![]() Get a value for w, where 8 years = 96 months. You can override the start points and specify your own values.Īfter examining the terms and plots, it looks like a 4 year cycle might be present. ![]() Fourier series models are particularly sensitive to starting points, and the optimized values might be accurate for only a few terms in the associated equations. The toolbox calculates optimized start points for Fourier fits, based on the current data set. The model results reflect some of these periods. Typically, the El Nino warming happens at irregular intervals of two to seven years, and lasts nine months to two years. Smaller terms are less important for the fit, such as a6, b6, a5, and b5. This is stronger than the 7 year cycle because the a2 and b2 coefficients have larger magnitude than a1 and b1.Ī3 and b3 are quite strong terms indicating a 7/3 or 2.3 year cycle. Similarly, a1 and b1 terms give 7/1, indicating a seven year cycle.Ī2 and b2 terms are a 3.5 year cycle (7/2). The toolbox provides this trigonometric Fourier series form. ![]() It is represented in either the trigonometric form or the exponential form. a7 and b7 indicate the annual cycle is the strongest. The Fourier series is a sum of sine and cosine functions that describes a periodic signal. Look at the a7 term in the model equation: a7*cos(7*x*w).
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