π)/3774 weeks
89-.26792 -.21855 (89*2π)/3774 weeks
90-.3748 -.47582 (90*2π)/3774 weeks
91-.53953 -.23789 (91*2π)/3774 weeks
92-.30471 -.34785 (92*2π)/3774 weeks
93-.34459 -.22933 (93*2π)/3774 weeks
94-.24909 -.26382 (94*2π)/3774 weeks
95-.39359 -.23741 (95*2π)/3774 weeks
96-.48267 -.20121 (96*2π)/3774 weeks
97-.34214 -.35383 (97*2π)/3774 weeks
98-.21844 -.07228 (98*2π)/3774 weeks
99-.39713 -.26201 (99*2π)/3774 weeks
100-.49356 -.26011 (100*2π)/3774 weeks
101-.52289 -.18745 (101*2π)/3774 weeks
102-.47562 -.11036 (102*2π)/3774 weeks
103-.34243 -.09335 (103*2π)/3774 weeks
104-.3669 -.20556 (104*2π)/3774 weeks
105-.42896 -.08008 (105*2π)/3774 weeks
106-.19216 -.15826 (106*2π)/3774 weeks
107-.15894 -.27451 (107*2π)/3774 weeks
108-.30199 -.29019 (108*2π)/3773 weeks
109-.37146 -.28436 (109*2π)/3773 weeks
110-.28485 -.23299 (110*2π)/3773 weeks
111-.15824 -.37521 (111*2π)/3773 weeks
112-.451 -.38549 (112*2π)/3773 weeks
113-.55915 -.10622 (113*2π)/3773 weeks
114-.39921 -.14396 (114*2π)/3773 weeks
115-.26557 -.15888 (115*2π)/3773 weeks
116-.27316 -.28848 (116*2π)/3773 weeks
117-.32378 -.25469 (117*2π)/3773 weeks
118-.34815 -.35107 (118*2π)/3773 weeks
119-.42031 -.26163 (119*2π)/3773 weeks
120-.60537 -.17075 (120*2π)/3773 weeks
121-.52841 -.02706 (121*2π)/3773 weeks
122-.37195 .01508 (122*2π)/3773 weeks
123-.34861 -.24165 (123*2π)/3773 weeks
124-.35102 -.01104 (124*2π)/3773 weeks
125-.32498 -.09229 (125*2π)/3773 weeks
126-.33659 .01696 (126*2π)/3773 weeks
127-.07509 -.09748 (127*2π)/3773 weeks
128-.23883 -.37777 (128*2π)/3773 weeks
129-.51405 -.222 (129*2π)/3773 weeks
130-.52723 -.09008 (130*2π)/3773 weeks
131-.33509 .11426 (131*2π)/3773 weeks
132-.40996 .00417 (132*2π)/3773 weeks
133-.18287 .02267 (133*2π)/3773 weeks
134-.35642 -.17004 (134*2π)/3773 weeks
135-.30873 -.11941 (135*2π)/3773 weeks
136-.48306 -.11624 (136*2π)/3773 weeks
137-.40126 .02352 (137*2π)/3773 weeks
138-.33384 .00978 (138*2π)/3773 weeks
139-.2559 -.00631 (139*2π)/3773 weeks
140-.40583 -.22369 (140*2π)/3773 weeks
141-.64938 .08201 (141*2π)/3773 weeks
142-.20859 .18351 (142*2π)/3773 weeks
143-.28209 -.08033 (143*2π)/3773 weeks
144-.37931 .02557 (144*2π)/3773 weeks
145-.25573 -.04021 (145*2π)/3773 weeks
146-.21827 .06231 (146*2π)/3773 weeks
147-.06445 -.14938 (147*2π)/3773 weeks
148-.23761 -.14367 (148*2π)/3773 weeks
149-.26109 -.03443 (149*2π)/3773 weeks
150-.2235 -.24789 (150*2π)/3773 weeks
151-.47887 -.25139 (151*2π)/3772 weeks
152-.44471 .05672 (152*2π)/3772 weeks
153-.3247 .03542 (153*2π)/3772 weeks
154-.19698 .0561 (154*2π)/3772 weeks
155-.37156 -.00271 (155*2π)/3772 weeks
156-.20176 .08365 (156*2π)/3772 weeks
157-.16528 -.01715 (157*2π)/3772 weeks
158-.32161 .16416 (158*2π)/3772 weeks
159-.26684 .23474 (159*2π)/3772 weeks
