A New Algorithm to Accelerate Harmonic Analysis of Time Series

Table 1

Harmonic content of the synthetic time series.

𝑓^a	𝑆^b	𝐶^c	𝑆𝑆^d	𝐶𝐶^e
0.001	1.000	3.000	0.000	0.000
0.200	2.000	1.000	0.000	0.000
0.003	2.000	2.000	0.000	0.000
0.040	0.000	5.000	0.000	0.000
0.005	−3.000	1.000	−0.005	0.002

^aFrequencies included in the functional model (in cycles per unit of time).
^bLinear coefficient of the sinus Fourier term for the frequency that appears at the same row.
^cLinear coefficient of the cosinus Fourier term for the frequency that appears at the same row.
^dLinear coefficient of the sinus mixed secular term for the frequency appearing at the same row.
^eLinear coefficient of the cosinus mixed secular term for the frequency that appears at the same row.