fourier¶

mdhelper.fit.fourier.fourier(x: ndarray, omega: float, a0: float, *args: float) → ndarray[source]¶

General Fourier series model.

\[y=a_0+\sum_{k=1}^na_i\cos{(k\omega x)}+b_i\sin{(k\omega x)}\]

Parameters:

xnumpy.ndarray: \(x\)-values.
omegafloat: Fundamental frequency \(\omega\) of the signal.
a0float: Constant (intercept) term \(a_0\) for the \(k=0\) cosine term.
*argsfloat: Fitting parameters for the Fourier series term(s), ordered as \(a_1,\,b_1,\,a_2,\,b_2,\ldots,\,a_n,\,b_n\), where \(n\) is the number of terms in the model. As such, the number of variable positional arguments must be even.

Returns:

fitnumpy.ndarray: Fitted \(y\)-values.

Examples

Generate \(x\)- and \(y\)-values (with error), and then use scipy.optimize.curve_fit() to fit coefficients for a one-term Fourier series model.

>>> from scipy import optimize
>>> rng = np.random.default_rng()
>>> x = np.linspace(0, 5, 20)
>>> err = (2 * rng.random(x.shape) - 1) / 10
>>> y = 1 + 2 * np.cos(x / 2) + 3 * np.sin(x / 2) + err
>>> pk, _ = optimize.curve_fit(
        lambda x, omega, a0, a1, b1: fourier(x, omega, a0, a1, b1), x, y
    )
>>> pk
array([0.51185734, 1.15090712, 1.87471839, 2.87117784])

Evaluate the fitted \(y\)-values using the coefficients.

>>> fourier(x, *pk)
array([3.0256255 , 3.39422104, 3.72217562, 4.00354785, 4.23324026,
       4.40709163, 4.52195238, 4.57574164, 4.56748494, 4.49733187,
       4.36655334, 4.1775186 , 3.9336523 , 3.63937245, 3.30001035,
       2.92171405, 2.51133696, 2.07631367, 1.62452525, 1.16415655])