160-.15879 .04814 (160*2π)/3772 weeks
161-.26336 .078 (161*2π)/3772 weeks
162-.16671 .0107 (162*2π)/3772 weeks
163-.19852 .01164 (163*2π)/3772 weeks
164-.0588 -.21147 (164*2π)/3772 weeks
165-.33209 -.26954 (165*2π)/3772 weeks
166-.20311 -.10547 (166*2π)/3772 weeks
167-.31642 -.2078 (167*2π)/3772 weeks
168-.35895 -.16225 (168*2π)/3772 weeks
169-.28745 .06758 (169*2π)/3772 weeks
170-.20094 -.12712 (170*2π)/3772 weeks
171-.39344 -.03761 (171*2π)/3772 weeks
172-.31676 .18908 (172*2π)/3772 weeks
173-.32428 .15816 (173*2π)/3772 weeks
174-.0639 .33877 (174*2π)/3772 weeks
175-.01096 -.0802 (175*2π)/3772 weeks
176-.24857 -.11427 (176*2π)/3772 weeks
177-.01836 .04976 (177*2π)/3772 weeks
178-.3846 -.20972 (178*2π)/3772 weeks
179-.54744 .07439 (179*2π)/3772 weeks
180-.21482 .24157 (180*2π)/3772 weeks
181-.18854 -.17724 (181*2π)/3772 weeks
182-.51127 -.07742 (182*2π)/3772 weeks
183-.38207 .15924 (183*2π)/3772 weeks
184-.25698 .19564 (184*2π)/3772 weeks
185-.15444 .0763 (185*2π)/3772 weeks
186-.02435 .04177 (186*2π)/3772 weeks
187-.07916 .0252 (187*2π)/3772 weeks
188-.10087 -.03596 (188*2π)/3772 weeks
189-.10087 .03596 (189*2π)/3772 weeks
190-.07916 -.0252 (190*2π)/3772 weeks
191-.02435 -.04177 (191*2π)/3772 weeks
192-.15444 -.0763 (192*2π)/3772 weeks
193-.25698 -.19564 (193*2π)/3772 weeks
194-.38207 -.15924 (194*2π)/3772 weeks
195-.51127 .07742 (195*2π)/3772 weeks
196-.18854 .17724 (196*2π)/3772 weeks
197-.21482 -.24157 (197*2π)/3772 weeks
198-.54744 -.07439 (198*2π)/3772 weeks
199-.3846 .20972 (199*2π)/3772 weeks
200-.01836 -.04976 (200*2π)/3772 weeks
201-.24857 .11427 (201*2π)/3772 weeks
202-.01096 .0802 (202*2π)/3772 weeks
203-.0639 -.33877 (203*2π)/3772 weeks
204-.32428 -.15816 (204*2π)/3772 weeks
205-.31676 -.18908 (205*2π)/3772 weeks
206-.39344 .03761 (206*2π)/3772 weeks
207-.20094 .12712 (207*2π)/3772 weeks
208-.28745 -.06758 (208*2π)/3772 weeks
209-.35895 .16225 (209*2π)/3772 weeks
210-.31642 .2078 (210*2π)/3772 weeks
211-.20311 .10547 (211*2π)/3772 weeks
212-.33209 .26954 (212*2π)/3772 weeks
213-.0588 .21147 (213*2π)/3772 weeks
214-.19852 -.01164 (214*2π)/3772 weeks
215-.16671 -.0107 (215*2π)/3772 weeks
216-.26336 -.078 (216*2π)/3772 weeks
217-.15879 -.04814 (217*2π)/3772 weeks
218-.26684 -.23474 (218*2π)/3772 weeks
219-.32161 -.16416 (219*2π)/3772 weeks
220-.16528 .01715 (220*2π)/3772 weeks
221-.20176 -.08365 (221*2π)/3772 weeks
222-.37156 .00271 (222*2π)/3772 weeks
223-.19698 -.0561 (223*2π)/3772 weeks
224-.3247 -.03542 (224*2π)/3772 weeks
225-.44471 -.05672 (225*2π)/3772 weeks
226-.47887 .25139 (226*2π)/3772 weeks
227-.2235 .24789 (227*2π)/3772 weeks
228-.26109 .03443 (228*2π)/3772 weeks
229-.23761 .14367 (229*2π)/3772 weeks
230-.06445 .14938 (230*2π)/3772 weeks
231-.21827 -.06231 (231*2π)/3772 weeks
