raised cosine basis functions

cosine_basis.py

import matplotlib.pyplot as plt
import numpy as np

def raised_cos(t, loc, scale, amp):
    """
    Raised, 1d-cosine basis functions tiling [0, 2 * pi)
    These functions have the property of summing to a
    constant amplitude at all points (i.e. uniform
    tiling of space).

    Parameters
    ----------
    t : array
        Points to evaluate function.
    
    loc : float
        Peak of the basis function.
    
    scale : float
        Scaling factor for t, larger values result in more
        sharply peaked basis functions.
    
    amp : float
        Amplitude of the tuninf 
    """
    x = ((t - loc) + np.pi) % (2 * np.pi) - np.pi
    x = np.clip(scale * x, -np.pi, np.pi)
    return 0.5 * amp * (1 + np.cos(x))
    


if __name__ == "__main__":
    fig, axes = plt.subplots(3, 2, sharey=True)
    tt = np.linspace(-np.pi, np.pi, 200)
    
    for ax, scale in zip(axes, [1, 2, 3]):
        locs = np.linspace(-np.pi, np.pi, 2 * scale + 1)[:-1]
        z = np.zeros_like(tt)
        for loc in locs:
            ax[0].plot(raised_cos(tt, loc, scale, 1))
            z += raised_cos(tt, loc, scale, 1)
        ax[1].plot(z)
    
    axes[0, 0].set_title("basis functions")
    axes[0, 1].set_title("sum of basis functions")
    fig.tight_layout()