9.5.1. Fourier Transform
The real and imaginary parts of the series in the frequency domain can be displayed, as well as the corresponding magnitude and phase values and their plots.
where ap and bp are the real and complex components in the frequency domain respectively and atan2 function returns the arctangent of bp / ap in radians. The following inverse relationships should also hold:
If you wish to express the phase angle in degrees, rather than radians, then you may use a conversion factor of π / 180. The same conversion can be performed by the program automatically by entering the following line in Documents\Unistat10\Unistat10.ini file under the [Options] section:
FFTPhaseDegree=1
Example
Open DEMODATA and select Statistics 2 → Fourier Analysis → Fourier Transform. From the Variable Selection Dialogue select Interest (C4) as [Real] to obtain the following results:
Fourier Transform
Real: Interest
|
|
Real |
Imaginary |
Magnitude |
Phase (Radian) |
|
1 |
5408.4193 |
0.0000 |
5408.4193 |
0.0000 |
|
2 |
21.4881 |
-416.1937 |
416.7481 |
-1.5192 |
|
3 |
223.7763 |
-122.4555 |
255.0905 |
-0.5007 |
|
4 |
-29.7381 |
-13.8112 |
32.7888 |
-2.7068 |
|
5 |
-14.7492 |
32.7994 |
35.9630 |
1.9934 |
|
6 |
-30.7761 |
37.7633 |
48.7159 |
2.2546 |
|
7 |
42.1814 |
-18.9490 |
46.2421 |
-0.4222 |
|
8 |
-3.1800 |
39.3871 |
39.5152 |
1.6514 |
|
9 |
0.4593 |
-15.9255 |
15.9321 |
-1.5420 |
|
10 |
-5.0154 |
-50.0637 |
50.3142 |
-1.6706 |
|
11 |
14.9913 |
-45.5162 |
47.9215 |
-1.2526 |
|
12 |
-10.0253 |
-21.5218 |
23.7422 |
-2.0067 |
|
… |
…16.0507 |
… |
… |
… |
|
48 |
-24.6684 |
-34.0238 |
42.0256 |
-2.1981 |
|
49 |
4.8234 |
-13.0566 |
13.9190 |
-1.2169 |
|
50 |
-21.2454 |
25.1352 |
32.9112 |
2.2725 |
|
51 |
20.7350 |
11.7082 |
23.8122 |
0.5140 |
|
52 |
40.1326 |
2.0183 |
40.1833 |
0.0502 |
|
53 |
16.0507 |
-12.5679 |
20.3857 |
-0.6643 |
|
54 |
-10.0253 |
21.5218 |
23.7422 |
2.0067 |
|
55 |
14.9913 |
45.5162 |
47.9215 |
1.2526 |
|
56 |
-5.0154 |
50.0637 |
50.3142 |
1.6706 |
|
57 |
0.4593 |
15.9255 |
15.9321 |
1.5420 |
|
58 |
-3.1800 |
-39.3871 |
39.5152 |
-1.6514 |
|
59 |
42.1814 |
18.9490 |
46.2421 |
0.4222 |
|
60 |
-30.7761 |
-37.7633 |
48.7159 |
-2.2546 |
|
61 |
-14.7492 |
-32.7994 |
35.9630 |
-1.9934 |
|
62 |
-29.7381 |
13.8112 |
32.7888 |
2.7068 |
|
63 |
223.7763 |
122.4555 |
255.0905 |
0.5007 |
|
64 |
21.4881 |
416.1937 |
416.7481 |
1.5192 |
Since there are only 58 rows in the variable Interest, it is first padded by the program automatically up to the next power of 2 (64) by the mean value of the variable.