232-.25573 .04021 (232*2π)/3772 weeks
233-.37931 -.02557 (233*2π)/3772 weeks
234-.28209 .08033 (234*2π)/3772 weeks
235-.20859 -.18351 (235*2π)/3772 weeks
236-.64938 -.08201 (236*2π)/3772 weeks
237-.40583 .22369 (237*2π)/3772 weeks
238-.2559 .00631 (238*2π)/3772 weeks
239-.33384 -.00978 (239*2π)/3772 weeks
240-.40126 -.02352 (240*2π)/3772 weeks
241-.48306 .11624 (241*2π)/3772 weeks
242-.30873 .11941 (242*2π)/3772 weeks
243-.35642 .17004 (243*2π)/3772 weeks
244-.18287 -.02267 (244*2π)/3772 weeks
245-.40996 -.00417 (245*2π)/3772 weeks
246-.33509 -.11426 (246*2π)/3772 weeks
247-.52723 .09008 (247*2π)/3772 weeks
248-.51405 .222 (248*2π)/3772 weeks
249-.23883 .37777 (249*2π)/3772 weeks
250-.07509 .09748 (250*2π)/3772 weeks
251-.33659 -.01696 (251*2π)/3772 weeks
252-.32498 .09229 (252*2π)/3771 weeks
253-.35102 .01104 (253*2π)/3771 weeks
254-.34861 .24165 (254*2π)/3771 weeks
255-.37195 -.01508 (255*2π)/3771 weeks
256-.52841 .02706 (256*2π)/3771 weeks
257-.60537 .17075 (257*2π)/3771 weeks
258-.42031 .26163 (258*2π)/3771 weeks
259-.34815 .35107 (259*2π)/3771 weeks
260-.32378 .25469 (260*2π)/3771 weeks
261-.27316 .28848 (261*2π)/3771 weeks
262-.26557 .15888 (262*2π)/3771 weeks
263-.39921 .14396 (263*2π)/3771 weeks
264-.55915 .10622 (264*2π)/3771 weeks
265-.451 .38549 (265*2π)/3771 weeks
266-.15824 .37521 (266*2π)/3771 weeks
267-.28485 .23299 (267*2π)/3771 weeks
268-.37146 .28436 (268*2π)/3771 weeks
269-.30199 .29019 (269*2π)/3771 weeks
270-.15894 .27451 (270*2π)/3771 weeks
271-.19216 .15826 (271*2π)/3771 weeks
272-.42896 .08008 (272*2π)/3771 weeks
273-.3669 .20556 (273*2π)/3771 weeks
274-.34243 .09335 (274*2π)/3771 weeks
275-.47562 .11036 (275*2π)/3771 weeks
276-.52289 .18745 (276*2π)/3771 weeks
277-.49356 .26011 (277*2π)/3771 weeks
278-.39713 .26201 (278*2π)/3771 weeks
279-.21844 .07228 (279*2π)/3771 weeks
280-.34214 .35383 (280*2π)/3771 weeks
281-.48267 .20121 (281*2π)/3771 weeks
282-.39359 .23741 (282*2π)/3771 weeks
283-.24909 .26382 (283*2π)/3771 weeks
284-.34459 .22933 (284*2π)/3771 weeks
285-.30471 .34785 (285*2π)/3771 weeks
286-.53953 .23789 (286*2π)/3771 weeks
287-.3748 .47582 (287*2π)/3771 weeks
288-.26792 .21855 (288*2π)/3771 weeks
289-.5049 .35657 (289*2π)/3771 weeks
290-.36728 .35737 (290*2π)/3771 weeks
291-.46022 .32777 (291*2π)/3771 weeks
292-.28343 .27814 (292*2π)/3771 weeks
293-.48495 .10272 (293*2π)/3771 weeks
294-.76875 .42617 (294*2π)/3771 weeks
295-.60941 .50051 (295*2π)/3771 weeks
296-.35968 .54047 (296*2π)/3771 weeks
297-.52243 .78117 (297*2π)/3771 weeks
298-.01118 .69864 (298*2π)/3771 weeks
299-.00408 .38954 (299*2π)/3771 weeks
300-.2834 .21973 (300*2π)/3771 weeks
301-.18504 .53797 (301*2π)/3771 weeks
302-.42254 .496 (302*2π)/3771 weeks
303-.23105 .62525 (303*2π)/3771 weeks
