# SINTREND

## Purpose:

Fits y(x) =
A + Bx +
C sin(Dx +
E) using the FFT.

## Syntax:

SINTREND(series)

(fit, coef) = SINTREND(series)

series |
- |
A series or array. |

## Returns:

A series, the fitted sine curve.

(fit, coef) = sintrend(series)

returns both the fit and the coefficients as a series.

## Example:

W1: 5 + 3 * gsin(1000, .001, 10) + gline(1000, .001,
20, 0)

W2: sintrend(W1);overp(W1, lred)

overplots the original data with the calculated sine fit.

## Example:

(fit, coef) = sintrend(W1)

fit is the same series as in W2

coef == {5.2861, 19.4272, 3.0032, 62.8249, 0.0035}

Note: since D == coef[4] == 2*pi*F,
in this case, F = 62.8249 / (2*π*)
= 9.9989.

## Remarks:

SINTREND first calculates and removes the linear trend in the data,
fits a sine, then adds in the calculated linear trend. The resulting fit
is of the following form:

The frequency and phase terms are in radians.

SINTREND uses SINFIT to find the dominant frequency
present in the series.

## See Also:

FFT

LINFIT

LSINFIT

SINFIT

TREND