304-.18013 .27106 (304*2π)/3771 weeks
305-.45938 .72193 (305*2π)/3771 weeks
306-.05026 .63856 (306*2π)/3771 weeks
307-.20636 .26801 (307*2π)/3771 weeks
308-.67126 .43745 (308*2π)/3771 weeks
309-.32872 .69684 (309*2π)/3771 weeks
310-.25757 .46844 (310*2π)/3771 weeks
311-.53909 .37267 (311*2π)/3771 weeks
312-.46835 .75043 (312*2π)/3771 weeks
313-.16101 .59109 (313*2π)/3771 weeks
314-.21414 .58152 (314*2π)/3771 weeks
315-.24345 .55719 (315*2π)/3771 weeks
316-.08559 .35538 (316*2π)/3771 weeks
317-.01568 .32117 (317*2π)/3771 weeks
318-.21274 .20983 (318*2π)/3771 weeks
319-.72488 .29969 (319*2π)/3771 weeks
320-.65229 .67431 (320*2π)/3771 weeks
321-.31112 .92561 (321*2π)/3771 weeks
322-.16317 .7606 (322*2π)/3771 weeks
323-.30313 .54139 (323*2π)/3771 weeks
324-.5747 .65676 (324*2π)/3771 weeks
325-.39667 .85014 (325*2π)/3771 weeks
326-.42935 1.12949 (326*2π)/3771 weeks
327-.29455 1.0448 (327*2π)/3771 weeks
328.14702 .79671 (328*2π)/3771 weeks
329-.03411 .52612 (329*2π)/3771 weeks
330-.06638 .90402 (330*2π)/3771 weeks
331-.01893 .86818 (331*2π)/3771 weeks
332.09558 .48935 (332*2π)/3771 weeks
333-.42363 .44574 (333*2π)/3771 weeks
334-.10425 .65846 (334*2π)/3771 weeks
335-.41934 .19351 (335*2π)/3771 weeks
336-.75109 .57829 (336*2π)/3771 weeks
337-.83881 .35793 (337*2π)/3771 weeks
338-.72035 .87685 (338*2π)/3771 weeks
339-.77788 .48368 (339*2π)/3771 weeks
340-1.70904 .55513 (340*2π)/3771 weeks
341-1.50067 1.93799 (341*2π)/3771 weeks
342-.38577 1.72158 (342*2π)/3771 weeks
343-.37245 1.10008 (343*2π)/3771 weeks
344-.70287 1.03155 (344*2π)/3771 weeks
345-.59727 1.22558 (345*2π)/3771 weeks
346-.67966 1.90208 (346*2π)/3771 weeks
347.13157 2.05467 (347*2π)/3771 weeks
348.21587 1.17123 (348*2π)/3771 weeks
349.00139 1.23703 (349*2π)/3771 weeks
350.16133 1.09889 (350*2π)/3771 weeks
351-.77853 1.85759 (351*2π)/3771 weeks
352.12698 1.92909 (352*2π)/3771 weeks
353-.09932 1.22542 (353*2π)/3771 weeks
354.09557 1.12881 (354*2π)/3771 weeks
355-.83768 1.49632 (355*2π)/3771 weeks
356-.72774 2.60234 (356*2π)/3771 weeks
357-.26423 2.30811 (357*2π)/3771 weeks
358-.34126 1.857 (358*2π)/3771 weeks
359.44018 2.76487 (359*2π)/3771 weeks
360-1.28293 1.58795 (360*2π)/3771 weeks
361-2.34333 3.46761 (361*2π)/3771 weeks
362.25339 4.42129 (362*2π)/3771 weeks
363.71633 3.21847 (363*2π)/3771 weeks
3641.34432 3.12354 (364*2π)/3771 weeks
365.03942 2.66834 (365*2π)/3771 weeks
366-1.77565 3.02059 (366*2π)/3771 weeks
3671.62426 3.77993 (367*2π)/3771 weeks
368.12267 2.23061 (368*2π)/3771 weeks
369-3.99984 4.09654 (369*2π)/3771 weeks
370-.8169 5.76426 (370*2π)/3771 weeks
371-3.2296 5.70954 (371*2π)/3771 weeks
372-4.15713 11.50268 (372*2π)/3771 weeks
373-.22054 14.04673 (373*2π)/3771 weeks
3747.35096 16.79179 (374*2π)/3771 weeks
3755.27244 14.04532 (375*2π)/3771 weeks